Robustness monitoring for PID control systems

This paper attempts to provide an algorithm for monitoring robustness stability of PID control systems. In traditional control design, time domain information such as the set-points, the controller output and the process output signals are presented for monitoring performance and robustness. Time domain signals do not give clear indication of the stability of the closed-loop system. Gain and phase margin plots are direct indicators of the stability robustness. Therefore, these plots can supplement the time domain signals to give clear indication of the stability robustness of the closed-loop system. However, the plots of gain and phase margins could not be determined easily. A set of nonlinear equations have to be solved numerically online and in real-time for every sample. This paper shows how the nonlinear equations for the PID control systems can be solved analytically with acceptable approximation. It also shows that when the solutions are used together with an estimator that gives an estimate of the process dynamics, the gain and phase margins can be calculated on-line and in real-time. The algorithms for monitoring the gain and phase margins are implemented in the framework of a knowledge-based system which is tested on a heat exchanger pilot plant