Abstract
An unsolved ancient problem in position control of robot manipulators is to find a stability analysis that proves global asymptotic stability of the classical PID control in closed loop with robot manipulators. The practical evidence suggests that in fact the classical PID in industrial robots is a global regulator. The main goal of the present paper is theoretically to show why in the practice such a fact is achieved. We show that considering the natural saturations of every control stage in practical robots, the classical PID becomes a type of saturated nonlinear PID controller. In this work such a nonlinear PID controller with bounded torques for robot manipulators is proposed. This controller, unlike other saturated nonlinear PID controllers previously proposed, uses a single saturation for the three terms of the controller. Global asymptotical stability is proved via Lyapunov stability theory. Experimental results are presented in order to observe the performance of the proposed controller.
Highlights
Stability of PID control in robot manipulators has been subject of extensive research in past and recent years
It has been proved that PID controllers guarantee semiglobal asymptotical stability of the closed‐loop equilibrium point in the case of set‐point control [1]‐[7]
Experimental tests were carried out to show the performance of the proposed nonlinear PID with bounded torques
Summary
Stability of PID control in robot manipulators has been subject of extensive research in past and recent years. It has been proved that PID controllers guarantee semiglobal asymptotical stability of the closed‐loop equilibrium point in the case of set‐point control [1]‐[7]. Since PID controllers, until now, have only been proved to be semiglobally asymptotically stable, several nonlinear PID controllers have been proposed [8]‐[10]. Unlike linear PID controllers, the nonlinear PIDs yield global asymptotical stability of the closed‐loop equilibrium point. A particular case of the class of nonlinear global PID regulators originally proposed in [10] was presented in [11]. A “delayed” PID, which switched from a PD control to a PID control after a short transient, achieving global asymptotic stability was proposed in [12]
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