Typical controller design and tuning methods for unstable processes usually require a detailed knowledge of the process model. However, due to their unstable and complex nature, such a process model is difficult to obtain either empirically or theoretically. Furthermore, frequent changes in operating conditions and disturbances pose another problem for sophisticated controller design methods. An ideal solution is to develop automatic tuning methods which require little a priori information about the unstable process and are able to provide good on-line tuning control

Thorough analysis of trajectory characteristics of a relay feedback system is a challenging task since the system may exhibit strange behaviour such as non-uniqueness of solutions, fast switching or chattering, sliding motion and chaos. We investigated these problems and used relay feedback systems for auto-tuning of advanced control systems.

The case of decentralized relay feedback (Figure 1) for multivariable processes is even more complicated since it may lead to three different modes of oscillations: a common frequency, different frequencies, or mixed frequencies. One needs to find not only the existence conditions of each mode, but also the characteristics of each mode in terms of process dynamics, without which process identification may be impossible. We aim to develop effective techniques for analysing limit cycle behaviour and to establish criteria for determining the stability of limit cycles. These theoretical results may then be exploited to derive new methods/algorithms for relay identification and control.

Figure 1: Decentralised relay feedback system.

There are very few results reported in the literature for multi-input-multi-output (MIMO) processes under relay feedback. It is thus timely to thorough study of MIMO relay feedback and limit cycle behaviour such as solution existence, uniqueness and stability, and involves principles of nonlinear multivariable systems. Effective techniques to analyse limit cycles behaviour for unstable and MIMO relay feedback for existence and stability are established (Figure 2). We developed algorithms for identification of unstable SISO and stable MIMO processes under relay feedback and step inputs. The developed methods can be effectively applied for MIMO PID, single-loop controller and IMC controller auto-tuning. The results of this work have potential applications in control and automation industry.

Figure 2: Convergence to a limit cycle.

This work was performed in collaboration with Professor TH Lee.