New tuning methods for PID control of unstable processes

摘要

The purpose of this study is to propose several new methods for tuning the P1 or the PID controller settings of UFOPOT processes. In contrast to known PID tuning rules that result on overshoot in the closed-loop response or require the modification of the feedback control structure, the proposed methods ensure smooth response and robustness against parametric uncertainty while retaining the classical PI or PID structure. This improved behavior is plausible by the use of a number of set-point filters and by the application of some simple rules for setting the values of the controller parameters. In particular, in the paper; we examine two alternative PI controller with set-point filter feedback control structures: one with a first-order set-point filter and the other with a fourth-order set-point filter. We also analyze a PID controller with a second order set point filter feedback structure. The proposed tuning rules rely on some new accurate approximations of the crossover frequency and either are expressed in terms of an adjustable parameter that can be selected to ensure overdamped response or minimization of the integral of squared error plus normalized square controller output deviation (ISENSCOD) criterion, or they are based on the simultaneous satisfaction of gain and phase margin specifications. It is worth noting, at this point, that explicit and precise rules and formulas, for the selection of the adjustable parameters are proposed in the paper. The proposed methods require small computational effort and they are particularly useful for on-line applications. In the paper; a variety of simulation studies have been performed and the performance of the proposed methods is compared to that of both the conventional PI/PID controller and the two-stage IMC method. This comparison reveals, that the proposed methods provide faster attenuation of step load disturbances, in addition to enhanced closed-loop response in set-point changes. As it is shown in the paper, the proposed methods are favorably compared to the already known tuning methods in terms of stability robustness. Finally, an application of the proposed methods on an open loop unstable biological reactor with hard input constraint and significant measurement delay is also presented.