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Roberto ZANASI

Professore Ordinario presso: Dipartimento di Ingegneria "Enzo Ferrari"


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Pubblicazioni

2021 - Modeling Control and Robustness Assessment of Multilevel Flying-Capacitor Converters [Articolo su rivista]
Zanasi, Roberto; Tebaldi, Davide
abstract

When performing AC/DC-DC/AC power conversions, multilevel converters provide several advantages as compared to classical two-level converters. This paper deals with the dynamic modeling, control, and robustness assessment of multilevel flying-capacitor converters. The dynamic model is derived using the Power-Oriented Graphs modeling technique, which provides the user with block schemes that are directly implementable in the Matlab/Simulink environment by employing standard Simulink libraries. The performed robustness assessment has led to the proposal of a divergence index, which allows for evaluating the voltage balancing capability of the converter using different voltage vector configurations for the extended operation of the converter, namely when the number of output voltage levels is increased for a given number of capacitors. A new variable-step control algorithm is then proposed. The variable-step control algorithm safely enables the converter extended operation, which prevents voltage balancing issues, even under particularly unfavorable conditions, such as a constant desired output voltage or a sudden load change. The simulation results showing the good performances of the proposed variable-step control as compared to a classical minimum distance approach are finally provided and commented in detail.


2021 - Power-Oriented Modeling of Epicyclic Gear Trains [Relazione in Atti di Convegno]
Zanasi, Roberto; Tebaldi, Davide
abstract

Model-based simulations are important in the automotive industry to study and evaluate the vehicle behavior. In this paper, the Power-Oriented Graphs (POG) technique is used as a tool for modeling epicyclic gear trains. A full elastic dynamic model of the system is first derived, which can then be reduced by neglecting the elastic contact points between the gears while still being able to recover the time behaviors of the spring tangential forces. The proposed modeling method is then applied to two epicyclic gear trains, and the design of a suitable control allowing to minimize the system dissipations is presented and applied to the second case study.


2020 - Estimation of Physical Parameters Using a New Discrete-time Derivative Algorithm [Relazione in Atti di Convegno]
Tebaldi, Davide; Morselli, Riccardo; Zanasi, Roberto
abstract

The paper presents a parameters estimation procedure for physical systems modeled using the POG (Power-Oriented Graphs) technique. The coefficients defining the constitutive relation for both static and dynamic physical elements within the system can be estimated, as well as the coefficients describing energy conversions taking place either within the same energetic domain or between two different energetic domains. The evolution of the state vector over time is supposed to be known, whereas its first derivative is supposed to be unknown and is obtained by using a new algorithm for computing the discrete-time derivative of a sampled signal, which is effective even in presence of disturbances affecting the signal samples. As long as the unknown parameters appear linearly within the system differential equations, the system is allowed to exhibit any nonlinear function of the state vector and its first derivative. The procedure is finally applied to two different case studies: a linear one and a nonlinear one.


2020 - Instantaneous Gearshift Model Based on Gear-dependent Angular Momentum [Relazione in Atti di Convegno]
Tebaldi, Davide; Zanasi, Roberto
abstract

The paper presents a new gearbox dynamic model for the effective simulation of simultaneous multi-clutches lock/unlock, by exploiting the Power-Oriented Graphs (POG) modeling technique. The generalized structure of the proposed model allows to simulate various gearbox configurations, which may foresee a change in terms of equivalent moment of inertia on the primary or secondary shaft, depending on the internal clutches configuration being function of the currently engaged gear. The peculiarity of the model lies in the instantaneous engagement of the new gear by skipping the slipping transient related to change of the internal clutches configuration, while preserving the natural loss of energy associated to it. The effectiveness of the presented gearbox model is finally tested and compared with classical gearbox modeling solutions with the aid of some simulation results.


2020 - Modeling and Simulation of a Multiphase Diode Bridge Rectifier [Relazione in Atti di Convegno]
Tebaldi, Davide; Zanasi, Roberto
abstract

In this paper, an analytical approach for modeling a multiphase diode bridge rectifier suitable for control purposes is presented. The model has been implemented in Matlab/Simulink by means of a function performing the AC/DC current conversion and takes into account the main non-idealities of semiconductor diodes, such as the turn-on voltage and the on/off resistances. The developed Matlab function makes the simulation of the multiphase diode bridge rectifier very straightforward and its effectiveness has been tested by comparing the simulation results with those obtained by using the rectifier model provided by the PLECS circuit simulator.


2020 - Modeling Control and Simulation of a Series Hybrid Propulsion System [Relazione in Atti di Convegno]
Tebaldi, Davide; Zanasi, Roberto
abstract

This paper deals with the modeling control and simulation of a series hybrid propulsion system for driving a Wheel Loader by relying upon the Power-Oriented Graphs (POG) modeling technique. The considered propulsion system is composed of the following elements: an ICE (Internal Combustion Engine), two controlled PMSMs (Permanent Magnet Synchronous Motors), a supercapacitor as energy storage device and the transmission system of the vehicle itself from the gearbox all the way down to the vehicle wheels. A strategy for the control of the considered hybrid architecture is studied, with the objective of minimizing the ICE specific fuel consumption. Simulation results showing the operation of the presented strategy are finally reported and commented in detail.


2020 - Modeling of Complex Planetary Gear Sets using Power-Oriented Graphs [Articolo su rivista]
Zanasi, Roberto; Tebaldi, Davide
abstract

In this paper, a systematic approach for the dynamic modeling of complex planetary gear sets is presented. The approach relies upon a set of rules for building the system matrices and vectors of the system full dynamic model for any planetary gear set. A congruent state-space transformation is applied to obtain a reduced-order rigid model of the system, which allows for faster simulations. The behavior of the tangential forces accounting for the gears interactions is proven to be obtained from the reduced-order model. Furthermore, the kinematic relations of the considered planetary gear set are automatically generated when developing the reduced-order rigid model. As an example, two systems of interest in the vehicle industry are then modeled with the proposed approach and simulated in Matlab/Simulink: a Ravigneaux planetary gear set and a double-stage planetary gear set.


2019 - Modeling and Control of a Power-Split Hybrid Propulsion System [Relazione in Atti di Convegno]
Tebaldi, Davide; Zanasi, Roberto
abstract

In this paper, the Power-Oriented Graphs (POG) technique is used to model a Hybrid Propulsion System for driving an agricultural tool. The main elements present in the system are: an ICE (Internal Combustion Engine), two PMSMs (Permanent Magnet Synchronous Electric Motors) equipped with two inverters in order to be properly driven, a planetary gear, an energy storage device and an agricultural tool. Based on the system dynamic model, a dedicated control strategy has been developed allowing to efficiently control the system by reducing the ICE specific consumption as much as possible. Simulation results showing the operation of the control strategy are finally reported and commented in detail.


2019 - Planetary Gear Modeling Using the Power-Oriented Graphs Technique [Relazione in Atti di Convegno]
Zanasi, Roberto; Tebaldi, Davide
abstract

In this paper, the Power-Oriented Graphs (POG) technique is used to model Planetary Gear transmission systems. The full elastic dynamic model of the system is obtained using a fast and direct method which can be easily applied to any type of planetary gear. The rigid and reduced dynamic model of the system when the stiffness coefficients go to infinity is then obtained using a POG congruent state space transformation allowing the user to select which angular speeds are to be maintained in the reduced model. Another interesting aspect of the presented method is that the obtained reduced model is still able to provide the time behaviors of the tangential forces present between each couple of gears of the considered planetary gear system. The presented fast and direct method is then applied to two practical case studies, and simulative results in Matlab/Simulink showing the effectiveness of the method are finally reported and commented.


2019 - Power Flow Efficiency of Linear and Nonlinear Physical Systems [Relazione in Atti di Convegno]
Zanasi, Roberto; Tebaldi, Davide
abstract

In this paper, an analytical procedure to derive the efficiency of linear and nonlinear physical systems is presented. This procedure allows to compute the efficiency map both on the plane of the input power variables and on the plane of the output power variables. Additionally, the paper highlights the parameters to be adjusted in order to enlarge the high-efficiency region of the system. The presented procedure can also be used in conjunction with a least square algorithm in order to estimate the unknown parameters of the considered physical system. The effectiveness of the procedure has been tested in Matlab/Simulink to estimate the parameters of an actual PMSM electric motor. The obtained results show a very good matching between the actual and the estimated efficiency maps.


2019 - Study of the Bidirectional Efficiency of Linear and Nonlinear Physical Systems [Relazione in Atti di Convegno]
Zanasi, Roberto; Tebaldi, Davide
abstract

In this paper, a study of the bidirectional efficiency of linear and nonlinear physical systems is performed. The methodology to compute the bidirectional efficiency map of the system is described, highlighting which is the power flow orientation giving the maximum system efficiency. The designer can therefore easily evaluate whether a physical system, such as for instance an electric machine, is more suitable for being used in forward motor mode rather than in reverse generator mode or viceversa. Three different types of physical systems are modeled and simulated in Matlab/Simulink, and the different characteristics they exhibit in terms of efficiency are highlighted. Finally, the properties that the efficiency maps exhibit if the linear system is affected by symmetric or nonsymmetric nonlinearities are studied and commented in detail.


2016 - A Novel Cooling Device for Targeted Brain Temperature Control and Therapeutic Hypothermia: Feasibility Study in an Animal Model. [Articolo su rivista]
Giuliani, Enrico; Magnoni, Sandra; Fei, Marco; Addis, Alessandro; Zanasi, Roberto; Stocchetti, Nino; Barbieri, Alberto
abstract

BACKGROUND: Therapeutic hypothermia (i.e., temperature management) is an effective option for improving survival and neurological outcome after cardiac arrest and is potentially useful for the care of the critically ill neurological patient. We analyzed the feasibility of a device to control the temperature of the brain by controlling the temperature of the blood flowing through the neck. METHODS: A lumped parameter dynamic model, with one-dimensional heat transfer, was used to predict cooling effects and to test experimental hypotheses. The cooling system consisted of a flexible collar and was tested on 4 adult sheep, in which brain and body temperatures were invasively monitored for the duration of the experiment. RESULTS: Model-based simulations predicted a lowering of the temperature of the brain and the body following the onset of cooling, with a rate of 0.4 °C/h for the brain and 0.2 °C/h for the body. The experimental findings showed comparable cooling rates in the two body compartments, with temperature reductions of 0.6 (0.2) °C/h for the brain and 0.6 (0.2) °C/h for the body. For a 70 kg adult human subject, we predict a temperature reduction of 0.64 °C/h for the brain and 0.43 °C/h for the body. CONCLUSIONS: This work demonstrates the feasibility of using a non-invasive method to induce brain hypothermia using a portable collar. This device demonstrated an optimal safety profile and represents a potentially useful method for the administration of mild hypothermia and temperature control (i.e., treatment of hyperpyrexia) in cardiac arrest and critically ill neurologic patients.


2016 - Dynamic modeling of multi-phase hybrid stepper motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Fei, Marco
abstract

The paper presents the dynamic modeling of Multi-phase Hybrid Stepper Motors (MHSM). The model is as general as possible and it is obtained using a Lagrangian approach in the frame of the Power-Oriented Graphs (POG) technique. The obtained dynamic models can be directly implemented in Simulink and they can be used to simulate also the Permanent Magnet and the Variable Reluctance stepper motors. Some simulation results are finally presented.


2016 - Dynamic models of thermal systems using an energy-based modeling approach [Articolo su rivista]
Grossi, F.; Zanasi, R.
abstract

The aim of this work is to give a new approach to obtain compact dynamic thermal models suitable for a variety of systems where the heat transfer can be caused by conduction, internal convection (not at the boundary), and evaporation/condensation of water. The structural properties of the proposed dynamic model are presented and discussed in this paper. These properties guarantee conservation of energy and mass within the system, thus giving a good confidence in the correctness of the model. This paper shows that the proposed model has a simple structure, can be easily implemented in SIMULINK, and provides simulation times much shorter compared with those usually obtained using CFD programs. The proposed model proves to be suitable for real-time simulations and for control design purposes.


2015 - Dynamic Modeling of a Double Clutch for Real-Time Simulations [Relazione in Atti di Convegno]
Grossi, Federica; Zanasi, Roberto
abstract

In this paper a new approach to model a double clutch system is presented with the aim of obtaining a model suitable for real-time simulations. The proposed model is obtained with a proper coordinate transformation of the system equations: the transformed system is described by two new state variables that correspond to the weighted relative speeds of the clutch plates. In this way one unique model can be used to describe all the conditions of the clutch: free, slipping and lockup. Using this approach, very efficient numerical simulations can be performed without switching among different models and using variables which are not affected by chattering. Moreover this approach allows to implement a discrete model that can be used in real-time simulations for Hardware-in-the-loop automotive applications.


2015 - Qualitative graphical representation of Nyquist plots [Articolo su rivista]
Zanasi, Roberto; Grossi, Federica; Biagiotti, Luigi
abstract

In this paper, the procedure for manually drawing the Nyquist plot of a generic transfer function is revised and, in particular, two novel parameters (ΔτΔτ, ΔpΔp), which allow to simplify this process, are presented. Thanks to these parameters, the analysis of the frequency response at low and high frequencies is considerably enhanced, with a very little effort. These parameters allow to predict initial and final directions of the polar curve in the vicinity of initial and final points and consequently the sectors of the complex plane where the plot starts/ends. In many cases it is possible to obtain a qualitative Nyquist plot, able to correctly predict the stability properties of the closed-loop system, by simply joining the initial and final tracts found with the proposed procedure. Moreover, the analysis based on these parameters can aid to correctly interpret the plots obtained with computer programs which often, in particular when poles at the origin are present, hide the behavior of the frequency response in the area close to the origin of the complex plane.


2014 - A Novel Instructional Approach to the Design of Standard Controllers: Using Inversion Formulae [Articolo su rivista]
Lorenzo, Ntogramatzidis; Zanasi, Roberto; Cuoghi, Stefania
abstract

This paper describes a range of design techniques for standard compensators (Lead-Lag networks and PID controllers) that have been applied to the teaching of many undergraduate control courses throughout Italy over the last twenty years, but that have received little attention elsewhere. These techniques hinge upon a set of simple formulas-herein referred to as Inversion Formulae -for the computation of the parameters of the controller as functions of the typical specifications of steady-state performance, stability margins, and crossover frequency.


2014 - Dynamic modeling of a Full Toroidal Variator: the Power-Oriented Graphs approach [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica; Fei, Marco
abstract

The Full Toroidal Variator is the core element in many mechanical hybrid systems for vehicle applications like Kinetic Energy Recovery System and Infinitely Variable Transmission because it allows to manage the power transfer with continuous variation of the speed-ratio. In this paper the model of a Full Toroidal Variator is addressed using Power-Oriented Graphs (POG) that is an energy-based modeling technique. Modeling with POG allows to easily transform and reduce the model when some dynamics of the system go to zero. An extended and reduced POG model of the Full Toroidal Variator are given. Simulation results of the modeled system are shown.


2014 - Extended and reduced POG dynamic model of an automatic corking machine for threaded plastic caps [Articolo su rivista]
Zanasi, Roberto; Grossi, Federica; N., Giuliani
abstract

The aim of this work is to show how the modeling of an electromechanical system can be addressed using the energy-based graphical modeling technique named “Power-Oriented Graphs” (POG). Differences and analogies of POG against Bond Graphs modeling technique are discussed. The paper presents the POG dynamic model of an automatic corking machine for threaded plastic caps: the system is composed by two electric motors moving a ball screw/spline that realizes the linear/rotary motion necessary to screw a plastic cap on a bottle. First an extended POG model is presented, together with the equivalent Bond Graph model, then some proper congruent state space transformations and a POG-based graphical method are introduced to transform and reduce the system dynamic model. Simulation and experimental results are finally presented and compared.


2014 - Open and closed logarithmic Nyquist plots [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

The Nyquist plot is a fundamental tool in the investigation of the stability of control systems. Usually Nyquist polar diagrams are plotted in a linear scale and often, in particular when poles at the origin are present, the diagrams need different levels of magnification in order to inspect the behavior of the frequency response in the areas very close to or very far from the origin of the complex plane. In this paper a new logarithmic Nyquist plot is proposed where the amplitude is in a logarithmic scale and the diagram is entirely contained and shown in a circle of finite radius. This method does not need to zoom in or zoom out the plot. All the considerations made by Nyquist stability criterion can be done with this plot which maintains all the properties of polar plots such as gain and phase margins, intersection points with the real axis, encirclements of the critical point. The design of first order lead and lag compensators can be done on this diagram in a simple way. The proposed new Nyquist plot is implemented in a Matlab function available to users.


2014 - The power-oriented graphs for modeling mechanical systems with time-varying inertia [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

The aim of this paper is to show how mechanical systems with time-varying inertia can be modeled by using the Power-Oriented Graphs technique. The reduced time-varying system is obtained starting from an extended Power-Oriented Graph model with masses and elasticities and applying a rectangular congruent transformation which eliminates the elasticities. The presented method is compared with the well established Bond Graphs modeling technique. The model of a crank-connecting rod system is considered as an example.


2013 - Dynamic Modeling and Control of Power-Split HEV with Multi-phase Electric Machines under Fault Condition [Relazione in Atti di Convegno]
Grossi, Federica; Fei, Marco; Zanasi, Roberto
abstract

The aim of this paper is to provide a dynamic model of the Toyota Hybrid System (THS) for simulation and control purposes in the case of fault of one of the electric machines. The two three-phase electric machines that are commonly used in THS are here replaced by two five-phase machines. The model of the whole system is realized by using the Power-Oriented Graphs modeling technique and includes the dynamics of the engine, electric machines, planetary gear, transmission and vehicle. A rule-based control strategy is used to operate the vehicle in different operation modes and a fault-tolerant control is applied in the case of electrical machine failure. Simulation results are given in both healthy and fault condition to show the effectiveness of the dynamic model and the robustness of the proposed control.


2013 - Dynamic modeling and simulation of a drying system with recuperation of the condensate [Relazione in Atti di Convegno]
Grossi, Federica; Zanasi, Roberto
abstract

The aim of this work is to build a lumped parameter model of a closed loop drying system with recuperation of the condensate to be used in analysis, simulation and control design. The proposed approach is based on an energy-based modeling technique which guarantees the conservation of energy within the system. The whole system involves thermodynamics, air-water interaction with evaporation and condensation and humid air flows dynamics. The proposed model can be used to make a dynamic analysis of the system, to predict some non-measured variables, to make some sensitivity analysis for different parameters, to investigate the best operation point acting on factors affecting the drying quality and power consumption. Some simulation results are presented and compared to experimental results.


2013 - Real and complex models of multi-phase permanent magnet synchronous motors [Articolo su rivista]
Zanasi, Roberto; Grossi, Federica; Fei, Marco
abstract

This paper deals with the modelling of multi-phase permanent magnet synchronous machines (PMSM) with an arbitrary number of phases and arbitrary shape of the rotor flux. The aim of the paper is to propose new dynamic models for the multi-phase electrical machines based on the use of real and complex state space transformations which are invariant with respect to power. The dynamic models of the motor are obtained using a Lagrangian approach in the frame of the power-oriented graphs technique. The obtained dynamic models can directly be implemented in Simulink whatever the number of phase is. The state space transformations presented in the paper (both real and complex) are compared to the main other transformations know in the literature. Some simulation results are finally presented.


2012 - Analytical and Graphical Design of PID Compensators on Nyquist plane [Relazione in Atti di Convegno]
Zanasi, Roberto; Cuoghi, Stefania
abstract

This paper focuses on the design of PID compensator to exactly satisfy the gain margin, the phase margin and the gain or phase crossover frequency specifications. The design problem is numerically solved using the so called PID inversion formulae method. A graphical interpretation of the solution on the Nyquist plane is presented. This could be suitable on education environment to deeply understand the design of PID compensators. Simulations results show the effectiveness of the presented method.


2012 - Dynamic models of multilevel converters by using the power oriented graph technique [Relazione in Atti di Convegno]
Zanasi, Roberto; Cuoghi, Stefania
abstract

The advances in power electronics and new needs in renewable energy sources lead the multilevel converters to be advantageous compared to 2-level converters. Since modeling tools can be helpful to design new converter topology, this paper presents the dynamic models of the three basic topologies of multilevel converters: the Diode-Clamped, the Flying-Capacitor and the Cascaded H-Bridge converters. These models have been obtained by using the Power Oriented Graph (POG) technique, that is easy to be employed and implemented in Matlab-Simulink® environment. The proposed models are suitable to simulate high frequency sliding mode control and can be easily modified to model hybrid topologies. Simulation results confirm the validity of the presented models.


2012 - Modeling of an internal combustion engine using Power-Oriented-Graphs and electrical analogy [Articolo su rivista]
Grossi, Federica; Zanasi, Roberto; A., Palladino; G., Fiengo
abstract

In this paper the Power-Oriented Graphs (POG) technique is used for modeling an internal combustion engine through electrical analogy. The aim of the authors, starting from an analogy with electrical systems, is to simplify the approach eliminating the space dynamics, while preserving the time dynamics. In this way, one can obtain an engine description similar to an electric circuit, with all the useful consequences in term of existence and numerical availability of the solution. The advantages are in the specific correspondence found between the engine components and variables with electrical counterparts . The main benefit achievable with this methodology is the simplicity to compose the whole engine model and customize it including the differential equations of the engine in state space form. The POG technique is a graphical modeling technique which uses only two basic blocks for modeling physical systems and the state space mathematical model of a system can be ``directly'' obtained from the corresponding POG representation.


2012 - Multi-phase synchronous motors: Minimum dissipation fault-tolerant controls [Relazione in Atti di Convegno]
Fei, Marco; Zanasi, Roberto
abstract

Multi-phase electrical motors offer high reliability thanks to their capability to operate safely even in case of faults such the loss of one or more phases. This paper presents a new vectorial approach that allows to obtain the optimal current references for a multi-phase permanent magnet synchronous motor under open-phase fault condition. The approach is as general as possible: the proposed control law can be used for any shape of the rotor flux, for a generic odd number of phases and in presence of one or more phase failures. The presented control ensures to obtain the desired torque without ripple, minimizing the dissipation, even in fault condition. Some simulation results validate the proposed control law.


2012 - Open-loop and Closed-loop Filters for Optimal Trajectory Planning under Time and Frequency Constraints [Relazione in Atti di Convegno]
Biagiotti, Luigi; Zanasi, Roberto
abstract

Dynamic filters for real-time trajectory generation can be designed in different ways with quite different levels of performances and complexity. However, one can observe that the configurations of such filters are based on two main schemes: systems composed of a chain of integrators with a feedback control and systems formed of a sequence of linear filters disposed in a cascade configuration. According to these schemes, it is possible to obtain minimum-time trajectories under constraints of velocity, acceleration, jerk and even higher derivatives. In both cases, the degree of continuity of the resulting trajectory depends on the order n of the filter, which can be designed according to a modular approach. After a short overview of the structure of the trajectory generators, pro and cons of the two approaches are analyzed. In particular, the attention is focussed on linear filters, since their structure allows a straightforward characterization of the trajectory from a frequency point of view. As a consequence, the generator can be designed by taking into account frequency constraints, besides more standard time constraints (i.e. limits on velocity, acceleration, etc.). The proposed method combines the advantages of minimum-time trajectories with those of input shaping techniques. Moreover, it is possible to prove that, under additional hypotheses, the same chain of linear filters proposed for minimum-time trajectories generation can be used for obtaining uniform B-spline curves, that are widespread in the robotic field when the interpolation of a set of given via-points is required. In this case, the additional constraints do not allow to impose limits on the velocity or acceleration, but only to properly shape the trajectory in the frequency domain. It is therefore possible to select the trajectory/filter parameters with the purpose of suppressing residual vibrations, that may be present because elastic phenomena affecting the robotic system.


2012 - Power-Oriented Graph in automotive application: VVT modeling on Lamborghini V12 engine [Relazione in Atti di Convegno]
Christian, Corvino; Zanasi, Roberto
abstract

In automotive applications the emission reduction and fuel consumption are relevant goals for manufactures so that several devices are introduce in the engine. One of such devices is Variable Valve Timing (VVT), modeled in this paper, that represents a complex multi physic system designed to control the intake camshaft: by opening and closing time of inlet and outlet valves are modified so that the engine conditions can satisfy the gaols in term of torque improvement in all the speed ranges as well as increasing fuel economy and reducing exhaust emission. In this paper the Power Oriented Graph (POG) technique has been used for modeling the considered electromechanical system allowing to detect some hide variables not readable by the sensors. The effectiveness of the proposed model has been validated using an experimental set-ut.


2011 - Analytical and Graphical Design of Lead-Lag Compensators [Articolo su rivista]
Zanasi, Roberto; Cuoghi, Stefania; L., Ntogramatzidis
abstract

In this paper an approach based on inversion formulae is used for the design of lead-lag compensators which satisfy frequency domain specifications on phase margin, gain margin and phase (or gain) crossover frequency. An analytical and graphical procedure for the compensator design on the Nyquist and Nichols planes is presented with some numerical examples.


2011 - Analytical Design of Lead-Lag Compensators on Nyquist and Nichols Planes [Relazione in Atti di Convegno]
Zanasi, Roberto; S., Cuoghi; L., Ntogramatzidis
abstract

In this paper the dynamic structure and the control properties of a new form of lead-lag compensator with complex zeros and poles are presented. A simple and exact analytical and graphical method on the Nyquist and Nichols planes for the design of lead-lag compensators satisfying design specifications on gain margin, phase margin and crossover frequency is proposed. Simulations results show the good performances of the presented method.


2011 - Complex dynamic model of a multi-phase asynchronous motor with harmonic injection [Relazione in Atti di Convegno]
Zanasi, Roberto; Azzone, Giovanni
abstract

In this paper a new complex dynamic model for multi-phase asynchronous motors has been presented using the Power-Oriented Graphs (POG) technique. This new model is obtained using a complex rectangular transformation that reduces the number of the used complex state space variables. The odd harmonic injection has also been considered in order to describe the most general dynamics of the machine by using a compact model. Finally some simulation results have been reported to prove the effectiveness of the new transformation and to show the contribution of the harmonic injection in terms of torque enhancement.


2011 - Complex Dynamic Models of Multi-phase Permanent Magnet Synchronous Motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica; Fei, Marco
abstract

In the paper two power-invariant real and complex state space transformations for modeling multi-phase electrical machines in a compact and general form are proposed. In particular the paper deals with the modeling of multi-phase permanent magnet synchronous machines with an arbitrary number of phases and an arbitrary shape of the rotor flux. The dynamic model of the motor is obtained using a Lagrangian approach and in the frame of the Power-Oriented Graphs technique. The obtained models are equivalent from a mathematical point of view and can be directly implemented in Simulink. The complex transformed model is quite compact and uses a reduced order state vector. Some simulation results end the paper.


2011 - Complex dynamic models of star and delta connected multi-phase asynchronous motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Azzone, Giovanni
abstract

This paper addresses the complex modeling of a multi-phase asynchronous motor with star-connected and delta-connected stator phases. The model is obtained using a complex rectangular transformation that reduces the number of complex internal variables and is graphically represented using the Power-Oriented Graphs technique. The dynamic equations have been defined considering the stator phases star-connected and delta-connected, proving that in both cases the internal complex model does not change. Finally some simulation results have been presented to show the effectiveness of the modeled system and the contribution of the star-delta transformation in terms of provided torque.


2011 - Control of a five-phase synchronous motors with third harmonic constrained injection [Relazione in Atti di Convegno]
Fei, Marco; Zanasi, Roberto
abstract

This paper deals with the torque control of five-phase permanent magnet synchronous machines with first and third harmonics injection. A new vectorial approach to describe the voltage and current limits is proposed. Starting from the transformed dynamic equations and using the voltage and current constraints, the optimal current references minimizing the dissipation and maximizing the torque is obtained. The proposed control law holds for an arbitrary shape of the rotor flux. Some simulation results validate the proposed control law.


2011 - Design of lead-lag compensators for robust control [Relazione in Atti di Convegno]
Zanasi, Roberto; S., Cuoghi
abstract

n this paper three different methods for the synthesis of lead-lag compensators that meet design specifications on the phase margin and the gain crossover frequency are presented. These numerical and graphical methods are based on the choice of a degree of freedom of the regulators. These procedures aim to satisfy an additional specification for robust control: the gain margin, the complementary modulus margin or a specification on the settling time of the controlled system.


2011 - Differences and common aspects of POG and EMR energy-based graphical techniques [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

Three main modeling techniques have been proposed in the past years: Bond Graphs (BG), Power-Oriented Graphs (POG) and Energetic Macroscopic Representation (EMR). These modeling techniques are energy-based graphical techniques which exploits the power interaction between subsystems as basic concept for modeling. In this paper a comparison between the POG and EMR techniques is presented. These techniques have many aspects in common and also differences that are pointed out in the paper. The POG schemes have a well-defined mathematical structure and use vectorial compact forms when the system complexity increases. The EMR constitutes a graphical tool useful for modeling, simulation and control of dynamical systems.


2011 - Direct method for digital lead-lag design: analytical and graphical solutions [Relazione in Atti di Convegno]
Zanasi, Roberto; S., Cuoghi
abstract

The paper presents a direct digital method to the design of a discrete lead-lag compensator for a robust control. The design specifications on phase margin, gain margin and crossover frequency of the close-loop system can be obtained by using numerical and graphical solutions. The discrete design method proposed in the paper is also compared with the continuous-time case. Some numerical examples are presented. The proposed method can be useful both on educational and industrial environments.


2011 - Direct methods for the synthesis of PID compensators: Analytical and graphical design [Relazione in Atti di Convegno]
Zanasi, Roberto; S., Cuoghi
abstract

In this paper direct methods for the synthesis of continuous and discrete PID compensators for a robust control are proposed. Analytical and graphical techniques on the Nyquist plane to meet specifications on phase margin, gain margin and crossover frequency of the close-loop system are presented. Numerical examples demonstrate the effectiveness and the simplicity of the proposed approach, that can be useful both on educational and industrial applications.


2011 - Dynamic modeling and control of a new automatic corking machine for threaded plastic caps [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica; N., Giuliani
abstract

The aim of this work is to model a new electromechanical system for applications in the field of automated corking machines. The paper presents the dynamic modeling of a new automatic corking machine for threaded plastic caps. The model is obtained using the energy-based modeling technique named “Power-OrientedGraphs” (POG). The considered corking machine is an electromechanical system with two degrees of freedom composed by two electrical motors moving a ball screw/spline that realizes the linear/rotary motion necessary to screw a plastic cap on a bottle. The paper presents the dynamic model of the machine and the interaction between the cap and the bottle. In the paper a control algorithm is proposed. Some simulation results are presented and compared to experimental results.


2011 - Efficient Simulation of Static and Dynamic Friction for Automotive Applications [Relazione in Atti di Convegno]
Biagiotti, Luigi; Zanasi, Roberto
abstract

In this paper, a technique for modeling frictional phenomena among several bodies that move relatively is proposed with the purpose of optimizing the dynamic simulation of a complex system such as the driveline of a vehicle based on a dual clutch transmission. The proposed method considers together the inertial and frictional properties of the different subsystems, but decouples a main dynamics, that describes their average motion and does not depend on friction, from a proper number of relative dynamics. In this way, for each of these dynamics a standard static friction models can be used, leading to a very efficient numerical simulation. In this sense, the method adopted can be considered an enhancement of Karnopp model.


2011 - Esercizi di Controlli Automatici. Compiti d'esame svolti. [Monografia/Trattato scientifico]
Zanasi, Roberto
abstract

Questo libro raccoglie una serie di esercizi di Controlli Automatici che sono stati proposti agli studenti della Facoltà di Ingegneria di Modena nelle prove d'esame di Controlli Automatici A, Controlli Automatici B e Controlli Automatici nel periodo 1998-2010 per i Corsi di Laurea di Ingegneria Informatica, Elettronica e delle Telecomunicazioni dell'Università di Modena e Reggio Emilia. Il libro è suddiviso in varie sezioni, ognuna delle quali è dedicata ad uno specifico argomento di base di Controlli Automatici: analisi temporale, analisi frequenziale, sistemi retroazionati, reti correttrici, non linearità e sistemi discreti. Ciascuna sezione è costituita da alcune note introduttive, da una serie di domande teoriche a riposta multipla e da una serie di esercizi d'esame svolti. Le note introduttive hanno lo scopo di richiamare i principali aspetti teorici riguardanti l'argomento della sezione e di dare alcuni suggerimenti agli studenti sul modo migliore di risolvere i compiti d'esame proposti. Queste note vengono fornite a completamento' della parte teorica del corso di Controlli Automatici attualmente attivo presso la Facoltà di Ingegneria di Modena.Le domande teoriche a risposta multipla e gli esercizi d'esame svolti inseriti in ciascuna sezione hanno invece lo scopo di verificare la preparazione teorica e pratica dello studente sulle principali tematiche di un corso base di Controlli Automatici.Gran parte dei grafici riportati in questo libro sono stati ottenuti in ambiente Matlab utilizzando i comandi del Control System Toolbox. Molti di questi grafici possono anche essere ottenuti utilizzando il programma di progettazione assistita TFI (Transfer Function Interpreter) sviluppato dal Prof. Marro in ambiente Matlab.


2011 - Field Oriented Control of a Multi-Phase Asynchronous Motor with Harmonic Injection [Relazione in Atti di Convegno]
Zanasi, Roberto; Azzone, Giovanni
abstract

The paper presents a new complex dynamic modeling of multi-phase asynchronous motors and investigates the Field-Oriented control applied to this type of machines. The newdynamic model is obtained in the state space using a complex rectangular transformation. The obtained model is complex, reduced-order and takes into account also the odd harmonicinjection of the motor. The Field-Oriented control is considered and discussed in the multi-phase general case and then implemented in Matlab/Simulink considering a specific numeric case. The simulation results validate the obtained complex model and the implemented control design.


2011 - Lead-Lag compensators: Analytical and graphical design on the Nyquist plane [Relazione in Atti di Convegno]
Zanasi, Roberto; Cuoghi, Stefania; Lorenzo, Ntogramatzidis
abstract

This paper presents a design method for the synthesis of a general class of lead-lag compensators to exactly satisfy gain and phase margins specifications. A free parameter of the compensator is used as a degree of freedom in order to satisfy additional requirements on the phase and/or gain crossover frequencies. A graphical procedure for the compensator design on the Nyquist plane is presented with some numerical examples.


2011 - Model of soft-switching converter and power control for smart grid applications [Relazione in Atti di Convegno]
Zanasi, Roberto; Cuoghi, Stefania
abstract

The advances in computing and communication technologies allow to connect inverters of energy generation systems in smart grids, to well control the power flows. Modeling tools would be helpful in the design of required new inverter topology. This paper presents a modeling technique, so called Power Oriented Graph, easy to use and to be implemented in Matlab-Simulink environment. This technique has been used for modeling a recently proposed soft-switching grid-connected DC/AC power converter for photovoltaic systems. Modifications in the structure of the DC/DC converter and in the control of the DC/AC converter for smart grid applications are proposed. Simulation results confirm the effectiveness of the presented models and the introduced improvements.


2011 - Model of soft-switching converter and power control of grid-connected photovoltaic systems [Relazione in Atti di Convegno]
Zanasi, Roberto; S., Cuoghi
abstract

This paper presents a modeling technique, so called Power Oriented Graph, suitable for designing and simulating new topologies of inverter in energy generation system and reducing production cost. This technique is used for modeling a recently proposed soft-switching grid-connected DC/AC power converter for photovoltaic systems. Modifications in the structure of the DC/DC converter and in the control of the DC/AC converter are proposed. Simulation results confirm the effectiveness of the presented model and the introduced improvements.


2011 - Modeling of multi open phase fault condition of multi-phase permanent magnet synchronous motors [Relazione in Atti di Convegno]
Fei, Marco; Zanasi, Roberto
abstract

This paper deals with the modeling of multi-phase permanent magnet synchronous motors under multi open phase fault condition. The presented model is suitable for generic number of phases, generic shape of the rotor flux and generic number of open circuit faults. The motor model in fault condition can be used for faults occurring on both adjacent and not adjacent phases. The model can be very useful both for simulation and implementation of fault-tolerant control strategies.


2011 - Modeling of multi-phase permanent magnet synchronous motors under open-phase fault condition [Relazione in Atti di Convegno]
Fei, Marco; Zanasi, Roberto; Grossi, Federica
abstract

This paper deals with the modeling of multi-phase permanent magnet synchronous motors under open-phase fault condition. Multi-phase electrical motors offer high reliability thanks to their capability to operate safely even in case of faults such the loss of some phase. In this paper the model of a multi phase PM machine in the case of open phase fault condition is proposed. The model is suitable for faults occurring at any phases: the faults can happen on one single phase or more than one phase (both adjacent and not adjacent phases). Moreover the model holds for any shape of the rotor flux and for a generic odd number of phases.


2011 - Multi-phase vectorial control of synchronous motors with currents and voltages saturations [Relazione in Atti di Convegno]
Fei, Marco; Zanasi, Roberto
abstract

This paper deals with the torque control of ms-phase synchronous machines where the first odd harmonics below ms are injected. A new vectorial approach to describe the voltage and current limits is proposed. Starting from the transformed dynamic equations and using the voltage and current constraints, the optimal current references is obtained. It holds for an arbitrary number of star connected phases and an arbitrary shape of the rotor flux. Some simulation results for a 7-phase motor validate the proposed control law.


2011 - Power control of grid-connected photovoltaic systems [Relazione in Atti di Convegno]
Zanasi, Roberto; S., Cuoghi
abstract

In this paper the Power Oriented Graph technique is used for modeling a grid-connected single-phase 3 kW DC/AC power converter for solar energy conversion system. A DC/DC stage, controlled by a maximum power point tracking (MPPT) technique, is used to boost the time-varying input voltage provided by photovoltaic panels. A buck DC/AC stage, including a PWM inverter, is implemented to transfer the active power to the grid. A new control scheme for the DC/AC stage is proposed.


2010 - Complex Dynamic Model of a Multi-phase Asynchronous Motor [Relazione in Atti di Convegno]
Zanasi, Roberto; Azzone, Giovanni
abstract

The paper presents a new complex and reduced dynamical model of a multi-phase asynchronous motor using the Power-Oriented Graphs modeling technique. The new reduced model is obtained in the state space using a complex and rectangular “congruent” transformation. The model describes the electric motor using a reduced number of complex state space variables. The characteristic polynomial of the new model has complex coefficients: its roots and the complex conjugate of these roots are exactly the eigenvalues of the considered asynchronous motor. The complex steady-state equations of the new reduced model are given and discussed. Some simulation results end the paper.


2010 - Dynamic Filters for Online Planning Optimal Trajectories [Relazione in Atti di Convegno]
Biagiotti, Luigi; Melchiorri, Claudio; Zanasi, Roberto
abstract

Filters for time-optimal trajectory generation can be obtained in different ways with quite different performances and complexity levels. However, one can easily observe that the configurations of such filters are based on two main schemes: systems composed by a chain of integrators with a feedback control and systems formed by a sequence of Finite Impulse Response (FIR) filters disposed in a cascade configuration. Both trajectory generators are characterized by the order $n$ that defines the degree of continuity of the resulting trajectory and both can be designed according to a modular approach that allows to obtain the $n$-th order filter from that of $n-1$ order. In this paper, after having presented the structure and the analytical expression of the two types of trajectory filters, their common features (possibility of generating online time-optimal trajectories under constraints of velocity, acceleration, jerk, etc.) but especially the main differences are analyzed. In particular, the possible applications of the two systems are considered. Trajectory filters with a feedback loop are able to track generic input signals (and not only step functions) guaranteing the compliance of the output with the given constraints but are characterized by a complexity that limits their use to the third order. Conversely, the simple structure and the low computational cost make open-loop filters desirable for point-to point motions, even with an high degree of smoothness ($n=4$ or $5$). Moreover, the low-pass response of this type of filters allows to characterize (and to design) the output trajectory from a frequency point of view, but, on the other hand, it may cause large delays and distortions between input and the output signals.


2010 - Energetic Model of the Tire-Ground Interaction and Comparison with LuGre Friction Model [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

In this paper the energetic dynamic model of the tire-ground interaction in a vehicle is presented and a comparison with the LuGre friction model is given. The Power-Oriented Graphs (POG) technique is exploited for both representing and analyzing the two dynamic systems. In particular the LuGre model is analyzed showing some drawbacks and a modified model is proposed in order to guarantee dissipativity. Simulation results end the paper comparing the two dynamic models of the tire-ground interaction.


2010 - Modeling and Control of Power-Split Hybrid Electric Vehicles [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

In this paper a Power-split hybrid automotive system is considered, including a multi-phase synchronous motor, an internal combustion engine and a planetary gear as key element to split power in this propulsion system. The dynamic model of a planetary gear with internal elasticity is presented and the model of the whole vehicle is given using the Power-Oriented Graphs approach. A global control is designed to obtain different operation modes of the vehicle: engine start, battery charging, hybrid traction, recovery of braking energy. Simulation results of the modeled HEV are provided showing the effectiveness of the proposed model and control.


2010 - Modelling Hybrid Automotive Systems with the POG Technique [Articolo su rivista]
Zanasi, Roberto; Grossi, Federica
abstract

In this paper the Power-Oriented Graphs (POG) technique is used for modelling planetary gears and hybrid automotive systems. The POG technique allows to graphically describe the dynamic model of any type of physical system (in different energetic domains) putting in evidence the power flows within the modelled systems. The POG schemes are easy to use, easy to understand even by a neophyte and can be directly implemented in Simulink. Because of the POG modular structure, complex physical systems can be modelled by composing subsystems models. Following this approach a whole power-split hybrid vehicle is modelled, starting from modelling its main subsystems: planetary gear, multi-phase synchronous motor and vehicle dynamics. Simulation results of the modelled hybrid system are reported at the end of the paper.


2010 - Online trajectory planner with constraints on velocity, acceleration and torque [Relazione in Atti di Convegno]
Biagiotti, Luigi; Zanasi, Roberto
abstract

A filter for trajectories smoothing is presented. The filter provides an output reproducing the input trajectory if this is compliant with given constraints on the velocity, the acceleration and the torque required for tracking it. Otherwise, the filter approximates the input profile guaranteeing that the output trajectory satisfies all the kinematic and dynamic limits. The tracking of the input signal is optimal in the sense that at each time instant the limit value of one among velocity, acceleration and torque is reached. The filter, based on a variable structure controller, is designed in the continuous-time domain but can be implemented by discretization as a sampled system. It can therefore used in mechatronic and robotic applications driven by digital controllers in order to filter trajectories planned without considering the above mentioned constraints or to generate realtime smooth trajectories by simply providing basic inputs such as step or ramp functions.


2010 - POG Modeling of a Cascaded Doubly-Fed Induction Generator [Relazione in Atti di Convegno]
Zanasi, Roberto; Azzone, Giovanni
abstract

In this paper a Cascaded Doubly-Fed Induction Generator (CDFIG) has been modeled using the Power-Oriented Graphs (POG) technique. The dynamic equations of the system have been obtained using a Lagrangian approach. The system equations have been described with respect to a rotating reference frame to clearly show the internal dynamic structure of the system. An Indirect Rotor Field-Oriented control that let the grid voltage frequency to be constant, even when the rotor speed is variable, has been given and implemented. Finally, some simulation results have been reported to validate the presented control law and the effectiveness of the model.


2010 - Saturated Vectorial Control of Multi-phase Synchronous Motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Fei, Marco
abstract

This paper deals with the torque control of multi-phase permanent magnet synchronous machines. The dynamic model of these motors is obtained using the Power-Oriented Graphs technique. This graphical modeling technique allows to write the dynamic equations of the system in a very compact form. Starting from the dynamic equations, a torque control law with saturated input voltages is proposed based on a new current vector approach for describing the voltage constraint. Some simulation results validate the proposed control law.


2010 - The Power-Oriented Graphs Technique: system modeling and basic properties [Relazione in Atti di Convegno]
Zanasi, Roberto
abstract

In this paper the Power-Oriented Graphs (POG) technique is introduced and its basic graphical properties are compared with those of the Bond Graph (BG) technique. The two techniques are based on the same concepts, are equivalent from a mathematical point of view and use two different graphical representations for modeling physical systems. The BG schemes are quite compact and more flexible in the exact description of all the power connections within the system. The POG schemes are easier to use for beginners and use vectorial compact forms when the system complexity increases. The paper ends describing some “dissipative” properties of the POG state space models.


2010 - Time-Optimal Regulation of a Chain of Integrators with Saturated Input and Internal Variables: An Application to Trajectory Planning [Relazione in Atti di Convegno]
Biagiotti, Luigi; Zanasi, Roberto
abstract

The design of a planner for time-optimal trajectories with constraints on velocity, acceleration, jerk, . . . , is translated into a regulation problem for a chain of integrators with saturations not only in the input but also in all the internal (state) variables. Then the problem is solved by designing a regulator, based on the variable structure control, able to steer the state vector to the origin in minimum time, being compliant with all the constraints. For this purpose, a modular structure with a cascade of controllers, each one devoted to the regulation to the origin of a specific component of the state vector, is demonstrated to be effective and ideally suitable to cope with systems of any order. Analytical examples are provided for filters of first, second and third order.


2009 - Discrete Inversion Formulas for the Design of Lead and Lag Discrete Compensators [Relazione in Atti di Convegno]
Zanasi, Roberto; Morselli, Riccardo
abstract

In the paper, new discrete inversion formulas suitable for the design of lead and lag discrete compensators in the frequency domain are presented. These formulas can be very useful for teaching in Automatic Control courses. The links of these discrete formulas with the continuous inversion formulas are deeply investigated. A simple graphical procedure for the design of discrete compensators on the Nyquist plane is also presented. Finally, some numerical examples illustrate the presented results.


2009 - Dynamic Behavior of Multi-phase Asynchronous Motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica; Azzone, Giovanni
abstract

The goal of this paper is the analysis of the dynamic behavior of a multi-phase asynchronous motor. The Power-Oriented Graphs technique has been used for modeling the system and a very simple and compact model has been obtained. The steady-state equations of the system have been studied finding remarkable relations between the motor voltage and current vectors. The eigenvalues of the electrical part of the motor have been mathematically expressed as function of thesystem parameters. Some simulations have been presented to validatethe effectiveness of the model.


2009 - Modelling and control of a vehicle with tire-road interaction using energy-based techniques [Relazione in Atti di Convegno]
Grossi, Federica; W., Lhomme; Zanasi, Roberto; A., Bouscayrol
abstract

In this paper a vehicle with the modelling of its tire-road interaction is described using two different energy-based graphical techniques: power-oriented graphs (POG) and energetic macroscopic representation (EMR). The main features of both approaches are presented and an integration between them is proposed: they can be used together to model different parts of the same system. Using the two techniques the whole vehicle can be represented with either a mathematical or a macroscopic view. From EMR an inversion-based control is given in order to control the vehicle velocity.


2009 - Modelling and control of a vehicle with tire-road interaction using Power-Oriented-Graph and Energetic-Macroscopic-Representation formalisms [Relazione in Atti di Convegno]
Grossi, Federica; W., Lhomme; Zanasi, Roberto; A., Bouscayrol
abstract

In this paper a vehicle is described using two different energetic graphical techniques: power-oriented graphs (POG) and energetic macroscopic representation (EMR). As these techniques have different features and purposes, they can be used together to model different parts of the same system. The POG technique is used to model the interaction between tire and road in order to have a dynamic energetic model, while the EMR technique is used to repreIn this paper a vehicle is described using two different energetic graphical techniques: Power-Oriented Graphs (POG) and Energetic Macroscopic Representation (EMR). As these techniques have different features and purposes, they can be used together to model different parts of the same system. The POG technique is used to model the interaction between tire and road in order to have a dynamic energetic model, while the EMR technique is used to represent the whole system and deduce the control structure through the inversion-based methodology. Thanks to the use of both techniques the whole vehicle can be represented and a structure to control the vehicle velocity is given.sent the whole system and deduce the control structure through the inversion-based methodology. Thanks to the use of both techniques the whole vehicle can be represented and a structure to control the vehicle velocity is given.


2009 - The POG technique for modeling multi-phase asynchronous motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica; Azzone, Giovanni
abstract

In this paper the dynamic model of a multi-phase asynchronous motor has been obtained using the power-oriented graphs (POG) technique and applying the Lagrangian approach. The power internal structure of the motor has been clearly identified. The steady-state behaviour of the motor has been analyzed putting in evidence the mathematical relations between the current and voltage vectors in the transformed rotating frame. In particular an interesting expression for the generated motor torque has been obtained. Some simulation results are finally reported.


2009 - The POG technique for modeling planetary gears and hybrid automotive systems [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

In this paper the Power-Oriented Graphs (POG) technique is used for modeling planetary gears and hybrid automotive systems. Some basic properties of the POG technique are firstly given. An extended dynamic model of a planetary gear with internal elasticity is presented. Then a POG congruent state space transformation is used to transform and reduce the system when the elasticities or the inertias go to zero. The obtained reduced model is used as central element of an hybrid automotive power structure (endothermic engine, multi-phase synchronous motor and vehicle dynamics). Simulation results of the modeled hybrid system ends the paper.


2009 - The POG technique for modelling engine dynamics based on electrical analogy [Relazione in Atti di Convegno]
Grossi, Federica; A., Palladino; G., Fiengo; Zanasi, Roberto
abstract

In this paper the Power-Oriented Graphs (POG) technique is used for modelling an internal combustion engine. The POG technique is focused on a new modular, physically based and lumped parameter approach, leading to a complete and coherent engine model structure. The aim of the authors, starting from an analogy with electrical systems, is to simplify the approach eliminating the space dynamics (multi-zone combustion and wave effects), while preserving the time dynamics. In this way, it is possible to obtain an engine description similar to an electrical circuit, with all the useful consequences in term of existence and numerical availability of the solution. The advantages are in the specific correspondence that is found between the engine components and variables (as throttle valve, cylinder, inertial flows) with electrical counterparts (current, voltage, resistance). The main benefit achievable with this methodology is the simplicity to compose the whole engine model and customize it including the differential equations of the engine in state space form, using the POG technique. The POG technique is a graphical modelling technique which uses only two basic blocks (the ldquoelaborationrdquo and ldquoconnectionrdquo blocks) for modelling physical systems. The state space mathematical model of a system can be ldquodirectlyrdquo obtained from the corresponding POG representation. The POG model of the considered combustion engine shows its internal structure from a ldquopowerrdquo point of view.


2009 - Vectorial control of multi-phase synchronous motors using POG approach [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

This paper deals with the vectorial control of multiphase permanent magnet synchronous machines. The dynamic model of the motor is obtained using the power-oriented graphs technique which clearly shows the power flows within the system and allows to write the dynamic equations of the system in a proper rotating reference frame. Moreover the obtained model can be directly implemented in Simulink. Starting from the model of the motor, a torque control law with saturated input voltages is proposed based on a new ¿current¿ approach. The obtained control is very effective and with a simple structure. Simulation results are provided.


2008 - Control of port Hamiltonian systems by dissipative devices and its application to improve the semi-active suspension behaviour [Articolo su rivista]
Morselli, Riccardo; Zanasi, Roberto
abstract

The port Hamiltonian framework is a powerful tool for modeling a wide class of nonlinear systems such as robots and, more generally, mechatronic systems. The standard approaches used for the control of the port Hamiltonian systems are not applicable to a wide variety of mechatronic systems. This happens, forexample, when the input control variable acts directly on some dissipative components of the system. In these cases the controlled devices can only dissipate power and the problem is to find a proper control law in order to meet the control requirements. This paper proposes four control laws for the controlled dissipative components which allow to satisfy a set of control requirements by acting on the energy stored in a subsection of the given system or by controlling the power flowing through a physical section of the system. Although some important issues remain open, the example of the semi-active suspension shows that some positive results can be achieved by applying the proposed approach.


2008 - Different energetic techniques for modelling traction drives [Relazione in Atti di Convegno]
Zanasi, Roberto; G. H., Geitner; A., Bouscayrol; W., Lhomme
abstract

In this paper the traction system of an automatic subway isdescribed using four different energetic graphical techniques:Bond-Graph (BG), Energetic Macroscopic Representation (EMR),Power-Oriented Graphs (POG) and Vectorial Bond-Graph (VBG). Theaim of this paper is to highlight the analogies and thedifferences between these modelling techniques in the analysis andsimulation of the considered system.


2008 - Different Graphical Descriptions of Clutch Modelling for Traction Systems [Relazione in Atti di Convegno]
W., Lhomme; Zanasi, Roberto; G. H., Geitner; A., Bouscayrol
abstract

In this paper the friction clutch of a vehicle is modelled using three special graphical tools which are developed to model power flow through physical systems: energetic macroscopic representation, power oriented graph and bond graph. Due to its non-linear behaviour, the modelling of the clutch is a challenging point. Indeed, it connects or disconnects mechanical parts, which can have similar or diverging rotation speeds. The aim of the paper is to highlight the features of each tool for the clutch modelling, the simulation and the analysis of such systems including non-linearities.


2008 - Multi-phase Synchronous Motors: POG Modeling and Optimal Shaping of the Rotor Flux [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

In the paper the Power-Oriented Graphs (POG) technique is used for modelling m-phase permanent magnet synchronous motors and a study on the rotor flux is given. The POG model of the considered electrical motor shows its internal structure from a ``power'' point of view. The dynamic model of the motor is as general as possible and it considers an arbitrary odd number of phases. Generalized orthonormal transformations allow to write the dynamic equations of the system in a very compact form. The rotor flux is analyzed, in particular in order to minimize currents needed for the torque generation. An optimal shape for the rotor flux is presented. The model is finally implemented in Matlab/Simulink and some simulations are carried out.


2008 - Optimal rotor flux shape for multi-phase permanent magnet synchronous motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

In the paper the power-oriented graphs (POG) technique is used for modeling m-phase permanent magnet synchronous motors and a study on the optimal rotor flux is given. The POG model shows the ldquopowerrdquo internal structure of the considered electrical motor: the electric part interacts with the mechanical part by means of a ldquoconnectionrdquo block which neither stores nor dissipates energy. The dynamic model of the motor is as general as possible and it considers an arbitrary odd number of phases. The rotor flux is analyzed, in particular in order to minimize the currents needed for the torque generation, and its optimal shape is given. The model is finally implemented in Matlab/Simulink and the presented simulation results validate the machine model and the rotor flux choice.


2007 - The POG technique for Modelling Multi-phase Permanent Magnet Synchronous Motors [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica
abstract

In the paper the Power-Oriented Graphs (POG) technique is used for modelling n-phase permanent magnet synchronous motors. The POG technique is a graphical modelling technique which uses only two basic blocks (the elaboration and connection blocks) for modelling physical systems. Its main characteristics are the following: it keeps a direct correspondence between pairs of system variables and real power flows; the POG blocks represent real parts of the system; it is suitable for representing physical systems both in scalar and vectorial fashion; the POG schemes can be easily transformed, both graphically and mathematically; the POG schemes are simple, modular, easy to use and suitable for education. The POG model of the considered electrical motor shows very well, from a ``power'' point of view, its internal structure: the electric part of the motor interacts with the mechanical part by means of a ``connection'' block which neither store nor dissipate energy. The dynamic model of the motor is as general as possible and it considers an arbitrary odd number of phases and an arbitrary number of harmonics of the rotor flux waveform. Generalized orthonormal transformations allow to write the dynamic equations of the system in a very compact way. The model is finally implemented with Matlab/Simulink software. The Simulink structure of the motor clearly reflects its POG representation. Simulation results are then presented to validate the machine model.


2007 - Three-dimensional Energetic Dynamic Model of the Tire-Soil Interaction [Relazione in Atti di Convegno]
Zanasi, Roberto; Grossi, Federica; Morselli, Riccardo
abstract

In the paper a three-dimensional dynamic model of the tire-soil interaction is presented. The power-oriented graphs (POG) technique is used for modelling the system. An important feature of the proposed model is the use of an elastic element for describing the interaction of the tire with the ground. The proposed model solve some particular limits of the Pacejka formulas. For example it can be used also when the car or wheel velocities are zero or when the vehicle is at rest on an inclined surface. Moreover, the skidding and the slipping phenomena that in the Pecejka's formulas are mixed, in the proposed model are kept separate so allowing a more direct correspondence of the model with the physical meaning of the described phenomena. The effectiveness of the proposed model has been tested in simulation on a four wheel car.


2006 - Control of Mechatronic Systems by Dissipative Devices: Application to Semi-Active Vehicle Suspensions [Relazione in Atti di Convegno]
Morselli, Riccardo; Zanasi, Roberto
abstract

A wide variety of mechatronic systems are controlled by operating dissipative components such as variable resistors, variable dampers, clutches, some electro-valves and more. Facing the limitation that the controlled devices can only dissipate power, the issue is to find a proper control law to satisfy the control requirements. The mechatronic systems can usually be divided into two or more subsystems that are connected by a power preserving connections. This paper proposes to choose the control inputs to lead the power towards a certain subsystems in order to satisfy the requirements by controlling the energy stored or the power dissipated in that subsystem. To this aim, the port Hamiltonian framework is used to model the mechatronic systems. A slight extension of the definition of port Hamiltonian system is proposed to allow the description of a larger set of mechatronic systems and to obtain an explicit representation of the energy flowing to a subsystem. Some of the control laws presented in literature about the control of semi-active suspensions are derived again by following the proposed approach and adding an energetic interpretation.


2006 - Detailed and reduced dynamic models of passive and active limited-slip car differentials [Articolo su rivista]
Morselli, Riccardo; Zanasi, Roberto; Sandoni, Germano
abstract

Passive and active limited-slip differentials are used in high-performance cars to optimize the torque distribution on the driving wheels for traction maximization, driving comfort, stability and active safety of the vehicle. In this paper, detailed and reduced dynamic models for the simulation of four kinds of differential are presented. The models refer to the limited-slip steering differential with two clutches. The model of the conventional differential, of the mechanical limited-slip differential and of the controlled limited-slip differential can be obtained by simplification. The detailed model allows the simulation of the internal phenomena that influence the differential dynamics. The reduced model focuses only on the main dynamic behaviour of the differential. Some simulations show the use of the reduced model to compare the effects of the four differentials on the vehicle dynamics.


2006 - Modelling and simulation of static and Coulomb friction in a class of automotive systems [Articolo su rivista]
Morselli, Riccardo; Zanasi, Roberto; P., Ferracin
abstract

Static and Coulomb frictions are extensively used in automotive mechanical systems to control the synchronization between two shafts or two axles. Clutches, gearboxes and limited-slip differentials are some examples. This paper proposes a method for the efficient simulation of a wide class of automotive mechanical systems with static and Coulomb friction phenomena. The modelling approach is based on the port-Hamiltonian representation of the dynamic systems and the computation of the friction forces requires only the zero crossing detection. A slight approximation allows faster and sufficiently accurate simulations even without an accurate zero crossing detection. The proposed approach has been used to simulate the behaviour of a complex gearbox provided by some high level farm tractors.


2005 - Discrete Second Order Trajectory Generator with Nonlinear Constraints [Relazione in Atti di Convegno]
Morselli, Riccardo; Zanasi, Roberto; S., Stramigioli
abstract

A discrete second order trajectory generator for motion control systems is presented. The considered generator is a nonlinear system which receives as input a raw reference signal and provides as output a smooth reference signal satisfying nonlinear constraints on the output derivatives. The trajectory is generated on-line and the imposed constraints can also be changed during system operation withoutmodifying the system stability. Moreover, almost minimum time response is ensured with guaranteed no overshoot. The performances of the nonlinear generator are tested through experiments on a linear motor.


2004 - Are ring currents still useful to rationalize the benzene proton magnetic shielding? [Articolo su rivista]
RG, Viglione; ZANASI, Roberto; LAZZERETTI, Paolo
abstract

The conventional interpretation of proton NMR chemical shifts is supported by large basis set ab initio quantum mechanical calculations. The benzene protons are predicted to lie within the deshielding zone defined in terms of the out-of-plane magnetic shielding domain. However, ring currents by themselves are not sufficient to account quantitatively for the observed benzene proton downfield chemical shift. or-Electron contributions must also be taken into account. The conventional explanation for the ethyne proton chemical shift is valid.


2004 - Modellistica Dinamica di un Attuatore Elettroidraulico [Articolo su rivista]
Morselli, Riccardo; Zanasi, Roberto; E., Sereni; E., Bedogni; E., Sedoni
abstract

Gli attuatori idraulici comandati elettronicamente sono utilizzati in molte applicazioni nelle quali è necessario controllare elevate forze e potenze non ottenibili convenientemente attraverso dispositivi elettrici. In questo articolo si propone un modello dinamico dettagliato di un attuatore idraulico con elettrovalvola corrente-pressione per frizioni in bagno d'olio. Il modello proposto è stato validato mediante misure sperimentali e permette di simulare il comportamento dinamico del sistema idraulico di attuazione al fine di valutare a priori l'effetto di modifiche strutturali o di verificare nuove strategie di controllo.


2003 - Celle di carico ad estensimetri elettrici: i vantaggi di una soluzione digitale [Articolo su rivista]
Zanasi, Roberto; L., Diacci
abstract

Le celle di carico ad estensimetri elettrici sono trasduttori di forza estremamente diffusi in quanto per effetto delle molteplici geometrie costruttive realizzabili consentono di coprire un campo estremamente vasto di applicazioni. Sono oggi disponibili in versione analogica (le più diffuse) od in versione con tecnologia digitale. I principi e le considerazioni di base sono tuttavia le stesse.


2003 - Control Structures and Physical Requirements for Steer-By-Wire Systems [Relazione in Atti di Convegno]
Bertacchini, Alessandro; Morselli, Riccardo; Zanasi, Roberto; Pavan, Paolo; Bertoli, A.
abstract

Starting from the dynamic model of a conventional steering system, this paper proposes some hardware-independent control structures for the implementation of a steer-by-wire system for ground vehicles. Moreover the proposed approach allows the definition of the physiscal requirements on the real implementation and it can be used as a desgin tool fore the evaluation of the dynamic behaviour of al the steer-by-wire mechatronic devices.


2003 - Discrete minimum time tracking problem for a chain of three integrators with bounded input [Articolo su rivista]
Zanasi, Roberto; Morselli, Riccardo
abstract

Based on the theoretical results from optimal control theory and sliding mode control, this paper proposes a discrete time nonlinear control law that guarantees the minimum time global stabilization of a chain of three integrators with bounded control input. Moreover, the proposed control law allows the minimum time trajectory tracking for a wide class of reference signals (such as step, ramp, saw tooth, etc.) and it can be used as nonlinear /lter for the trajectories generation.


2003 - Energetic Approach for Steer-by-Wire in Off-highway Vehicles [Relazione in Atti di Convegno]
Morselli, Riccardo; Bertacchini, Alessandro; Reggiani, W.; Pavan, Paolo; Zanasi, Roberto
abstract

Starting from an energetic model of a traditional steering system, this paper proposes three different kinds of architecture for the implementation of a steer-by-wire system on off-highway vehicles. The force feedback and the rack hydraulic control cannot be ideal systems and this affects the overall vehicle dynamics, moreover the effects on the vehicle behavior depends on the chosen architecture. The hardware independent approach proposed in the paper drives the definition of the control requirements on the steering wheel control and on the rack control subsystems and it allows to appreciate the effects of the architecture on the implementation of a steer-by-wire system.


2003 - Smooth profile generation for a tile printing machine [Articolo su rivista]
C., Guarino Lo Bianco; Zanasi, Roberto
abstract

In this paper a digital filter is proposed for the generation of smooth set points for motion control systems. The proposed nonlinear filter produces profiles with bounded velocity and acceleration starting from rough reference signals (steps and ramps). An actual implementation of the filter for a tile printing machine is presented and experimental results are reported.


2003 - Testing Steer-by-Wire Controllers for Off-Highway Vehciles by Hardware-in-the-Loop Experiments [Capitolo/Saggio]
Bertacchini, Alessandro; Morselli, Riccardo; Pavan, Paolo; Zanasi, Roberto
abstract

The control laws and the hardware architecture for the implementation of a steer-by-wire system for off-highway vehicles are proposed. This paper describes how the hardware-independent control laws for the steer-by-wire actuators have been obtained, it explains the motivations for the choice of the force feedback actuator and of the steering rod electro-hydraulic actuator and finally it presents some hardware-in-the-loop simulation results that test the electro-hydraulic rod actuator and the electronic control unit dedicated to the steering rod


2003 - Testing Steer-by-Wire Controllers for Off-Highway Vehicles by Hardware-in-the-Loop Experiments [Relazione in Atti di Convegno]
Bertacchini, Alessandro; Morselli, Riccardo; Pavan, Paolo; Zanasi, Roberto
abstract

The control laws and the hardware architecture for the implementation of a steer-by-wire system for off-highway vehicles are proposed. This paper describes how the hardware-independent control laws for the steer-by-wire actuators have been obtained, it explains the motivations for the choice of the force feedback actuator and of the steering rod electro-hydraulic actuator and finally it presents some hardware-in-the-loop simulation results that test the electro-hydraulic rod actuator and the electronic control unit dedicated to the steering rod.


2001 - Output regulation of nonlinear systems by sliding mode [Articolo su rivista]
Bonivento, Claudio; Marconi, Lorenzo; Zanasi, Roberto
abstract

This paper focuses on the design of an output feedback sliding mode regulator able to achieve the asymptotic tracking of a reference trajectory for nonlinear systems. It is assumed that the reference trajectory is generated by means of a neutrally stable unforced system (exosystem) whose state is known. The design methodology is based on the center manifold theory and on the equivalent control concept and can be applied to both minimum and nonminimum-phase systems.


2000 - Nonlinear filters for the generation of smooth trajectories [Articolo su rivista]
Zanasi, Roberto; C., Guarino Lo Bianco; Tonielli, Alberto
abstract

A nonlinear variable structure (VS) system is presented, suitable for smooth trajectory generation in motion control system. Joined to a rough reference trajectory generator (step, ramp, etc.) it provides smooth output signals according to user-selectable bounds on trajectory derivatives. The bounds on output derivatives can be changed during system operation without impairing system stability. Moreover, minimum time response with guaranteed no overshoot is ensured both in the continuous and discrete-time implementations. The main contribution of the paper lies in the discrete-time version of the trajectory generator. The performance of the proposed nonlinear filters is tested through simulation experiments. Simulation results concerning the use of the discrete filter in a position tracking control system are also presented.


1998 - Discrete Variable Structure Integral Controllers [Articolo su rivista]
Bonivento, Claudio; M., Sandri; Zanasi, Roberto
abstract

The subject of this paper is the analysis and the design of a class of robust discrete-time Variable-Structure controllers of integral type. We refer to the Discontinuous Integral Control (DIC) technique, already developed by the authors for the time-continuous case, where a nonlinear integral action is used for estimating the external disturbance and keeping small the discontinuous term in the control law and the subsequent chattering effect. A discretised version of the DIC algorithm, which is properly modified in order to take into account the time-derivative information on the controlled variable, is introduced and discussed. The so-obtained discrete-time controller shows to be very effective in reducing the chattering when the system parameters are known. Moreover, to cope with a specific case of unknown parameters, a new adaptive control structure is proposed and analysed. The local asymptotic stability of the resulting closed-loop system is proved in the case of constant external disturbances. Finally, simulation results on the velocity control of a DC motor end the paper.


1997 - Magnetic properties of C-60 calculated by continuous transformation of the origin of the current density [Articolo su rivista]
Zanasi, Roberto; Lazzeretti, Paolo; Fowler, P. W.
abstract

The strongly diamagnetic character of an isolated molecule of C-60, predicted by several theoretical treatments, is confirmed by a gauge-origin-independent calculation, performed within the CTOCD method at the Hartree-Fock level of approximation and using a large properties-oriented basis set.


1995 - Ab initio and experimental study of NMR coupling constants in bicyclo [1.1.1]pentane [Articolo su rivista]
Lazzeretti, Paolo; M., Malagoli; Zanasi, Roberto; Ew, Della; Ij, Lochert; Cg, Giribet; MC RUIZ DE, Azua; Rh, Contreras
abstract

The different dependences of NMR spin-spin coupling constants of a medium-sized molecule on the quality of the ground-state wavefunction is studied using three different basis sets of increasing size, namely, 6-31G, 6-31G* and 6-31G**. Calculations of the Fermi contact terms were also carried out using partially uncontracted s and p atomic orbitals with the same exponents as those of the 6-31G basis set. Bicyclo[1.1.1]pentane was chosen as a model compound; it was synthesized for the measurement of several couplings as part of this work in order to compare theoretical results with experimental values. The through-space transmission of couplings via the interaction of rear lobes of orbitals inside the bicyclic cage were studied with the IPPP approach using the above basis sets.


1995 - Coupled Hartree-Fock calculations of origin-independent magnetic properties of benzene molecule [Articolo su rivista]
Lazzeretti, Paolo; M., Malagoli; Zanasi, Roberto
abstract

Conventional coupled Hartree–Fock approach and two computational methods based on continuous transformation of origin for the electronic current density induced by a magnetic field have been employed to calculate magnetic susceptibilities and nuclear magnetic shieldings of carbon and hydrogen in benzene. Near Hartree–Fock estimates have been obtained by using a basis set of 492 gaugeless contracted Gaussians containing ad hoc polarization functions. Theoretical magnetic susceptibility and nuclear shieldings evaluated in the present work via pointwise coordinate transformation are independent of the origin of the reference system. A series of sum rules for gauge independence of computed results and charge-current conservation has been tested to document the high accuracy of the calculation of magnetic properties.


1995 - Molecular magnetic properties within continuous transformations of origin of the current density [Articolo su rivista]
Zanasi, Roberto; Lazzeretti, Paolo; M., Malagoli; F., Piccinini
abstract

A new method for the calculation of molecular magnetic susceptibility and nuclear magnetic shielding is presented. It is based on continuous transformations of origin of the current density which make the transverse part of the paramagnetic current vanish. For any molecule all the components of the nuclear magnetic shielding tensor provided by the new method are independent on the origin of the gauge, whereas the components of the magnetizability tensor are translationally invariant only for center-symmetric molecules (they, in general, show a linear dependence on the shift of origin). This method, termed CTOCD-PZ, has been implemented for the theoretical determination of molecular magnetic properties via numerical integration techniques and, from preliminar results obtained for methane and carbon dioxide molecules, reveals reliable.


1994 - A Cascade Structure For Robust Control Design [Articolo su rivista]
Bonivento, Claudio; A., Nersisian; Tonielli, Alberto; Zanasi, Roberto
abstract

In the context of robust control theory and applications, the well-known Variable Structure approach and the so-called Binary Control approach, offer both interesting properties and disadvantages. In this note, the idea of combining the two techniques in order to define a cascade structure exploiting the desirable features of both approaches is discussed, and its natural applicability to the control of a nonlinear electrical actuator is shown by a simulation case.


1994 - ELECTRONIC CURRENT-DENSITY INDUCED BY NUCLEAR MAGNETIC DIPOLES [Articolo su rivista]
Lazzeretti, Paolo; Malagoli, M; Zanasi, Roberto
abstract

Magnetic point-group symmetries of high order in molecules can be described via the electronic current density vector field induced by a set of ideal magnetic dipoles properly placed in space. The expression for the diamagnetic Larmor-type current density induced in the electrons of a molecule by intrinsic nuclear magnetic dipole moments can be obtained via classical electrodynamics, but quantum mechanics is necessary to account for other terms: the Ramsey relations for paramagnetic spin-orbit, spin-dipolar, Fermi contact, and cross Fermi contact/spin-dipolar contributions to (indirect) spin-spin nuclear magnetic coupling can be rewritten in terms of second-rank current density tensors. Maps of current densities induced by two nuclear dipoles could be used to visualize the electron coupled interaction between two nuclei and to rationalize the coupling mechanism.


1994 - THEORETICAL-STUDY OF THE MAGNETIC-PROPERTIES OF A METHANE MOLECULE IN A NONUNIFORM MAGNETIC-FIELD [Articolo su rivista]
CAPUTO, MC; FERRARO, MB; LAZZERETTI, Paolo; MALAGOLI, M; ZANASI, Roberto
abstract

Contributions to magnetic susceptibility and magnetic shielding of the nuclei, arising from electronic magnetic-quadrupole moments interacting with a magnetic field with a spatially uniform gradient, have been determined for a methane molecule, by a large-basis-set calculations within the random-phase approximation. The Hartree-Fock limit of accuracy has been achieved and the quality of the calculations has been confirmed via tests based on sum rules for the origin dependence of the response properties.


1994 - VICINAL PROTON-PROTON COUPLING-CONSTANTS .4. EFFECT OF INDIVIDUAL SUBSTITUENTS WITH 2ND ROW ALPHA-ATOMS [Articolo su rivista]
Sanfabian, J; Guilleme, J; Diez, E; Lazzeretti, Paolo; Malagoli, M; Zanasi, Roberto; Esteban, Al; Mora, F.
abstract

An assessment of the effect upon 3J(HH) of individual substituents with second row alpha-atoms has been carried out both theoretically, at ab initio and semi-empirical levels of approximation, and empirically, by parametrization of Karplus type equations. The Fermi-contact contributions calculated with a 6-31G** basis set to determine substituent effects DELTAJ(X) in monosubstituted ethanes CH3CH2X(X = CH3, NH2, OH and F), show a decay with the relative electronegativity of substituent DELTA(chi)x towards a constant value like that presented by the experimental data. Similar quadratic or exponential decays are calculated with the same basis set for the two largest parameters in the Karplus equation, i.e. for the angle independent term C0 and for the coefficient C2 of cos 2phi. By contrast, for the coefficient S2 of sin 2phi a proportional dependence on DELTA(chi)x is calculated. These calculated dependences upon DELTA(chi)x for C0, C2 and S2 have been confirmed by empirical parametrization of the corresponding Karplus type equations using an appropriate dataset of experimental 3J(HH) couplings.


1993 - A Modified Variable Structure Control Algorithm for Stabilization of Uncertain Dynamical Systems [Articolo su rivista]
A., Nersisian; Zanasi, Roberto
abstract

A modified VS feedback is suggested for robust stabilization of continuous-time dynamical systems in the presence of parametric and external time-varying disturbances. The main feature of the proposed algorithm is that it contains additional switching integral parts which track the unknown disturbances and make it possibleto achieve typical VSS robustness with arbitrarily small coefficients for the switching parts of the control signals.


1993 - Calculation of Dynamic Electric Dipole Polarizability, Nuclear Electric Shieldings, and their Cauchy Moments in Benzene [Articolo su rivista]
Lazzeretti, Paolo; Malagoli, M; Turci, L; Zanasi, Roberto
abstract

Theoretical methods based on the random-phase approximation have been applied to evaluate near Hartree-Fock dynamic electric polarizability and shielding tensors of carbon and hydrogen nuclei in the benzene molecule. Cauchy moments of the various properties have been determined. The results obtained in different gauges (dipole length, velocity, and acceleration) are reported.


1993 - CALCULATION OF INFRARED AND VIBRATIONAL CIRCULAR-DICHROISM INTENSITIES VIA NUCLEAR ELECTROMAGNETIC SHIELDINGS [Articolo su rivista]
Faglioni, Francesco; Lazzeretti, Paolo; Malagoli, M; Zanasi, Roberto; Prosperi, T.
abstract

Infrared and vibrational circular dichroism intensities have been evaluated theoretically for trans-(1S,2S)-dideuteriooxirane, trans-(1S,2S)-dideuteriocyclopropane, (S)-propylene oxide, and trans-(1R,2R)-dimethyl-cyclopropane molecules, via electric and electromagnetic nuclear shielding tensors determined by random-phase approximation within the framework of 6-31g, 6-31g**, 6-31gext, and 6-31gpol Gaussian basis sets. Differentiation of matrix elements is avoided by the procedure adopted in this work. By comparing the results provided by several numerical tests it is found that reliable force fields of Hartree-Fock quality can be obtained at the 6-31g** and 6-31gex level; 6-31gpol basis provides the most accurate polar and axial atomic tensors. The nuclear shieldings are to be calculated with great accuracy in order to achieve a good prediction of the intensity patterns, as they bias the overall quality of theoretical oscillator strengths and rotational strengths. Comparison with available experimental data and previous ab initio calculations demonstrates the practicality of the present method for small and medium size molecules. The Hartree-Fock accuracy of the theoretical estimates of vibrational intensities is also proven by analyzing constraints for translational and rotational invariance which should be exactly fulfilled in the limit of complete basis sets. These results document the competitivity of the nuclear shielding method with the analytic derivative procedure.


1993 - CALCULATION OF MOLECULAR MAGNETIC-PROPERTIES IN THE ISOELECTRONIC SERIES PH2-, PH3 AND PH4- [Articolo su rivista]
Caputo, Mc; Ferraro, Mb; Bochicchio, Rc; Lazzeretti, Paolo; Malagoli, M; Zanasi, Roberto
abstract

Ab initio coupled Hartree-Fock perturbation theory has been used to evaluate magnetic susceptibility and magnetic shielding tensors of P-31 and H-1 nuclei in PH2-, PH3 and PH4+. Good agreement between theoretical and experimental data and a satisfactory degree of origin independence of computed values has been found by adopting large polarized basis sets developed ad hoc for magnetic properties.


1993 - CALCULATION OF MOLECULAR MAGNETIC-PROPERTIES WITHIN THE LANDAU GAUGE IN HYDROGEN-FLUORIDE, AMMONIA, AND METHANE MOLECULES [Articolo su rivista]
Ferraro, Mb; Herr, Te; Lazzeretti, Paolo; Malagoli, M; Zanasi, Roberto
abstract

The magnetic susceptibility and the nuclear magnetic shielding tensors of HF, NH3, and CH4 molecules in the presence of a spatially uniform time-independent magnetic field have been calculated within the Landau gauge for the vector potential. The random-phase approximation has been used, adopting flexible Gaussian basis sets of large size. Magnetic susceptibilities are quite harder to evaluate accurately in the Landau gauge than in Coulomb gauge. Calculated nuclear magnetic shieldings are close to the Hartree-Fock limit. Sum rules for charge conservation and origin independence of magnetic susceptibility and nuclear magnetic shieldings are fairly well satisfied by basis sets of extended size.


1993 - Sliding Mode Using Discontinuous Control Algorithms of Integral Type [Articolo su rivista]
Zanasi, Roberto
abstract

This paper deals with the robust stabilization of continuous-time dynamical systems in the presence of parametric and external time-varying disturbances. Modified Variable Structure control algorithms with additional integral terms are considered here and analyzed. A comparison with a typical ``static'' VS algorithm is made. Static VS algorithms can reject completely the disturbance only if the amplitude of the switching term, in the control input, is larger than the amplitude of the disturbance itself. This paper shows how it is possible, by adding an integral term in the VS control algorithm, to reach and remain in the sliding mode if the amplitude of the switching term is smaller than the amplitude of the disturbance. Some simulations supporting the theoretical results are reported and discussed.


1992 - Calculation of molecular magnetic properties within the Landau gauge [Articolo su rivista]
MB, FERRARO; TE, HERR; LAZZERETTI, Paolo; M., MALAGOLI; ZANASI, Roberto
abstract

A theoretical procedure for calculating magnetic susceptibility and nuclear magnetic shieldings in molecules in the presence of a spatially uniform time-independent magnetic field, within the Landau gauge for the vector potential, is described. Sum rules for charge and current conservation and gauge invariance have been derived. A computational scheme based on the random-phase approximation has been used to calculate magnetic susceptibility and shielding tensors in the water molecule, adopting fairly flexible Gaussian basis sets of large size. The results show that very accurate molecular wave functions are needed to obtain paramagnetic contributions to the magnetic susceptibility of the same quality as those obtainable within the Coulomb gauge for the vector potential. The theoretical nuclear magnetic shielding tensors in the Landau gauge are characterized by the same quality as those in the Coulomb gauge.


1991 - Coupled Hartree-Fock calculations of magnetic properties of the benzene molecule: estimate of the Hartree-Fock limit for magnetic susceptibilities and nuclear shieldings [Articolo su rivista]
Lazzeretti, Paolo; M., Malagoli; Zanasi, Roberto
abstract

Five basis sets of gaussian functions have been developed to calculate magnetic properties of the benzene molecule within the framework of a coupled Hartree-Fock (CHF) approach exploiting the entire D6h symmetry. Separate contributions provided by k, sigma and pi-electrons have been evaluated in order to analyze the Pauling-London ring-current model. Our results are at variance with this classical model, as the contribution of k and sigma-electrons to the enhanced out-of-plane magnetic susceptibility is roughly 50% of the total value. In addition, k electrons provide a de-shielding of proton comparable with that of pi-electrons. The HF limits for electric dipole polarisability, magnetic susceptibility and magnetic shielding of hydrogen and carbon nuclei have been estimated.


1991 - Electromagnetic moments and fields induced by nuclear vibrational motion in molecules [Articolo su rivista]
Lazzeretti, Paolo; M., Malagoli; Zanasi, Roberto
abstract

A simple model Hamiltonian is analyzed within the framework of time-dependent perturbation theory to show how nuclear vibrations induce instantaneous electromagnetic moments in the electron cloud of a molecule. These moments can be rationalized in terms of nuclear electromagnetic shielding tensors. The vibrational motion of a nucleus also gives rise to induced electric and magnetic fields at the other nuclei. This effect is discussed introducing nuclear electric and magnetic coupling tensors, which are related to nuclear shieldings and other molecular properties. Nuclear electromagnetic couplings have been calculated for water, ammonia and methane molecules using the random-phase approximation.


1991 - Virial sum rules for nuclear electric shieldings and geometrical derivatives of dipole and quadrupole molecular moments [Articolo su rivista]
Lazzeretti, Paolo; M., Malagoli; Zanasi, Roberto
abstract

The virial theorem has been used to derive sum rules for dipole- and mixed-dipole-quadrupole nuclear electric shieldings and corresponding geometrical derivatives of dipole and quadrupole moments in a molecule. Test calculations have been carried out on a series of first- and second-row hydrides. The virial sum rules can be effective tools to prove the accuracy of theoretical nuclear shieldings and analytic geometrical derivatives. As the latter are related to ir intensities, the virial sum rules can give important indications on the reliability of theoretical predictions for this spectroscopical parameter.


1990 - AB INITIO CALCULATIONS OF ATOMIC POLAR AND AXIAL TENSORS FOR HF, H2O, NH3, AND CH4 [Articolo su rivista]
P. J., Stephens; K. J., Jalkanen; R. D., Amos; Lazzeretti, Paolo; Zanasi, Roberto
abstract

Atomic polar tensors, Ptp, and atomic axial tensors, M$, are calculated ab initio for HF, H20, NH3, and CH, at the SCFlevel of approximation. A variety of formalisms is used. Analytical derivative methods based on coupled Hartree-Fockperturbation theory are used to calculate length and momentum forms of Ptp, P&(b) and P&(r), and to calculate M$.The random-phase approximation is used to calculate length, momentum, and force forms of P&, P$(R), PiB(P), and P&(F),and angular momentum and torque forms of M&, M$f;) and M&(K). Pts and M2B tensors are calculated using a widerange of basis sets, both "conventional" and "polarized in type. tensors are calculated using different gauges and ata variety of origins. The results enable the relative accuracies of calculations using alternative formalisms, basis sets, andgauges to be assessed. Exact Pke and M$ tensors satisfy a variety of sum rules. The degree to which such sum rules aresatisfied is also used to assess the relative accuracies of alternative procedures for the calculation of Pks and M$ tensors.Our results provide a basis for the choice of optimum calculational procedures in predicting Pts and M2B tensors of moleculesand, thence, their vibrational absorption and circular dichroism spectra.