Symbolic control of systems with dead times using symbolic smith predictors

Abstract

Dead times exist in many physical plants. They degrade control performances and may make the plant unstable. A Smith predictor is a classical but commonly used approach to the improvement of the performance of the controller. On the other hand, a symbolic approach is useful for the design of an embedded controller. In this paper, we consider a control problem of a plant with a dead time, whose abstracted behaviors are given by a transition system with an FIFO queue to model the dead time. A desired behavior is also given by a transition system, and there exists a symbolic controller for the control specification in the case where there is no dead time. Then, we introduce a symbolic Smith predictor, and propose a configuration of a symbolic controller containing the symbolic Smith predictor. Using an approximate contractive alternating simulation relation between the controller and the plant, we show that the controlled plant exhibits a desired behavior.