Adaptive Fuzzy Dynamic Sliding Mode Control of Nonlinear Systems

Two phenomena can produce chattering: switching of input control signal and the large amplitude of this switching (switching gain). To remove the switching of input control signal, dynamic sliding mode control (DSMC) is used. In DSMC switching is removed due to the integrator which is placed before the plant. However, in DSMC the augmented system (system plus the integrator) is one dimension bigger than the actual system and then, the plant model should be completely known. To overcome this difficulty, a fuzzy system is employed to identify the unknown nonlinear function of the plant model and then, a robust adaptive law is developed to train the parameters of this fuzzy system. The other problem is that the switching gain may be chosen unnecessary large to cope on the unknown uncertainty. To solve this problem, another fuzzy system is proposed which does not need the upper bound of the uncertainty. Moreover, to have a suitable small enough switching gain an adaptive procedure is applied to increase and decrease the switching gain according to the system circumstances. Then, chattering is removed using the DSMC with a small adaptive switching gain (ASG). As a case study, nonlinear chaotic Duffing-Holmes system is selected.