Indirect adaptive fuzzy sliding mode control of 3D inverted pendulum

In this paper, an indirect adaptive fuzzy sliding mode controller for a 3-dimensional inverted pendulum as a fully actuated MIMO system is developed. This inverted pendulum, has four degrees of freedom and equations of the system are nonlinear and non-minimum phase. Thus, control of this system is a challenging issue. Accordingly, in this work, general basis of sliding mode control method with reaching rules is expressed for this system, then the fuzzy control theory is combined, and modeling uncertainties of the system are estimated by universal fuzzy approximation theory. Controller parameters are updated by a defined adaptation law to decrease the tracking error of the inverted pendulum. A supervisory control level is also utilized to monitor variations in the previous control level (adaptive sliding-mode) in order to keep input signals bounded. Simulation results illustrate that the closed-loop dynamics of the controlled system is stable and robust against external disturbances. Moreover, chattering phenomenon is decreased significantly in comparison with a typical sliding mode controller.