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

Abstract

This paper deals with the position control of robot manipulators with uncertain and varying-time payload. Proposed is a set of novel 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 differential feedback, and nonlinear integral control mode driven by a nonlinear function of position errors. 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: an attractive feature of our scheme is that N-PID regulators with asymptotic stable integral actions have the faster convergence, better flexibility and stronger robustness with respect to uncertain and varying-time payload, and then the 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

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

“…To put our contribution in perspective, we will briefly review the state feedback N-PID control law [7] , as follows:…”

“…To avoid this drawback, various PID-like controllers have been proposed to improve the transient performance. For example, PID-like controllers consisting of a linear PD feedback plus an integral action driven by PD controller [3] , a linear PD feedback plus an integral action driven by NP-D controller [4] , a saturated-P, and differential feedback plus a PI controller driven by a bounded nonlinear function of position errors [5] , a linear PD feedback plus an integral action of a nonlinear function of position errors [6] , and a set of N-PID regulators [7] 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, are presented recently.…”

Global Asymptotic Nonlinear PID Control With a New Generalized Saturation Function

“…In addition, Yarza introduced a nonlinear PID controller with bounded torques using a single saturation function that was globally asymptotically stable [15]. Liu proposed a set of globally stable output-feedback N-PID control laws that were dealing with the position control problem of designing asymptotically stable proportional plus integral regulators with only position feedback [16]. A saturated PID control was raised to address the global asymptotic regulation of robot under input constraints, both with and without velocity measurement by Su [17].…”