TOWARDS RELAY FEEDBACK AUTO-TUNING OF MULTI-LOOP SYSTEMS

Abstract

Many single-input/single-output (SISO) and multi-input /multi-output (MIMO) systems in the process industry have simple controllers mainly of PI/PID structures placed on them in a multi-loop fashion. This thesis is a step towards the autotuning of these controllers using the relay feedback technique. The thesis discusses the following; the effect of placing cascade and m x m multivariable plants under relay feedback, the information that can be derived from the oscillations that occur and how they can be used in the tuning of multi-loop controllers. In SISO cascade systems, relay feedback is used to tune the controllers in a sequential manner. The secondary loop is tuned followed by the primary loop. Subsequent re-tuning of either controllers can be done in closed loop. The ratio of the ultimate frequencies obtained in this two step tuning procedure also indicate the ratio of the speeds of the loops. This is a useful quantity which indicates the effectiveness of the cascade set-up. Two approaches are presented for the design of MIMO control systems. In the first approach the loops are placed on relay feedback one at a time and the controller for the individual loop tuned sequentially. In the second approach all the loops of a MIMO plant are placed on relay feedback in a multi-loop fashion and the controllers tuned simultaneously. In the proposed sequential design of multi-loop PI controllers using relay feedback the interactive nature of the MIMO plant is automatically accounted for when one loop is relay tuned while other previously relay tuned loops are closed. The technique also ensures stability at each stage of the design. An interaction indicator is developed from the amplitudes of the oscillations which when used in modifying the tuning of the controllers aid in the reduction_ of large interaction amplitudes observed in some systems when set-point changes are made. For the second approach, the describing function analysis is extended to MIMO systems. This enables the prediction of critical parameters for the plant which proved useful in tuning the controllers. Both necessary and sufficient conditions for limit cycle oscillations are derived in terms of the eigenvalues of the open loop system. In order to capture an accurate behaviour of MIMO systems under simultaneous relay feedback, a generalisation of the Tsypkin method for the prediction of forced oscillations in SISO systems is presented. It if shown that three modes of oscillations in the system are possible. 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. Exact necessary conditions are derived which show that these modes are related to the strength of the interactions in the respective loops. Design strategies for PI controllers are proposed for the plants that exhibit these modes. A notable point in these approaches to auto-tuning is that full knowledge of the process is unnecessary since the important design parameters are obtained from relay feedback.