Single-loop PID controller design for electrical flexible-joint robots

Most of previous approaches presented for electrical flexible-joint robots (EFJR) utilize back-stepping-based control strategy. In order to have a satisfactory performance in these approaches, the internal signals should converge to their desired trajectories defined by the designer. Usually, these desired trajectories are known as fictitious control signals. In EFJR, each joint is modeled by a fifth-order cascade differential equation. Thus, back-stepping-based approach seems complicated and time-consuming. Thus, the contribution of this paper is focusing on the convergence of the system output and meanwhile guaranteeing boundedness of other system's states. As a result, the control law dimension and its implementation costs are reduced. In other words, a single-loop PID controller for EFJR has been presented, while previous approaches contain multi-loop controllers. The controller design strategy is based on the actuators' electrical subsystem. Voltage saturation nonlinearity has been compensated in the control law. Hence, knowledge of the actuator/manipulator dynamics model is not required in the proposed method. The overall closed-loop controlled system is established as BIBO stable, and the link position-tracking errors are asymptotically stable based on the Lyapunov's stability concept. Numerical and experimental implementations support the viability of the proposed theoretical results.