Gain/phase decomposition and generalised predictive control of scalar systems

A convenient means of extending generalised predictive control to the multivariable case is through the use of singular value decomposition. However, owing to the bicausal nature of this decomposition, special care has to be taken to ensure that the overall control law is causal; this can be achieved by giving up some of the available degrees of freedom, but the results obtained in this way are suboptimal. It is the purpose of the paper to remove this difficulty. Owing to the complexity of the problem, consideration is given only to the scalar case for which the singular value decomposition reduces to a gain/phase decomposition; the proposed approach can be extended to the multivariable case but this is not undertaken here. The efficacy of the algorithm developed in the paper is demonstrated by means of a numerical example.