Optimal non-fragile controller realization algorithm and application to control problems

This paper derives an algorithm for minimization of fragility encountered in controller implementation. Fragility of a controller is a measure of extent to which small perturbations in controller parameters, caused by rounding-off errors or component tolerances, reduce system stability and performance. Different approaches are used for computation and minimization of controller fragility, i.e., weighted eigenvalue sensitivity and stability radii comparison. An efficient algorithm has been derived for the minimization of controller fragility that uses ordered complex Schur decomposition for obtaining suboptimal solution. The algorithm is tested for different control problems reducing fragility by a large margin. Different canonical forms are also analyzed for fragility, which include controllable canonical form, observable canonical form, modal canonical form, balanced realization and optimal (non-fragile) form. The different realizations are implemented through S-function discrete state space block. Open and closed loop controller realizations are compared with Simulink state space block. Results clearly indicate that optimal non-fragile controller realization shows better results both in open loop and closed loop realization.