Best achievable control system performance: the saturation paradox

This paper proposes a methodology for the quantification of the best achievable closed loop control system performance for a linear process in the presence of input saturation constraints. Closed loop stability is guaranteed through the use of a parametrization of all nonlinear stabilizing controllers in terms of a finite gain stable parameter Q. Closed loop performance is quantified with respect to a finite number of disturbances. The best achievable performance is quantified over a class of nonlinear stabilizing controllers parametrized in terms of absolutely summable second order Volterra operators. The proposed computational procedure involves the solution of a sequence of mixed integer linear programs. Through the example it is shown that, in certain cases, there may exist a value of the saturation bound for which the best achievable control system performance is significantly better than the corresponding best achievable linear performance