Composite nonlinear feedback control for general linear discrete-time multivariable systems with actuator nonlinearities

In this paper, we present a composite nonlinear feedback control technique for linear discrete-time multivariable systems with actuator saturation. The technique has been proven to yield much better performance compared to conventional linear state feedback design methods for linear continuous-time systems when certain condition relating the initial conditions, reference signals and control saturation levels is met. The goal of this work is to complete the theory for general discrete-time systems. We consider both the state feedback case and the measurement feedback case without imposing any restrictive assumption on the given systems. The composite nonlinear feedback control consists of a linear feedback law and a nonlinear feedback law without any switching element. Typically the linear feedback part is designed to yield a quick response at the initial stage, while the nonlinear feedback law is used to smooth out overshoots in the system output when it approaches the target reference. As such, the resulting closed-loop system generally has very fast transient response and small overshoots. It is applied to a magnetic-tape-drive servo system design and yields an improvement of more than 50% in settling time compared to that of standard LQ controller which does not violate control constraints.