Adaptive-Robust Control of a Class of EL Systems With Parametric Variations Using Artificially Delayed Input and Position Feedback

In this paper, the tracking control problem of an Euler–Lagrange system is addressed with regard to parametric uncertainties, and an adaptive-robust control (ARC) strategy, christened time-delayed ARC (TARC), is presented. TARC approximates the unknown dynamics through the time-delayed estimation, and the ARC provides robustness against the approximation error. The novel adaptation law of TARC, in contrast to the conventional ARC methodologies, requires neither complete model of the system nor any knowledge of predefined uncertainty bounds to compute the switching gain, and circumvents the overestimation and underestimation problems of the switching gain. Moreover, TARC only utilizes position feedback and approximates the velocity and acceleration terms from the past position data. The adopted state-derivatives estimation method in TARC avoids any explicit requirement of external low-pass filters for the removal of measurement noise. A new stability notion in the continuous-time domain is proposed considering the time delay, adaptive law, and state-derivatives estimation, which in turn provides a selection criterion for gains and sampling interval of the controller. Experimental results of the proposed methodology using a multiple degrees-of-freedom robot are presented, and improved tracking accuracy of the proposed control law is demonstrated compared with the conventional adaptive sliding mode control.