Pergamon Chemical Enyineerin~ Science, Vol. 50, No. 11, pp. 1695 1706, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009 2509/95 $9.50 + 0.00 0009-2509(94)00472-2 A NEW APPROACH TO DECENTRALISED CONTROL DESIGN Y. SAMYUDIA, P. L. LEE* and 1. T. CAMERON Computer Aided Process Engineering Centre, Department of Chemical Engineering,The University of Queensland, St. Lucia, QLD 4072, Australia and M. GREEN Department of Engineeringand Department of Systems Engineering,Research School of Physical Sciences and Engineering, The Australian National University, Canberra, ACT 2601, Australia (Received 29 April 1994; accepted in revised fi~rm 20 September 1994) Abstract--A decentralised control design methodology, which is based on ideas from robust stabilisation using the normalised left coprime factorisation and the gap metric, is developed. Some indicators for decentralised control design are proposed. These indicators are useful as a guideline for screening alternative control structures. A sufficient stability condition is formulated by making use of these indicators. Unlike the Relative Gain Array (RGA), these indicators can guarantee the stability and achievable performance of the system under decentralised control for given design specifications. This methodology has been applied to two industrial case studies in which the systems are open-loop unstable and/or non-minimum phase. 1. INTRODUCTION A decentralised control structure is often preferred to a centralised structure for controlling multi-unit (or complex) chemical processes, because it is simpler to design, implement and tune. The constraints on the controller structure invariably lead to performance degradation when compared with the system under centralised control. This is due to the interactions between units (or subsystems). Therefore, the interac- tions must be considered in deeentralised control design. In decentralised control design, interaction meas- ures such as the Relative Gain Array (RGA) (Bristol, 1966) and the Block Relative Gain Array (BRGA) (Manousionthakis et al., 1986) are commonly used, especially to screen alternative control structures. These measures are simple, but cannot guarantee the stability and achievable performance of the system under decentralised control. Recently, Grosdidier and Morari (1986) have pro- posed interaction measures based upon the structured singular value,/~. The/.t-measures consider the stabil- ity and performance of the closed-loop system. In deriving these measures, the interactions were modelled as multiplicative uncertainty, so the use of the /~-measures is limited to open-loop stable and minimum phase systems (Skogestad and Morari, 1987; Morari and Zafirrou, 1989). *Author to whom correspondence should be addressed. For system such as a forced circulation evaporator, the/~-measures or even RGA cannot be used directly because this process is not self-regulatory--there is a pole at the origin. The standard industrial approach in designing decentralised control for this system is to stabilise the non-self-regulatory variable by a heuris- tic approach and then use RGA analysis on the re- maining stable system (Newell and Lee, 1989). To deal with unstable processes, Hovd and Skoges- tad (1992a, b) have proposed an interaction measure, which is called the Performance Relative Gain Array (PRGA). This measure was derived using ideas from the Dynamic Relative Gain Array and only addressed the performance of the system under decentralised control. The stability problem must be considered separately using another method. Hence, this work is aimed at developing a method of measuring interactions which considers both the stability and achievable performance of the system under decentralised control. Additionally, this measure should be able to analyse the interactions for any plant which may be open-loop unstable and/or non-minimum phase. Finally, in order to screen alter- native control structures before the controllers are designed, the interaction measure should require only open-loop information. The proposed method was derived by using the gap metric and normalised coprime factorisation concepts of robust control theory (McFarlane, 1988; Georgiou, 1988; Glover and McFarlane, 1989; Georgiou and Smith, 1990; McFarlane and Glover, 1990, 1992). 1695