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 openloop modelling uncertainty and of the frequency-domain response of the designed cout.rollcr. The analysis met-hod is based on evaluation of Q suitable set of charactceist.ic functions on a standard Nyquist D contour. Therefore it leads to the formulation of addir.ioual requirements to be directly included in the set of specifications for tho 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 tho well-known separation theorem may also allow treatment of the uncertainty reducibility problem in two stages.

A Unified Approach for Designing Robust Linear Feedback Controllers

“…The stability condition (23) corresponds directly to those given e.g. in [3], [7], [9], [10], [13] and other papers concerning the singular value approach. Eqn.…”

“…This contrasts with nearly all known approaches to robust control, e.g. [7], [10], [17], [19] where the approximate model and the error model must be in parallel ( Fig. 1(a)).…”

“…The authors of [33], [34], [36] generalized the notion of stability margin as known from single-input single-output systems to multivariable control and investigated this property in connection with LQ-regulators. On the other hand, expressions for the l/O-behaviour of the original closed-loop system in terms of the closed-loop approximate model and the given open-loop model uncertainty bound are given in [7], [9], [10], [17], [19]j [27]. This provides a basis to check the behaviour of the closed-loop system according to the given design specifications and to assess the possible effects of the plant uncertainties.…”