A PID-Type Robust Input Delay Compensation Method for Uncertain Euler–Lagrange Systems

Robust delay compensation techniques for uncertain nonlinear systems with unknown input delays are, in general, lacking. The result in this brief extends a modified proportional-integral derivative (PID)-type controller that contains a distributed delay term to Euler-Lagrange systems with an unknown constant input delay. Additive disturbances and uncertainties in the nonlinear system were considered in the control development and stability analysis. The stability analysis also hinges upon Lyapunov-Krasovskii functionals that were designed to prove semiglobal uniformly ultimately bounded tracking. Experiments on a 3-degree of freedom robot were performed to depict the performance of the new controller.