Using Sliding Mode Control To Solve The Problem Of Under-actuated Systems

On the basis of sliding mode control a stable hierarchical sliding-mode controller model for a certain class of under-actuated systems is presented in this thesis. In this method, due to the structural characteristic of the system which can be subdivided into several subsystems, the hierarchical structure of the sliding surfaces is made up in the following manner. First, the under-actuated system is divided into several subsystems. For each subsystem a sliding mode surface is defined. Next, two states from two subsystems are chosen to construct the first-layer sliding mode surface. Then the constructed first layer sliding surface is combined together with one of the unused states to construct the second layer sliding surface. This process is repeated until the last layer sliding surface is obtained. The Lyapunov stability theory is used to obtain the sliding-mode control law. The control law can drive the subsystems toward their sliding surfaces and attain their desired values. Due to the novel design of sliding function the state trajectories of this system can now achieve asymptotic stability even if mismatched uncertainties exist when in sliding mode. The asymptotic stability of every layer sliding mode surface and the sliding mode surface of each subsystem is proven theoretically using the Lyapunov theory. The validity of this controller model is shown by simulation results for the stabilization control of an inverted pendulum system.