Reliable decentralised control of delayed MIMO plants

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Reliable decentralised proportional–integral–derivative controller synthesis methods are presented for closed-loop stabilisation of linear time-invariant plants with two multi-input, multi-output (MIMO) channels subject to time delays. The finite-dimensional part of plants in the classes considered here are either stable or they have at most two poles in the unstable region. Closed-loop stability is maintained with only one of the two controllers when the other controller is turned off and taken out of service. 1. Introduction In this work, a stabilising controller synthesis method is developed for linear time-invariant (LTI), multi-input multi-output (MIMO) systems that are subject to time delays. The controller structure is a two-channel block-decentralised controller configuration, where each of the two channels may have multiple inputs and outputs. The challenging objectives of decentra-lised closed-loop stabilisation, reliable stability in the case of complete failure of either one of the two channels and integral action are all achieved with simple low-order controllers. In addition to closed-loop stability, an important performance objective is asymptotic tracking of step-input references with zero steady-state error, which is achieved by designing controllers with integral action. The simplest integral action controllers are in the proportional–integral–derivative (PID) form (Goodwin, Graebe, and Salgado 2001), which are first order if the derivative term is zero (PI) or second order if the derivative term is non-zero. Although PID controllers are widely used in many control applications and preferred due to easy implementation and tuning, their simplicity also presents a major restriction that they can control only certain classes of unstable plants since the controller order cannot exceed two. For the delay-free case, and even without the decentralisation constraint, a complete character-isation of unstable plants that can be stabilised using PID controllers is not available. It was …