| A robust control design methodology is presented for systems subject to ellipsoidal uncertainty. Both the robust analysis problem and the robust synthesis problems are considered, and both discrete and continuous systems are considered. For continuous systems subject to ellipsoidal uncertainty, a frequency dependent rational function is constructed to measure the stability margin at each frequency. This rational function may have multiple minima, therefore a frequency search must be carried out to find the overall stability margin of the system.;An alternative method for testing robust stability is developed that is based on constructing a stable transfer function whose frequency response magnitude is equal to the stability margin of the system under consideration. The overall stability margin is then found as the H;A robust control synthesis procedure for systems subject to ellipsoidal uncertainty is also developed. This method consists of constructing a fixed order Youla parameter to achieve a robustly stable closed loop for the specified level of uncertainty. The appropriate coefficients of the Youla parameter are found through a constrained quasi-convex optimization. The design methodology is applicable to any nominally stabilizing controller, but the specific case of a predictive controller is considered in this work. The resulting controller is a predictive controller that is robust with respect to real parameter variations, and it also retains the nominal servo performance of the original predictive controller. The design procedure is easily modified to allow the incorporation of integral action into the robust controller, guaranteeing the offset-free rejection of asymptotically constant disturbances. It is also possible to incorporate a slightly restricted form of unstructured uncertainty into the design. |
