Nonlinear PI"D"-Type Control of Flexible Joint Robots by Using Motor Position Measurements Is Globally Asymptotically Stable

• Published in: IEEE transactions on automatic control Vol. 68; no. 6; pp. 3648 - 3655
• Main Authors: Moyron, Jeronimo, MorenoValenzuela, Javier, Sandoval, Jesus
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Asymptotic stability; Closed loop systems; Closed loops; Controllers; Feedback control; Flexible joint robot; global asymptotic stability; Lyapunov function; Manipulators; Nonlinear control; PD control; PI control; Position measurement; Proportional integral derivative; Regulation; Robot arms; Robot control; Robot kinematics; Robots; Subsystems; Symmetric matrices; Systems analysis
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3194043

An important subject that arises in the position control of robot manipulators is the local or global asymptotic stability of the closed-loop system equilibrium point, especially when an integral action is added to the control loop. For rigid joint robot manipulators, global nonlinear proportional-integral-derivative (PID) controllers have been introduced few years ago. However, for the case of flexible joint robot manipulators, the design and analysis of such nonlinear PID laws is much more challenging. Only local asymptotic stability results have been reported. Thus, a novel global regulator for flexible joint robots is presented in this document. The proposed controller considers a nonlinear integral action and it requires only motor position measurements because an estimator subsystem is used to replace the motor velocity measurements. In other words, a nonlinear proportional-integral-"derivative" (PI"D")-type controller is introduced. According to the closed-loop system analysis, conditions on the controller gains are established. Thus, the global asymptotic stability is concluded. Finally, experimental results on a two degrees-of-freedom serial flexible joint robot are shown and discussed.