Sliding mode control for systems with slow and fast modes

This dissertation addresses the problems of sliding mode control for systems with slow and fast dynamics. Sliding mode control is a type of variable structure control, where sliding surfaces or manifolds are designed such that system trajectories exhibit desirable properties when confined to these manifolds. A system using a sliding mode control strategy can display a robust performance against parametric and exogenous disturbances under the matching condition (Drazenovic's condition). This property is of extreme importance in practice where most systems are affected by parametric uncertainties and external disturbances.;First, we investigate a high gain output feedback sliding mode control problem for sampled-data systems with an unknown external disturbance. It is well-known that under high gain output feedback, a regular system can be brought into a singularly perturbed form with slow and fast dynamics. An output feedback based sliding surface is designed using some standard techniques for continuous-time systems. Next, we construct a discrete-time output feedback sliding mode control law for the sliding surface. The main challenge in this work is the appearance of the external disturbance in the control law. A remedy is to approximate the disturbance by system information of the previous time sampling period. The synthesized control law is able to provide promising results with high robustness against the external disturbance, which is demonstrated by the bounds of the sliding mode and state variables. These characteristics are further improved by a method which takes into account system information of two previous time instants in order to better approximate the disturbance. The stability and robustness of the closed-loop system under the proposed control laws are analyzed by studying a transformed singularly perturbed discrete-time system.;The second topic of the thesis is to study sliding mode control for singularly perturbed systems which exhibit slow and fast dynamics. A state feedback control law is designed for either slow or fast modes. Then, the system under that state feedback control law is put into a triangular form. In the new coordinates, a sliding surface is constructed for the remaining modes using Utkin and Young's method. The sliding mode control law is synthesized by a control method which is an improved version of the unit control method by Utkin. Lastly, the proposed composite control law consisting of the state feedback control law and sliding mode control is realized. It is shown that stability and disturbance rejection are achieved. Our results show much improvement when compared to the other works available in the literature on the same problem.;The problem of sliding mode control for singularly perturbed systems is also addressed by the Lyapunov approaches. First, a state feedback composite control is designed to stabilize the system. Then, Lyapunov functions based on the state feedback control law and the system dynamics are employed in an effort to synthesize a sliding surface. Two sliding surfaces and two sliding mode controllers are proposed in this direction. Theoretical and simulation results show the effectiveness of the proposed methods. Like composite approaches, the Lyapunov ones provide asymptotic stability and disturbance rejection.;We also study singularly perturbed discrete-time systems with parametric uncertainty. Proceeding along the same lines as in the continuous-time case, we propose two approaches to construct a composite control law: a state feedback controller to stabilize either slow or fast modes and a sliding mode controller designed for the remaining modes. It is shown that the closed-loop system under the proposed control laws is asymptotically stable provided the perturbation parameter is small enough.