Adaptive parameter estimation based PID controller for nonlinear robotic systems

Although the proportional-integral-derivative (PID) controller has been widely used in the robotic systems, the tuning of PID controller gains depends heavily on the experience of practitioners, while improper control gains may limit the control performance or even trigger instability. To address this problem, this paper proposes a parameter estimation based PID control design for nonlinear robotic systems with unknown dynamics, and proves the stability of the closed-loop control system. The key idea is to reformulate the PID controller for uncertain robotic systems as a PD controller with an unknown time-varying parameter denoting the nonlinear system dynamics. Then a constructive adaptive parameter estimation is designed to derive the explicit conditions to ensure the system stability. This leads to a parameter estimation based PID controller with a feasible parameter adjustment mechanism. By using this adaptive parameter estimation, a closed-loop system containing both the tracking error and parameter estimation error is obtained. Then the stability of the resulting closed-loop system is proved via the Lyapunov theorem, and the convergence of the tracking error is also analysed. Both simulation and experimental results are given to show the effectiveness of the proposed method.