On the optimality and performance of PID controller for robotic manipulators

This paper suggests an inverse optimal PID control design method for mechanical manipulators. We find the Lyapunov function and the control law satisfying the disturbance input-to-state stability by using the characteristics of Lagrange system. Also, we show that the inverse optimal PID controller satisfies the Hamilton-Jacobi-lsaacs equation. Hence, the inverse optimality of the closed-loop system dynamics was acquired through the PID controller, if some conditions for the control law are satisfied. Also, simple coarse/fine performance tuning laws are suggested based on the analysis for performance limitation of the inverse optimal PID controller.