TOPICS IN PID CONTROL : UNDER-DAMPED PROCESS DYNAMICS, ROBUSTNESS AND ON-LINE MODELING

Abstract

PI / PID controller are the most widely used controller in industry control and it is foreseeable that it will continue to play an important role in the industry for a long time. This thesis gives insights and findings on three topics of PI / PID control - under-damped process dynamics, robustness, and on-line modeling. The first topic is to extend the use of PID controller to a process with poorly damped poles. PID control for a process with under-damped response is not well studied or documented in the literature. In practice, experienced designers would tune the controller from their experience. But for inexperienced users, they may come to the wrong conclusion that. PID controllers are not applicable to process with underdamped response, based on some attempts to use the Ziegler-Nichols type of controller tuning procedure which is more suitable for over-damper dynamics [Hang and Åström, 1992]. In this thesis, fairly accurate and simple formulas are derived to tune the PID controller for a process with under-damped response to meet gain and phase margin specifications. The formulas are implemented in a self-tuning PID controller and tested on a pilot plant This thesis also investigate the performance and robustness of well-known PI tuning formulas. These formulas are usually derived based on time domain performance. It is however important to evaluate these formulas also from the robustness point of view as the process model we use is only an approximation of the system dynamics. Approximate analytical formulas to compute gain and phase margin are derived in this thesis for on-line robustness computation which will particularly be useful when implementing adaptive control or auto-tuning. The final topic of the thesis is on developing process models from relay oscillation. The relay feedback technique is used to generate an approximate process model online under closed-loop control. The effectiveness and robustness of the methods are substantiated by extensive simulation study.