Controller Fragility Minimization Algorithm and Comparison with Different Controller Realizations

This paper is about minimization of fragility encountered in controller implementation. Fragility of a controller is a measure of the extent to which small perturbations in controller parameters, caused by rounding-off errors or component tolerances, reduce system stability and performance. In this paper two different approaches are used for minimization of controller fragility, i.e., weighted eigenvalue sensitivity calculation and stability radii comparison. A more efficient algorithm has been derived for the minimization of controller fragility that uses Schur decomposition for convergence to suboptimal solution. The algorithm is tested and verified for different control problems reducing their fragility by a large margin. Furthermore different canonical forms are 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. The 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 system.