A Set of Globally Stable Output Feedback N-PID Regulators for Robotic Manipulators

Abstract

This paper deals with the position control problem of designing asymptotically stable proportional plus integral regulators with only position feedback for robot manipulators with uncertain and varying-time payload. Proposed is a set of output feedback N-PID regulators consisting of a linear combination of the proportional control mode, derivative control mode, nonlinear control mode shaped by a nonlinear function of position errors, linear integral control mode driven by derivative feedback, and nonlinear integral control mode driven by a nonlinear function of position errors, where the velocity feedback is replaced by a filtered position feedback. By using Lyapunov's direct method and LaSalle's invariance principle, the simple explicit conditions on the regulator gains to ensure global asymptotic stability are provided. The theoretical analysis and simulation results show that the output feedback N-PID control laws can be tuned to recover the performance of a state feedback control laws, that is, the output feedback control laws with the asymptotically stable integrators have the same fast convergence, good flexibility and strong robustness as the state feedback one, and then the same optimum response can be achieved by a set of control parameters in the whole control domain, even under the case that the payload is changed abruptly.