ROBUSTNESS MONITORING FOR PID CONTROL SYSTEMS

Abstract

Robustness is important in feedback control systems to deal with process uncertainties. A robust system is able to maintain closed loop stability in the face of variations in process parameters and model inaccuracies. In practice, the parameters of any industrial process always change due to nonlinearities and changes in operating condition. Therefore, it is important to monitor the stability robustness of a system to retain the desired performance. The Proportional-Integral-Derivative (PID) controllers are by far the most common and widely used controllers in the industry (Luyben, 1990; Zhuang et al., 1993). PIDs are sufficient when the process dynamics are benign and the performance requirements are modest. This thesis attempts to provide an algorithm for monitoring the stability robustness of PID control systems. In traditional control design, time domain information such as the set-point, the controller output, and the process output signals are presented for monitoring of performance and stability robustness. This thesis shows that the time domain signals do not give clear indication of the stability robustness in the PID controlled first-order plus dead-time model systems. Gain and phase margin plots are direct indicators of the stability robustness for a closed-loop system. Therefore, these plots can supplement the time domain signals to give clear indication of the stability robustness of the PID control systems. However, the plot of gain and phase margins for a PID control system cannot be determined easily. A set of nonlinear equations has to be solved numerically on-line and in real-time for every sample. This thesis depicts how the nonlinear equations can be solved analytically with acceptable approximation. When the solutions are used in conjunction with an estimator that gives an estimate of the first-order plus dead-time process dynamics, the gain and phase margins can be calculated on-line and in real-time (Ho et al., 1998). The gain and phase margins algorithms in association with time domain signals are implemented in a framework of knowledge-based system for the stability robustness monitoring. This system extends the range of conventional control algorithms by encoding the control knowledge with the design and operation heuristics by using the expert system techniques. The knowledge-based control system is tested on a heat exchanger pilot plant.