Studies on PID controller tuning and self-optimizing control - Hu, Wuhua (2012)
This thesis consists of two parts. The first part is devoted to analytically deriving proportional-integral-derivative (PID) tuning rules with different tuning methods and the second part is devoted to reporting some new results on self-optimizing control (SOC). The two parts are connected through the controlled variables (CVs) used in control. Firstly the problem of tuning PID controllers for integral plus time delay (IPTD) processes with specified gain and phase margins (GPMs) is approached and solved. Accurate expressions of GPMs in terms of the PID and process parameters are also obtained. Based on these results, simple PID tuning rules are then derived for typical process models. The new rules are shown to give improved disturbance rejection while maintaining the same peak sensitivities as compared to the well-known simple internal model control (SIMC) rules. We then present a systematic approach of combining two-degrees-of-freedom (2DOF) design with direct synthesis (DS) for designing controllers which give desired closed-loop transfer functions. Explicit PID tuning rules are obtained by approximating the ideal controllers appropriately as PID controllers or PID-C controllers (i.e., PID controllers in series with lead-lag compensators). Next we investigate the very recent closed-loop setpoint response (CSR) method for tuning PI controllers in an analytical manner. A common PI tuning rule is obtained without using explicit models for both IPTD and first-order plus time delay (FOPTD) processes. The rule has a form similar to a recent one concluded from numerical experiments and turns out to give satisfactory closed-loop performance for a broad range of processes. Conventionally, CVs are assumed to be known or given before a PID control design. The assumption, however, may neither be necessary nor be rational. It has been found in many applications that CVs need to be selected properly for maximizing product utility when a process is perturbed or the measurements are corrupted by noises. This has motivated the proposal of SOC for selecting CVs for near optimal operation. In the second part of the thesis, we firstly investigate the local solutions of available SOC further and then deal with two new problems arising in the SOC design. We give more complete analytical characterizations of the local solutions for SOC to minimize worst-case loss and average loss, respectively. The available solutions for SOC to minimize worst-case loss are extended in a more general form and the available solutions for SOC to minimize average loss are proved to be complete. The new results contribute to clarifying the relation between these two classes of solutions for SOC.