Performance Limitation and Autotuning of Inverse Optimal PID Controller for Lagrangian Systems

The PID trajectory tracking controller for Lagrangian systems shows performance limitation imposed by inverse dynamics according to desired trajectory. Since the equilibrium point cannot be defined for the control system involving performance limitation, we define newly the quasiequilibrium region as an alternative for equilibrium point. This analysis result of performance limitation can guide us the autotuning method for PID controller. The quasiequilibrium region is used as the target performance of autotuning PID trajectory tracking controller. The autotuning law is derived from the direct adaptive control scheme, based on the extended disturbance input-to-state stability and the characteristics of performance limitation. Finally, experimental results show that the target performance can be achieved by the proposed automatic tuning method.