Gerardo Espinosa-Pérez

Passivity-based control of a class of Blondel-Park transformable electric machines

Concerns the extension to the general rotating electric machine model of the passivity-based controller method for induction motors. The motors passivity properties are used at 2 levels. First, we prove that the motor model can be decomposed as the feedback interconnection of two passive subsystems (essentially, the electrical and mechanical dynamics). Then, we design a torque-tracking controller that preserves passivity for the electrical subsystem and leaves the mechanical part as a passive disturbance. This leads to the cascaded controller structure which is typically analyzed involving time-scale separation. Our aim is to characterize a class of machines for which such a passivity-based controller solves the output feedback torque-tracking problem. The class consists of machines whose nonactuated dynamics are damped and whose dynamics can be decoupled. This requires that the air-gap magnetomotive force must be suitably approximated by the first harmonic in its Fourier expansion. These conditions have a clear physical interpretation in terms of the couplings between its dynamics and are satisfied by many machines. The passivity-based controller presented reduces to the well-known indirect vector controller for current-fed induction machines. Our developments constitute an extension to voltage-fed machines of this de facto standard in industrial applications.

Global observability analysis of sensorless induction motors

The current problems to successfully apply sensorless controllers for induction motors are the existence of operation regimes for which the performance is remarkably deteriorated, due to the difficulties in estimating correctly motor speed and flux, and the lack of a theoretical explanation for this kind of behavior. In this paper a global observability analysis for these machines is carried out. It is first shown that all indistinguishable trajectories of the system, i.e. pairs of state trajectories with the same input/output behavior, can be described by a differential equation on a manifold, named here the indistinguishable dynamics. Studying the stability properties of this latter system it can be shown that the induction motor is not completely observable nor detectable in a local or in a global sense, and for every set of parameters. This implies that it is impossible to construct a state observer for the motor that converges for every trajectory of the system. Moreover, the indistinguishable dynamics provides a systematic method to study, understand and explain particular operation regimes, and this is illustrated by some case studies of practical relevant operating conditions.

A stable design of PI control for DC-DC converters with an RHS zero

The stability of boost and buck-boost DC-DC power converters under proportional plus integral (PI) control is discussed in this paper. A novel PI control configuration is proposed, which reveals the effect that the right-hand-side zero has on PI control stability. Tuning rules in terms of the converter parameters are derived and illustrated via numerical and experimental simulations.

An output feedback globally stable controller for induction motors

We present a globally stable nonlinear dynamic output feedback controller for torque tracking and flux regulation of induction motors. The control law is globally defined, requires only measurement of stator variables and rotor speed, and does not rely on cancellation of the systems nonlinearities. Our work extends the result of the paper by Ortega et al.(1993), where the torque tracking problem was solved for a model and the variables are expressed in a frame rotating at an arbitrary angular frequency (dq model). First, we obviate the need to transfer the dq control signals of the paper by Ortega et al., to the physical input variables in the stator frame, hence providing a directly implementable control law. Second, besides the torque tracking objective, we include the practically important rotor flux regulation task. Third, by choosing a more suitable representation of the motor model, we simplify the controller structure and provide a better understanding of its derivation and behavior. >

Tuning rules for the PI gains of field-oriented controllers of induction motors

The authors have previously shown that field-oriented controllers for induction motors preserve stability under a wide range of variations of the motor and controller parameters. However, as is well known, the transient performance critically depends on the tuning of the gains of the proportional-integral (PI) velocity loop, a task which is rendered difficult because of the high uncertainty on the rotor resistance. The problem we address in this paper is how to develop an offline procedure to choose these gains. The main contribution of our work is a very simple frequency-domain test that, for each setting of the PI gains, evaluates the maximum range of the relative rotor resistance estimate for which global stability is guaranteed. In this way, we provide a quantitative estimate of the performance of the PI controller. The stability result may also be used in a dual manner, fixing now the range of the rotor resistance, and estimating an admissible interval for the PI gains that preserves global stability. Instrumental for our study is the exploitation of an energy dissipation (strict passivity) property of the system.

Passivity-based control of switched reluctance motors with nonlinear magnetic circuits

In this paper, the control of switched reluctance motors is approached from a passivity-based control perspective. The proposed controller solves the torque/speed/position tracking problem by exploiting the passivity properties of the machine. The methodology design considers the feedback decomposition of the motor model into one electrical and one mechanical passive systems and is divided into the following three steps: control of the electrical subsystem to achieve current tracking, definition of the desired current behavior to assure torque tracking, and design of a speed/position control loop. The main characteristics of the presented result are: it belongs to the class of control schemes that take into account the saturation effects present in stator windings and, regarding torque generation, it considers the use of sharing functions. The contribution of the paper is threefold: The controller design is developed using energy-dissipation ideas, the mathematical formalization of the current engineering practice of controlling this kind of machines with a cascade approach, and an extension to previously reported passivity-based controllers for electric machines in the sense that Blondel-Park transformability properties are not required.

Stability of current-mode control for DC-DC power converters

Abstract DC–DC power converters are switched devices whose averaged dynamics are described by a bilinear second-order system with saturated input. In some cases (e.g., boost and buck–boost converters), the input output dynamics can be of nonminimum-phase nature. Current-mode control is the standard strategy for output voltage regulation in high dynamic performance industrial DC–DC power converters. It is basically composed by a saturated linear state feedback (inductor current and output voltage) plus an output voltage integral feedback to remove steady-state offset. Despite its widespread usage, there is a lack of rigorous results to back up its stabilization capability and to systematize its design. In this paper, we prove that current-mode control yields semiglobal stability with asymptotic regulation of the output voltage.

Observer-based control of a synchronous generator: a Hamiltonian approach

Abstract In this paper, we propose a controller design for a class of nonlinear systems using Passive and Hamiltonian design techniques. The result is applied to a synchronous generator in order to synthesize an excitation control, which allows stabilization of the generator at its equilibrium position. The main characteristics of this proposition are that neither the equilibrium point of the system must be known nor the state of the generator be available for measurement. The performance of the proposed controller is validated through digital simulations.

Simultaneous interconnection and damping assignment passivity-based control: the induction machine case study

We argue in this article that the standard two-stage procedure used in interconnection and damping assignment passivity-based control (IDA–PBC)–consisting of splitting the control action into the sum of energy-shaping and damping injection terms–is not without loss of generality, and effectively reduces the set of systems that can be stabilised with IDA–PBC. To overcome this problem we carry out, simultaneously, both stages and refer to this variation of the method as SIDA–PBC. To illustrate the application of SIDA–PBC we consider the practically important example given by the control problem of the induction machine. First, we show that torque and rotor flux regulation of the induction motor cannot be solved with two stage IDA–PBC. It is, however, solvable with SIDA–PBC. Second, we prove that with SIDA–PBC we can shape the total energy of the full (electrical and mechanical) dynamics of a doubly-fed induction generator used in power flow regulation tasks, while with two stage IDA–PBC only the electrical energy can be shaped. Simulation results of these examples are presented to illustrate the performance improvement obtained with SIDA–PBC.

Passivity-based control of the general rotating electrical machine

In this paper we are interested in the output feedback tracking control problem of a general rotating electrical machine model. Our main contribution is the characterization of a class of machines for which a passivity-based controller solves the problem. Roughly speaking, the class consists of machines whose nonactuated dynamics is suitably damped and whose electrical and mechanical dynamics can be decomposed into a cascade systems decomposition (Blondel-Parks transformable), giving the possibility to explicitly characterize a bounded behaviour inside the zero error space. These conditions have a clear physical interpretation in terms of the couplings between the electrical, magnetical and mechanical dynamics of the machine. Examples of machines belonging to this class are the classical Parks machine, the brushless DC motor, and synchronous motors.<<ETX>>