Feedback control of linear multivariable systems with uncertain description in the frequency domain

Abstract

The problem of using approximate, reduced order, models for control systems design is investigated. Assuming that both plant and simplified model are driven by the same feedback controller, the plant output uncertainty range with respect to the output of the simplified model is analysed and expressed in terms of the given open-loop modelling uncertainty and of the frequency-domain response of the designed controller. The analysis method is based on evaluation of a suitable set of characteristic functions on a standard Nyquist D contour. Therefore it leads to the formulation of additional requirements to be directly included in the set of specifications for the control problem when it is approached by means of frequency-domain design techniques. In the case where the control design is developed by using time-domain techniques, it is shown that the well-known separation theorem may also allow treatment of the uncertainty reducibility problem in two stages.