Control in Power Electronics : selected problems

M. R. Hestenes London: John Wiley. 1967. Pp. xii + 405. Price £5. Professor Hestenes has been a leading researcher on optimization theory since the early 1930's and this book contains much of his original work in the field. The first three chapters are of an introductory nature and contain the classical, calculus of variations, approach of first and second variations.

Calculus of Variations and Optimal Control Theory

The Mathematical Theory of Optimal Control. By L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko. Pp. vii, 340. 93s. 1964. (Pergamon.)

Switch observability for switched linear systems

A direct numerical method for optimal feedback control design of general nonlinear systems is presented in this chapter. The problem is generally infinite dimensional. In order to convert it to a finite dimensional optimization problem, a collocation type method is proposed. The collocation approach is based on approximating the control input function as a series of given base functions with unknown coefficients. Then, the optimal control problem is converted to the problem of finding a finite set of coefficients. To solve the resulting optimization problem, a new nature-inspired optimization paradigm known as Moth Flame Optimizer (MFO) is used. Validation and evaluating of accuracy of the method are performed via implementing it on some well known benchmark problems. Investigations presented in this chapter reveals the efficiency of the method and its benefits with respect to other numerical approaches. The chapter also consideres an in-depth literratur review and analysis of MFO.

Moth-Flame Optimization Algorithm: Theory, Literature Review, and Application in Optimal Nonlinear Feedback Control Design

The synthesis of time optimal feedback control of a single input continuous time linear time invariant (LTI) system is considered. If the control input u(t) is constrained to obey |u(t)| ≤ 1, then it is known that the optimal input switches between the extreme values ±1, according to some “switching surfaces” in the state space. It is shown that for systems with non-zero, distinct and rational eigenvalues, these switching surfaces are semi-algebraic sets and a method to compute them using Groebner basis, is proposed. In the process the null-controllable region for such systems is characterized and computed. Numerical simulations illustrate the proposed computational methods.

Computation of Time Optimal Feedback Control Using Groebner Basis

Sinusoidal LC filters are generally placed between the voltage source inverter (VSI) and squirrel cage induction motor (SQIM) to reduce the distortion in the output voltage of the VSI, voltage surges at the motor-terminals, core losses in the SQIM, bearing-current, and electromagnetic interferences. Rotor-flux oriented control (RFOC) of the SQIM is widely used in adjustable speed drives. However, the introduction of filter network may make the operating point of RFOC of SQIM drive unstable and may create sustained resonance frequency oscillations in the stator-current, stator-voltage of SQIM. This paper proposes a simple inverter-current-based active damping (AD) technique, which damps out the resonance frequency oscillation by emulating the virtual resistance connected in series with the filter inductor in its control structure. It also effectively stabilizes the unstable operating point of the closed-loop system without changing the parameters of the controllers used in RFOC. The idea of the proposed AD technique has been illustrated with mathematical expressions and justified through stability analysis. The instability of operating point and the impact of the AD technique are experimentally demonstrated on RFOC of VSI-fed SQIM with filters at different test conditions.

Deepak U. Patil

Papers

Computation of Time Optimal Feedback Control Using Groebner Basis

Stabilization of Rotor Flux-Oriented Control of Induction Motor With Filter by Active Damping

Indiscernible topological variations in DAE networks

Computation of feedback control for time optimal state transfer using Groebner basis

Re-entry trajectory tracking of reusable launch vehicle using artificial delay based robust guidance law