Model-based trajectory tracking in sliding mode control of continuous-time systems

Abstract

Controller design for uncertain continuous-time systems is a challenging task. It is vital to ensure that the effects of uncertainties on system dynamics are counteracted, while at the same time satisfying all state and input constraints. Counteracting the effect of uncertainties on the motion of the system can be achieved using sliding mode controllers (SMC). By confining the system representative point to a limited area in the state space, such controllers ensure that matched uncertainties are fully rejected. Nevertheless, sliding mode controllers are typically unable to impose any constraints on individual state variables, which may limit their applicability. In this work we propose a strategy, which allows one to impose strict constraints on state variables in sliding mode control while still maintaining its disturbance rejection property. In the proposed method, we introduce a particular reference model of the plant. This model is then used to design favorable, bounded target trajectories for the original system. These trajectories are obtained from a polynomial function, which is selected after taking the known initial conditions of the system into account. Finally, a sliding mode control strategy is used to drive the state of the original plant alongside that of the reference model. We have proven that, with the application of the proposed strategy, each state variable of the plant exactly follows the respective variable of the model, regardless of disturbance. As a result, state variables of the actual plant are bounded in exactly the same way as those of the reference model.