Controller design for unknown multivariable systems using monotone modelling errors

The problem of controller design for an unknown discrete or continuous multivariable system in the frequency domain based on open-loop step-response data alone is considered. The approach is based on the use of simple approximate plant models possessing the property that the resulting error in modelling the plant open-loop step response is both monotonic and sign-definite as a function of time. In such circumstances, the frequency-domain properties of the approximating feedback system and the error involved in predicting steady-state characteristics are sufficient data to predict the stability of the real feedback system. If integral controller elements are included, the results also provide sufficient conditions for exact tracking of step demands. Under certain circumstances, the technique has strong connections with the well known inverse Nyquist array design method and can be regarded in part as a modification and generalisation of that techniqiue to cope with unknown interaction dynamics.