Digital Implementation of Continuous-Time Sliding Mode Control

This paper deals with the case that an algorithm of continuous-time sliding mode control in which feedback gain coefficients are switched is digitally implemented in a digital computer. Since these coefficients are changed only at sampling instants, the system trajectory cannot be perfectly confined on a sliding hyperplane. As a results, the performance deterioration occurs. In this paper, the range is shown in which the switching control input guarantees to drive the state trajectory toward the sliding hyperplane and the swtching control algorithm is modified to be effective in it. A control algorithm is also proposed to keep the system trajectory in the narrowest neighborhood of the sliding hyperplane after the trajectory moving outside the range. The same discussion is further done for output tracking systems using sliding mode control. Finally, a numerical example is given for demonstrating the validity of the theoretical results