Evaluation of closed loop sensitivity to model uncertainty

An important step in automatic control system design is the evaluation of closed-loop sensitivity to uncertainty associated with the mathematical model of the system. The mapping between the uncertainty on the parameters and the closed-loop response characteristics is, however, very nonlinear, and approximate linearised analysis can be very misleading. This paper describes an approach to this problem based on the simple expedient of Monte Carlo stochastic simulation analysis. The probability distribution associated with the model parameters (normally Gaussian, defined by the vector of parameter estimates and the associated covariance matrix) is utilised to generate many random realisations of the closed-loop response, which is then defined in terms of the ensemble of time responses, frequency responses and closed-loop pole positions (called stochastic root loci). The closed-loop sensitivity is then defined by direct reference to these ensemble characteristics or to statistical measures obtained from them. This evaluation procedure forms part of the true digital control system design CAD program developed at Lancaster. The paper discusses the closed-loop sensitivity evaluation procedures in the context of this program