A probabilistic measure for model purposiveness in identification for control

Abstract

The question of whether the identified process model will lead to a stable closed loop is of practical relevance during iterative identification and controller design. It is known that, in the case of overly demanding closed-loop requirements, the model resulting from the iterative procedure might conflict with prior knowledge about the process. Nevertheless, in many cases the violation of the plausibility of the identified models does not necessarily violate its purposiveness. Therefore, it is a matter of practical importance to have a confident indication as to whether the given model will result in a stable closed-loop design or not. If not, the iterative identification and controller design should be stopped, that is more appropriate model structures should be chosen. In this paper, a probabilistic measure is proposed which relies on the estimated model error obtainable by the stochastic embedding technique. The idea behind it is to estimate the probability that the critical point ( -1,0) will not be encircled by the Nyquist curve of the return ratio transfer function of the true system. The results obtained from experiments on a motor-generator laboratory set-up show that the proposed probabilistic measure provides a reliable indication of the stability of the designed closed loop.