Searching for robust minimal-order compensators

A method of designing a family of robust compensators is presented. Each compensator's transfer function is found using a genetic-algorithm search for numerator and denominator coefficients that minimize the probability of unsatisfactory stability and performance, subject to uncertainty in the real parameters of the plant. As the search progresses, probabilities are estimated by Monte Carlo evaluation of stability and performance criteria. The design procedure employs a sweep from the lowest feasible transfer-function order to higher order, terminating either when design goals have been achieved or when no further improvement is evident. The study illustrates the evolution of pole and zero locations as compensator order increases for a benchmark problem in which settling-time and control-usage performance criteria must be satisfied subject to minimum likelihood of instability. The method provides a means for estimating the best possible compensation of a given order based on repeated searches.