Gerardo Espinosa

Torque regulation of induction motors

Abstract A controller design methodology to solve an output tracking problem for a class of systems described by its Euler-Lagrange equations with less control actions than degrees of freedom was recently presented by Ortega and Espinosa. The procedure is based on the idea of “shaping” the total energy of the closed-loop system with the nice feature that it achieves the tracking objective without the need of cancelling dynamics but by associating a natural reference (“steady state”) behaviour for all state variables. In this paper we use the procedure to solve the problem of torque regulation of a nonlinear induction motor model which includes both electrical and mechanical dynamics. We derive a nonlinear state observer plus state feedback control that insures exponential stability provided the desired torque does not exceed a given value. The latter condition can be removed if the motor full state is measurable. An adaptive version of the scheme that does not require exact knowledge of the rotor resistance or load torque is also shown to be asymptotically convergent. Three key features of the proposed scheme are: first, it attains the field orientation objective of the highly successful “vector control” strategies. Second, using the energy balance equation of the induction motor, identifies the nonlinear terms that represent “workless forces” to avoid (intrinsically nonrobust) exact cancellation of model nonlinearities. Third, the control law calculation is extremely simple and globally defined, thus the strategy is applicable for all motor operation regimes including start-up. Some simulation results illustrate the controller performance.

State observers are unnecessary for induction motor control

Abstract Induction motors constitute a theoretically interesting and practically important class of nonlinear systems, which are evolving into a benchmark example for nonlinear control. They are described by a fifth-order nonlinear differential equation with two inputs, and only three state variables available for measurement. A lot of research in the field has been devoted to the design of observers which, combined with a suitable control strategy, would yield stable behaviour. Our contribution in this paper is to show that the control objective can be achieved without reconstruction of the motor state. Specifically, we present a globally stable nonlinear dynamic output feedback controller for torque tracking of induction motors which does not rely on state reconstruction ideas. Another important feature of our sheme is that the control law is globally defined, even in startup. This stems from the fact that we do not aim at linearizing the system dynamics, but instead exploit the energy dissipation properties of the motor model. For the sake of illustration we present the result for a model described in the stator frame ( ab model), but the theory applies as well to models expressed in a rotating frame ( dq model). We also show how, as a particular case of torque tracking, we can solve the rotor speed tracking problem.

A controller design methodology for systems with physical structures: application to induction motors

The authors propose an extension of the controller design methodology used in robot motion control to solve an output tracking problem for a class of systems described by its Euler-Lagrange equations with fewer control actions than degrees of freedom. It is shown that the problem can solve a set of algebro-differential equations that define the controller dynamics and the attainable trajectories. To illustrate the procedure the authors solve the induction motor torque regulation problem.<<ETX>>

Analysis and Implementation of a Master-Slave Control based on a Passivity Approach for Parallel Inverters Operation

This paper presents the design and implementation of an instantaneous current sharing control for a master-slave strategy in parallel inverter operation. The control systems of the master and the slave inverters are based on a passivity approach and they have a good performance achieving that the current is divided between the two inverters, even in the presence of non-linear loads. Besides, the system presents a fast transient response and guarantee in its output a continue-sinusoidal waveform. The performance of the passivity based control for parallel operation is presented by means of simulation and experimental results, in order to verify the viability of the propose approach and the easy implementation

Advantages of the passivity based control in dynamic voltage restorers for power quality improvement

Abstract A better and feasible control strategy for dynamic voltage restorers (DVR) is presented in this paper: the passivity based control (PBC) allows a better compensation performance under transient and steady state operating conditions, and provides tracking with zero error of any reference for linear and nonlinear loads. The closed-loop source-DVR-PBC-load system is asymptotically stable at all operating points, with practically very slight constraints; its transient response is faster than with classical controllers, and does not present overshoots. These characteristics do not depend on source voltage disturbances, the kind of load, or parameter variations. The PBC uses less digital operations than the PI, and does not require dq transformations.

Adaptive Stabilization of Non-Linearizable Systems under a Matching Assumption

In this paper we study the problem of adaptive stabilization of linearly parametrized nonlinear systems that satisfy a matching assumption. We show that, under these conditions, adaptive regulation is possible for a class of non-feedback linearizable systems. This class consists of systems for which there exists a parametrized state feedback control such that the closed loop system defines a strictly passive map. Furthermore, we provide a constructive procedure to calculate the required control law, which consists of the solution of an inverse optimal nonlinear control problem.

Mechanical Test to Bovine Bone

The Young modulus in compression of fresh and inorganic bovine bone was obtained, in the longitudinal and transversal directions of the trabeculae, using an Instron universal machine. It was found that the elastic properties of the bone depend strongly on the orientation of the force regarding the direction of the trabeculae, specially for fresh bone.

Fast adaptive stabilization of first order plants with unknown sign of the high frequency gain

The problem of adaptively stabilizing a first order plant in the absence of information on the sign of the high frequency gain is addressed. It is shown that a time varying output feedback controller with a ‘standard’ parameter update law ensures simultaneous local stabilization of plants with positive and negative high frequency gains provided adaptation is sufficiently fast, i.e. high adaptation gain. The estimator does not rely on switching functions or parameter search procedures. Thus, from the practical viewpoint, it seems more attractive than the ‘Nussbaum gain’-based schemes.