Pole placement in uncertain dynamic systems by variance minimisation

Abstract The problem of pole placement in dynamic systems with uncertainties is addressed using a global optimisation approach. Variability between nominally identical systems, which arises from manufacturing tolerances, wear and environmental variability, is considered. In the proposed method, receptances are measured from one of the open-loop, nominal systems chosen at random. In this case, in addition to the variability about the parameter means, the parameter means are also random. The receptance method is then used to place the poles of the measured system such that their spread, due to parameter uncertainty, is minimised. The measure used to assess the spread is the variance, determined efficiently by a polynomial chaos expansion. Among the advantages of the method are: (i) there is no requirement to model the system since experimental receptances are used, (ii) it is not necessary to measure the mean system, and (iii) uncertainty in poles is quantified across its full range by using variances. Numerical and experimental examples are provided to illustrate the working of the proposed method.