Practical Time-Delay Control With Adaptive Gains for Trajectory Tracking of Robot Manipulators

This paper presents a practical adaptive time-delay control scheme (ATDC) and then applies it to robot manipulators. The proposed ATDC uses a time-delayed signal to cancel complex nonlinear dynamics and disturbances, and hence to provide a simple structure. The adaptive law of the proposed ATDC is developed to adjust the control gains appropriately while in operation and then to achieve good tracking performance with tolerant fluctuation and fast convergence speed. Such adaptive control gains are shown to have an effect of adding an adaptive auxiliary control to a conventional time-delay control (TDC). Moreover, the proposed ATDC includes a typical sliding-mode control as a second auxiliary control to suppress the time-delay estimation (TDE) errors caused by the time-delayed signal so that robust performance can be achieved. It is shown by the bounded input bounded output stability theory and a Lyapunov approach that the TDE errors are bounded and the tracking errors are uniformly ultimately bounded, respectively. The practical effectiveness of the proposed ATDC, or the synergistic effect of two auxiliary controls, is illustrated in simulations and experiments with robot manipulators.