TUNING 2-BY-2 MULTI-LOOP PI CONTROLLERS USING RELAY FEEDBACK

Abstract

Many multivariable plants in the process industry are controlled by placing controllers of the Proportional plus Integral (PI) structure or the Proportional plus Integral plus Derivative (PID) structure in a multi-loop fashion. This thesis aims to provide some insights into how multi-loop PI controllers in a two-input two-output plant can be tuned by using the relay feedback technique. Specifically, the behaviour of a multivariable plant under closed-loop relay feedback control and how multi-loop PI controllers can be tuned from the oscillations in such a system will be discussed. A multivariable system which is placed under multi-loop relay feedback control can display one of three possible modes of oscillations. The first mode consists of identical relay outputs which are square waves with precisely one fundamental frequency. The second mode is characterised by relay outputs which are square waves of different fundamental frequencies in each loop. The third mode is one of periodic complex oscillations consisting of multiple relay switches within one fundamental period. Using the necessary conditions for limit cycle oscillation, the relationship between the mode of oscillation and the coupling strength as well as the speed of the individual loops is discussed. As a multivariable plant under relay feedback control may display one of three possible modes of oscillations, different strategies for design are proposed in each case. First, a relay feedback experiment is performed using ideal relays with unity switching levels in all loops. If the plant displays Mode 1 or Mode 2 oscillations, then the oscillations may be used to design PI controllers much like the single-input single-output (SISO) case. If the plant displays Mode 3 oscillations, then the relay switching levels may be manipulated until Mode 1 oscillations results before the multi-loop PI controllers are designed. The proposed strategy is a simple method of obtaining a set of multi-loop PI controllers which gives a reasonable performance without requiring too much prior knowledge about the plant. Next, a methodology for estimating the range of relay switching levels that will result in Mode 1 oscillations is proposed. The algorithm is based on the Forced Oscillation phenomenon in SISO relay feedback systems. Finally, a relationship between controller performance and the relay switching level used for tuning the PI controller was studied. This led to a strategy for setting relay switchings so that the controllers tuned from the resultant oscillations is better able to handle the conflicting requirements of the different loops. All the proposed strategies are illustrated by simulations results.