Design of Optimal PID Controllers for PWM Feedback Systems With Bilinear Plants

This paper considers the optimal proportional-integral-derivative (PID) controller design for a class of pulsewidth-modulation (PWM) feedback systems with bilinear plants by using the orthogonal-functions approach (OFA). Based on the OFA, an algorithm only involving algebraic computation is derived in this paper for analyzing the PWM feedback systems with bilinear plants, and thus, the optimal PID controller design problem for a class of PWM feedback systems with bilinear plants is transformed into a static-parameters optimization problem represented by algebraic equations; this greatly simplifies the optimal PID control design problem. Then, for the static optimization problem, the hybrid Taguchi-genetic algorithm (HTGA) is employed to find both the optimal parameters of the PID controllers and the optimal PWM patterns for the PWM feedback systems with bilinear plants under the criterion of minimizing an integral quadratic performance index. The proposed new method, which integrates the OFA and the HTGA, is nondifferential, nonintegral, straightforward, and well-adapted to computer implementation. The computational complexity can, therefore, be reduced remarkably. An illustrative example for the electrohydraulic servo PWM feedback systems is given to show that the proposed method is an effective approach.