Optimal Super Twisting Sliding Mode Control of 3-DOF Manipulator

Abstract

The term "robot" is derived from the Czech word "robota," which means "forced labor" or "drudgery." Robotic manipulators are built from a series of links and joints. They are extremely intricate, unpredictable, and multi-input multi-output nonlinear systems with dynamic characteristics that fluctuate greatly over time. Robot manipulator trajectory control is challenging due to these factors. To track the joint trajectory of the manipulator accurately and efficiently, an optimal STSMC is proposed in this paper. It allows 3-DOF articulated robot manipulator to accurately track input trajectories while controlling the impact of uncertainty parameters on the manipulator. DH parameter is employed for forward kinematics, and algebraic method is employed for inverse kinematics of three degree of freedom robotic manipulator. By using Euler-Lagrange equation of motion nonlinear dynamic model of 3-DOF robotic manipulator is produced. For the investigation of the stability of the system, Lyapunov direct method was used. The settings of the controllers were fine-tuned using Particle swarm optimization (PSO) technique. The controller was implemented by using MATLAB/Simulink software and its performance was evaluated. Performance of Simulation result depicted that the proposed controller is chattering free. Step, ramp and sine wave tracking are discussed for STSMC, and position tracking to set point change is also discussed for STSMC controller. STSMC controller is compared with PID and SMC controllers. For 1st, 2nd and 3rd articulation the rise time of PID, SMC and STSMC are 0.2260s, 0.1101s, 0.1001s; 0.3891s, 0.2675s, 0.2967s; and 0.3602s, 0.2112s, 0.1228s respectively. In second link SMC has smaller rise time than STSMC, however in first link and in third link STSMC has smallest rise time. Settling time for 1st, 2nd and 3rd articulation using PID controller are 0.3543s, 3.2329s and 1.2746s respectively. For 1st, 2nd and 3rd articulation settling time using SMC controller are 0.2071s, 0.5316s, 0.4122s respectively. Using STSMC controller settling time for 1st, 2nd and 3rd articulation are 0.2051s, 0.5095s, 0.2683s respectively. According to the result STSMC controller achieves fastest convergence.