Robust tracking and disturbance rejection design for time delay systems

The paper is aimed to the design of a generalized class of continuous controllers for time delay systems. The proposed controllers ensure internal stability and simultaneous reference tracking and disturbance rejection. Several approximations for first order system with time delay were used. All of them can be covered by a second order transfer function. Then explicit formulas were derived for SISO systems with a feedback as well as with a feedback-feedforward structure of the controlled system. The proposed control synthesis is based on general solutions of Diophantine equations in the ring of proper and Hurwitz stable rational functions R_PS and the Youla-Kučera parametrization of controllers is utilized. The conditions for asymptotic tracking and disturbance rejection are obtained through the divisibility conditions in the ring R_PS. Robustness of proposed algorithms can be studied through the infinity norms (H_∞) and through the sensitivity functions of controlled systems. A scalar parameter m>0 is introduced for tuning and influencing of proposed controllers. A Matlab + Simulink program system for automatic design and simulation has been developed. The program system is suitable for a wide engineering applications without a deep insight into the control theory.