Asymptotic Stability of PID Controller for Nonlinear Mechanical Systems
非线性机械系统PID控制渐近稳定性分析

In this paper,we provide an answer to the long- standing question of designing global asymptotically stable proportional-integral-derivative(PID)regulators for uncertain nonlinear mechanical systems.Our main contribution is to es- tablish the semiglobal asymptotic stability of the controlled sys- tem with the commonly used linear PID controller by using Lya- punov direct method and LaSalle invariance principle.Further- more,an improved nonlinear proportional-integral plus deriva- tive(NPI-D)controller is proposed to speed up the transient and achieve the global asymptotic stability of the closed-loop system. Simulations performed on a two degree-of-freedom(DOF)robot manipulator demonstrate the improved performance of the pro- posed NPI-D controller.