Multi-valued robust control technique for uncertain systems

A variety of plants with high parametric uncertainties are usually controlled with signals that may assume only a finite number of values, both to simplify actuator's construction and minimize the operation cost. The design of multi-valued control laws which provide a control signal that is discontinuous in time and quantized in magnitude is then of particular interest in many practical applications. This paper presents a new technique for robust control design in order to force a SISO linear plant, subject to disturbances and parametric uncertainties, to track a given sufficiently regular reference trajectory. The proposed approach is based on Lyapunov method and allows designing a control law which guarantees to follow the reference trajectory with prefixed values of the tracking error and of its derivatives up to the n1-th, where n is the order of the plant. Moreover, the control law is quite robust and guarantees the convergence of the error in a prefixed time. The technique is applied to design controllers characterized by control signals that may assume only a finite number of values. In this case, the control law can be seen as a generalization of the traditional relay control laws and of the sliding mode ones, with a relatively low switching frequency. Finally, a simple example shows the advantages of the control law obtained with the proposed design methodology with respect to the classical approaches.