The design of stable multirate implementations of anti-windup schemes for input saturated discrete time systems

Many discrete time anti-windup schemes for input saturated stable systems to achieve certain stability and performance criteria have been proposed in the literature. It has been shown as well that an anti-windup scheme that involves directionality compensation (in the form of multivariable nonlinear algebraic loop) has an excellent transient performance. As in continuous time, however, implementation problems may arise due to the formation of an algebraic loop. In discrete time, an iterative algorithm to solve the algebraic loop that converges within a prescribed time sampling may be employed while preserving the stability and performance. Consequently, the speed of convergence may limit the application of anti-windup schemes. Alternatively, a closely related explicit static anti-windup scheme may be adopted, in which no iterative solution at each time step is required, but with a minor degradation in performance. To achieve both simple implementation and stability-performance preservation, two possible stable-multirate implementations are designed in this paper. Unlike an iterative algorithm, solving the algebraic loop is now executed only by finite number of iterations. Simulation result shows that a typical undershoot response of the explicit anti-windup scheme is now absent by allowing several iterations in this stable multirate implementation.