Fuzzy Robust Backstepping Control Design for Control of Underactuated Mechanical Systems with Two Degrees of Freedom

In this paper, a fuzzy robust backstepping control is presented to control of underactuated mechanical systems with two-degrees of freedom. To do this, the system is divided into two first and second subsystems. Subsequently, for each of these sub-systems, a robust backstepping controller is designed. The mathematical proof shows that the first and second subsystems, with the application of controllers in the presence of existing structured and un-structured uncertainties, have global asymptotic stability. Because this system only has one input, so simultaneous control of the first and second subsystems will not be possible. For this reason, for connecting sub-systems, a function with specific characteristics is defined, which can be used to control these subsystems simultaneously, and also the global asymptotic stability of closed loop system in the presence of existing uncertainties can be guaranty. Then, using fuzzy logic, a fuzzy approximator is presented to implement this particular function. Since the switching terms are used in proposed control input, the occurrence of undesirable chattering phenomenon in the control input is inevitable. Therefore, using fuzzy theory, a solution is proposed to overcome this phenomenon in the amplitude control input.