Robust Adaptive Proportional Integral Sliding Mode Control Based on Synthesis of Approximating State Feedback for Robotic Manipulator

In this paper, four paradigms are used to deal with a robot manipulator control problem. These paradigms are feedback linearization method, approximating control by Taylor truncation, sliding mode approach, and adaptive proportional integral method. Robotic manipulators are strongly nonlinear, strongly time-varying, and strongly coupled. There are several uncertain factors in robotic manipulator such as dynamic parameters (eg., inertia and payload conditions), dynamical effects (e.g., complex nonlinear frictions), and unmodeled dynamics. The conventional linear controllers are difficult to treat these behaviors. To eliminate this problem, sliding mode control (SMC) can be used as a robust controller. Application of traditional SMC in nonlinear system uses exact feedback linearization. Geometric differential theory is used to develop exact linearization transformation of nonlinear dynamical system, by using nonlinear cancellation and state variable transformation. Hence, the controller can be synthesized by using the standard sliding mode for linear system. The main weak point of the exact linearization is that its implementation is difficult. This study presents a synthesis SMC based on approximating state feedback for robotic manipulator control system. This approximating state feedback is derived from exact feedback linearization. Based on approximating state feedback, sliding mode controller is derived. The original sliding mode control (SMC) has many drawbacks limiting its practical applicability, such as chattering and excessive control input. To eliminate the problems, the discontinuous control signals in the original SMC are replaced by proportional integral (PI) controller. To compensate the uncertainties of the system, the parameters of the PI controller are updated in online manner. To guarantee the stability the knowledge of the system uncertainties is not required. Furthermore, the stability and convergence of the proposed scheme are proved by using Lyapunov like method. To show the effectiveness of the proposed method, the simulation of the proposed sliding mode controller is presented.