Practical tracking via finite-valued control for uncertain SISO plants

In this paper we present a new technique for control design, with controllers characterized by control signals that may assume only a finite number of values, in order to force a SISO linear plant, subject to disturbances and parametric uncertainties, to track a given sufficiently regular reference trajectory. The used approach is based on Lyapunov method and allows designing a control law, with prescribed levels of the control signal, which guarantees to follow the reference trajectory with specified values of the tracking error and of its derivatives until n-1 , where n is the order of the plant, and in particular with specified values of the error and of its first derivative. The proposed control law is a generalization of the traditional relay control laws and of the sliding mode ones. It is quite robust, guarantees the convergence of the error in a prefixed time, generally has a relatively low switching frequency and it can be easily realized with a low cost microcontroller. Moreover, we present a simple example that shows the advantages of the control law obtained with the proposed design methodology with respect to the ones obtained using sliding mode and classical relay approaches.