A Robust Controller of Multi DOF-Cooperating Planar Robotic Manipulators Using a Tuned PID Approach

Usually, a dynamic system with impact conditions is an interesting problem with practical applications in the fields of dynamics, vibrations, and control. One difficulty in controlling robotics (i.e., a multi DOF two-cooperating or two-link planar) is the subject to impact between the end-effectors of manipulators is that the dynamics (i.e., equations of motion) are different when the system status changes suddenly from a non-contact state to a contact state. In this paper, a Tuned PID controller with different design scenarios is developed to regulate the states of two dynamic systems that collide. Further, in this work, three types of errors are used to compare among different cases that are; (1) the steady state error, (2) the root mean square error, and (3) the final value error. The results of the Tuned PID controller are compared to those obtained by a classical PID controller. The PID controller is tuned using the Ziegler–Nicholas approach. The simulation results of the robotic manipulators confirmed the theoretical effectiveness of the proposed controller, based on MATLAB/Simulink. Unlike the classical PID results (i.e., the impact-induced force is found to be 2.0 N), the Tuned PID controller successfully determined the impact-induced force as same as the desired force (i.e., 0.6 N). Moreover, the Tuned PID satisfied all other desired design values.