Bojan Grcar

Nonlinear control of synchronous servo drive

The complete control design for a permanent magnet synchronous (PMAC) motor, derived from the input-output linearization, is presented in the paper. The motor model, written in the rotors d-q coordinates, is nonlinear with respect to the state variables and linear in the control. The input-output linearization makes it possible to write the motors model in Brunovski decoupled canonical form which makes the synthesis of linear controllers possible. The proposed control structure allows perfect tracking of smooth references in the case of nominal parameters. In relation to the bounded parameter perturbations, the robustness of the feedback system is improved by introducing an additional compensation signal which assures the stability of the perturbed system in Lyapunovs sense. The influence of parameter variations that prevents exact compensation of the control plant nonlinearities was analyzed for the PMAC motor. A description of the laboratory setup is given, and the experimental results of the proposed PMAC servo drive control are presented.

Calculation of the linear induction motor model parameters using finite elements

The paper presents the use of the finite element (FE) method for determining the parameters of a two-axis model of a three-phase linear induction motor. The model parameters are obtained from the FE field solutions. The saturation of the motor is taken into account in calculation of the flux distribution by using a static nonlinear vector potential solution. The linear time harmonic vector potential field solution is used for the determination of inductances. All inductances are determined at the nominal value of the magnetizing current. The parameters of the model obtained by the described identification procedure are compared with the parameters calculated in the conventional way and the agreement of results is quite good.

IM Torque Control Schemes Based on Stator Current Vector

This paper proposes an induction machine torque control derived from the model in the stator current vector reference frame. The required torque is produced by simultaneously manipulating the magnitude and the rotation speed of the stator current vector, thus forcing the rotor flux linkage vector to change implicitly in such a way that overall stability is preserved. Additional control features include maximal torque-per-ampere ratio in steady state and almost perfect command tracking even if the machine is magnetically saturated. The control adopts a cascaded structure and is based on a partial dynamic inversion of the reduced model that assures existence and uniqueness of the inverse mapping between the required torque, the rotor flux linkage vector, and the stator current vector. Singularity at zero rotor flux linkage represents no restriction for the control performance in the admissible machine operating range. The implementation of the proposed control requires the estimation of the torque-producing rotor flux component and cascaded stator current controllers. Experimental results confirm the key expectations and show the potential and benefits of the proposed control schemes.

Non-Holonomy in Induction Machine Torque Control

In this brief, induction machine (IM) torque control is studied as an example of a 3-D non-holonomic integrator including drift terms. By expanding Brocketts controller derived for the driftless systems, a control structure is proposed that provides simultaneous modulation of both the amplitude and the frequency of the sinusoidal stator current vector. Although not explicitly controlled or programmed, the rotor flux linkage vector is implicitly forced to track natural periodic orbits satisfying non-holonomic constraints of the IM. The proposed control assures high dynamics in the torque response, maximal torque per amp ratio during transients and in steady-state and global asymptotic stability. The overall IM control scheme includes cascaded high-gain current controllers based on measured electrical and mechanical quantities together with rotor flux linkage vector estimator. Simulation and experimental results illustrate the main characteristics of the proposed control.

Pulsating torque reduction for permanent magnet AC motors

Control methods for the pulsation of torque reduction for the surface-mounted permanent magnet motors are discussed. The pulsation torque is a consequence of the non-sinusoidal flux distribution and due to interaction of the rotors permanent magnets with the changing stator reluctance. The proposed control method is an estimator based. To ensure parameter convergence the Lyapunov direct method is used in the estimator design for the flux Fourier coefficients. A novel nonlinear torque controller based on the flux/torque estimate is introduced to reduce the influence of the flux harmonics. The influence of the cogging torque is considerably reduced at lower motor speed using the internal model principle and adaptive feedforward compensation technique. An overall control scheme and experimental results are also presented.

Simple adaptive control for stability improvement

Treats the simple adaptive control for stability improvement of a synchronous generator connected to an infinite bus. Presented are: the influence of the operating point on the eigenvalues of the synchronous generator simplified linear model, the simple adaptive power system stabilizer derived from the model reference adaptive control based on command generator tracker theory, the effects of changing the design parameters and the bursting phenomenon. The control system design was carried out for the simplified linear model of a synchronous generator but for the evaluation of the control system performance the full order non-linear model of the synchronous generator was used. Simulation and experimental results show the applicability of the presented approach.

A contribution to the control of the non-holonomic integrator including drift

In this paper a three-dimensional non-holonomic integrator (NI) with drift terms is considered. For this type of plant, the question how to obtain desired piecewise constant output functions with minimum norm control inputs is explored. It is shown that this can be achieved by a nonlinear controller that provides simultaneous modulation of both the amplitude and the frequency of the harmonic input vector. The internal states are implicitly forced to follow natural periodic orbits satisfying the non-holonomic constraints of the plant. Global asymptotic stability and high dynamics in the output response are achieved. The problem of singularity at zero initial state is solved by a time optimal control scheme for the internal states. By combining the nonlinear controller and the time-optimal controller using an appropriate switching strategy, a powerful control concept can be established. The torque control of an induction machine is considered as an illustrative example for the application of the control scheme. Experimental results of the closed loop feedback control system are presented.

Adaptive control for damping of power system oscillations

The paper treats the simple adaptive control for stability improvement of a synchronous generator connected to an infinite bus. Presented are: the influence of the operating point on the eigenvalues of the synchronous generator simplified linear model, the simple adaptive power system stabilizer derived from the model reference adaptive control based on command generator tracker theory, the effects of changing the design parameters and the bursting phenomenon. The control system design was carried out for the simplified linear model of a synchronous generator but for the evaluation of the control system performance the full order non-linear model of the synchronous generator was used. Simulation and experimental results show the applicability of the presented approach.

Discrete boundary layer current control for VSI-IM drive

This paper discusses the time-discrete switched variable structure field oriented current control of an IM (induction motor) drive. VSI (voltage source inverter) is directly controlled, exploiting boundary layers and quantized field rotation velocity for addressing the switching table. In current control design, the fact that the calculation of the stator voltage vectors from the d-q control components does not have a unique solution is exploited. This is considered as design freedom, which is further extended by introduction of preassigned-order switching according to the time scale separation of magnetization and the generation of torque currents. Boundary layers with different reaching dynamics introduce motor stator zero voltage, which is selected by finite automaton from nearest VSI state.

Induction Machine Torque Control with Self-Tuning Capabilities

In any torque control concept for induction machines the capability to produce a desired torque with the minimum stator current (maximum torque per ampere ratio) becomes a demanding requirement. In this contribution it is shown how a recently published torque control strategy which provides the maximum torque per ampere ratio feature can be augmented by some self-tuning capabilities. Since the behaviour of the proposed controller is mainly influenced by the rotor time constant which is subjected to variations due to thermal influences on the rotor resistance a method for an on-line tuning of this parameter is developed. It is based on the extremum seeking approach, which is well known from adaptive control. The performance of the control concept is demonstrated by experimental results.