Using time delayed disturbance compensation for sliding mode control

Under the framework of using Time Delay Control (TDC) for disturbance compensation in Sliding Mode Control (SMC), we address two practical problems. The first problem involves mitigating chattering in SMC caused by input delay, while the second problem focuses on designing TDC under conditions of limited measurements. Our research demonstrates that incorporating TDC as a phase lead compensator in the first problem can effectively accommodate larger input delays. To reduce the chattering, we propose a switching gain design, consisting of reference signals rather than measured states, resulting in an ultimately bounded solution. In the second problem, when acceleration measurements are unavailable, we provide stability conditions under which TDC can be designed with acceleration construction using delayed velocity signals. By constructing a modified sliding surface that incorporates the integral error remainder associated with the acceleration construction, our approach ensures switching gain are kept at minimal, with robust disturbance compensation at higher frequencies. We perform a simulation investigation of an autonomous underwater vehicle under input delay and disturbance to demonstrate the efficiency of the approach.