OPTIMAL FEEDBACK-CONTROL OF SISO SATURATION SYSTEMS OVER A CLASS OF NONLINEAR STABILIZING CONTROLLERS

This paper focuses on the feedback control of a linear single-input si ngle-output process in the presence of input saturation constraints. F irst, closed-loop stability is guaranteed through the use of a paramet rization of all nonlinear stabilizing controllers in terms of an S-sta ble parameter Q. Then, a performance measure is proposed that quantifi es closed-loop performance with respect to a finite number of disturba nces. Subsequently, the best achievable performance is quantified over a class of nonlinear stabilizing controllers parametrized in terms of absolutely summable second order Volterra operators. The resulting co mputational procedure involves the solution of a sequence of MILP's. A n illustrative example is employed to demonstrate the proposed procedu re. This example establishes that, for this performance measure, there may exist a value of the saturation bound for which the best achievab le control system performance of the saturating system is strictly bet ter than the corresponding best achievable linear performance. The sam e example also demonstrates that nonlinear control can perform strictl y better than linear control for a performance measure that employs a finite number of disturbances. (C) 1997 by John Wiley & Sons, Ltd.