Controller synthesis procedure for linear unstable plants

A new controller synthesis algorithm for use with linear unstable plants is developed. The procedure is based on a factorisation theory. It involves determination of a desired transfer function followed by a two layer optimisation approach. The outer level non-linear optimisation layer optimises the assumed locations of the poles of the coprime factors of the plant and the coprime factors that are solutions to the Bezout identity. For a given pole locations of coprime factors, the inner layer optimisation (which is based on a previously developed factorisation procedure) is utilised to obtain a model-matching controller. The procedure is demonstrated by solving a difficult to control unstable plant, and results are compared with two other techniques previously reported in the open literature.

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