Synthesis of optimal sliding mode control for robust DC drive

Two analytic solutions for the optimal switching vector for a third-order system are obtained. The tedious computation associated with the conventional trial and error selection of the weighting matrix and numerical solution of the Riccati equation in optimal control problems can be avoided. The novel design technique is shown to have identical results to that based on the minimization of the quadratic performance index with a suitable weighting matrix. Substantial improvement in performance over that reported in the literature is achieved. The performance obtained is insensitive to variations in system parameters and load disturbance.<>