Performance enhancement for a class of saturating systems

Current methodologies for designing control systems usually ignore the effects of control saturations. Resulting controllers often produce undesirable behavior such as integrator wind-up, large overshoots, long settling times, and even instability, when implemented on the saturating system. This paper presents a systematic procedure for adapting a nominal controller, designed while ignoring control saturation, to a higher-performance nonlinear controller that explicitly accounts for the saturating nonlinearities while guaranteeing stability. In particular, the Error Governor scheme proposed by Kapasouris, Athans, and Stein [1] is extended for the class of controllers modeled with a feedforward term. The utility of this procedure is demonstrated on the vehicle platooning system introduced by Sheikholeslam and Desoer [5], which uses a nonlinear vehicle model and allows for non-identical vehicles in the platoon. The nominal controller presented for this system is nonlinear and inherently decentralized, thus posing a significant test on the practicality of the proposed method. Performance of the nominal compensator without saturations, nominal compensator with saturations, Error Governor, and Extended Error Governor is compared for a platoon of 15 cars. Results are that the saturating system causes significant wind-up. The Error Governor corrected system can eliminate wind-up at a cost to steady-state performance [3]. The proposed Extended Error Governor, however, eliminates wind-up while delivering the same steady state performance as the original platoon design.