PIλDμ controller design for fractional order systems with random parameters

Mathematical representation of plant dynamics can suffer from random uncertainties caused by modeling errors, nonlinearities, manufacturing tolerances and operating conditions. The parametric stability and performance of a fractional order system can be inferred from the evolution of the statistical characteristics of the system´s output under the influence of random perturbations. A statistical analysis problem was constructed to determine how specific parametric perturbations affect output of a fractional order plant. Wiener-Askey polynomial chaos provided a framework for the statistical analysis of dynamic systems at a computational cost less than Monte-Carlo and Latin-Hypercube simulations. Therefore, it was used here to predict the mean and variance of output of fractional order systems with Gaussian random parameters. A robust PI^λD^μ controller for fractional order systems with random uncertainties was designed by nonlinear optimization of suitable performance criteria.