PID control of unstable time-delay systems: tuning and robustness

摘要

The paper is aimed to the design of a general class fo PID like linear controllers for first order systems with time delays. Several approximations for time delay were used. All of them can be covered by a second order transfer function. Then explicit PID formulas were derived for SISO systems with a feedback as well as with a feedback-feedforward structure of the controlled system. The approach si especially suitable for integrator and unstable first order time-delay systems. The proposed control synthesis is based on general solutions of disophantine equations in the ring of proper and Hurwitz stable rational functions R_(PH) and the Youla-Kucera parametrization fo controllers is utilized. The conditions for asymptotic tracking are obtained through the divisibility conditions in the ring R_(PH). The proposed methodology covers stable and unstable plants with time delays. Moreover, a scalar tuning parameter which influences properties fo the closed-loop system has been introduced. Robustness of proposed algorithms can be studied through the infinity (H_infinity) norms and through the sensitivity functions of controlled systems. A Matlab + Simulink program system for automatic design and simulation has been developed. The program system is suitable for a wide engineering utilization without a deep insight into he control theory. Some simulatiosn and Nyquist plots of unstable time-delay systems are included.