The Design and Comparison of Backstepping Fuzzy Control and Fuzzy Sliding Mode Control for Controlling Underactuated Mechanical Systems with Two Degrees of FreedomTwo Degrees of Freedom

In this paper, two control methods are presented to control a class of underactuated systems with two degrees of freedom. The design method of the proposed controllers and how to prove the stability of the closed-loop system using solutions such as backstepping control, sliding mode control, fuzzy logic and their combinations are presented in details. Mathematical proof shows that the closed-loop system under the proposed scheme has a global asymptotic stability in the presence of structural and un-structural uncertainties. Then, the advantages and disadvantages of the proposed controls are examined and then some criteria such as simplicity in practical implementation, the control input calculations volume, the adjustment of the control input coefficients, and the amplitude of the control input are used to make comparisons between the suggested controllers. Finally, to evaluate the performance of the proposed controllers, simulations are implemented on the cart-position system with a single-link inverted pendulum. The simulation results confirm the performance of the proposed solutions.