A Widely Adaptive Time-Delayed Control and Its Application to Robot Manipulators

This paper presents a widely adaptive time-delayed control (WATDC) without imposing any restrictions on allowable control gains to make the most of the advantages of time-delayed control (TDC) and, then, applies the WATDC to robot manipulators. Since the proposed WATDC can provide arbitrarily high gains by using the time-varying bounds of time-delayed estimation errors, it has a room for improving the tracking performance and robustness of the existing stabilizing TDCs that have narrow range of control gains depending on system parameters comprising the inertia of a robot manipulator. Furthermore, the proposed WATDC employs a fast adaptive law to generate wide-ranging and well-timed control gains that depend on the magnitude of tracking errors. In other words, timely adaptation over a wide range of control gains makes the WATDC provide suitable control effort for desirable output responses. Additionally, to suppress unfavorable inherent time-delayed estimation errors arising from one sample delayed measurements, the proposed WATDC works together with a sliding-mode control that has switching gains based on the time-varying bounds of time-delayed estimation errors. In simulations and experiments with robot manipulators, the proposed WATDC has better tracking performance and robustness than the existing TDCs due to a wide range of adaptive control gains and the time-delayed-estimation-error-dependent switching gains.