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), 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 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.

This paper proposes a new adaptive sliding mode control (ASMC) scheme for robot manipulators not only by designing a sliding variable and an adaptive law but also by compensating a time-delay estimation (TDE) error induced by time-delay control (TDC). Based on the operating cycle, because TDC utilizes the previous angular acceleration and input torque for the estimation of the dynamics of the manipulators, TDC produces an inevitable TDE error and this paper compensates the present TDE error by using the previous TDE error. For the ASMC, this paper constructs the sliding variable by additionally utilizing the previous error and its derivative. Also, this paper proposes an adaptive law, which guarantees the positive condition of the adaptive parameter, by using the current adaptive parameter value and the sampling period. For the stability analysis, this paper shows uniformly ultimately bounded (UUB) stability of the sliding variable for the manipulators controlled by the proposed ASMC scheme. The simulation and experimental results present the effectiveness of the proposed control schemes.

In this article, we propose an innovative model-free control (MFC) algorithm using an adaptive model uncertainty estimator (AMUE) that provides stable torque input while allowing more precise control, even in the presence of instantaneous disturbances, such as friction, payload, or trajectory changes. Unlike traditional time-delay estimation (TDE)-based controllers that directly use one-sample delayed signals to estimate unmodeled dynamics and uncertainties, the proposed algorithm achieves better tracking performance by considering not only the one-sample delayed signal but also its gradient with an adaptive gain. Furthermore, the proposed adaptive estimator works well independently of conventional TDE-based controllers, providing a wide range of control gains. This implies that the proposed approach provides the opportunity to strategically improve TDE-based controllers, which have performance limitations caused by conventional TDE technique errors. The proposed algorithm can be easily extended to different TDE-based controllers. Finally, the stability of the AMUE-MFC is guaranteed through the Lyapunov stability theory, and its performance is demonstrated via simulations and experiments with robotic manipulators.

This paper presents a new widely and stably adaptive sliding-mode control (WS-ASMC) with nonsingular terminal sliding variable to enhance the performance in reaching and sliding phases. The proposed WS-ASMC has developed new widely and stably adaptive switching gains (W-ASG and S-ASG). The W-ASG is based on an adaptive law with a fast adaptation rate to appropriately suppress the errors generated by using state information from previous time. Therefore, it provides a fast convergence rate in the reaching phase. The S-ASG is directly designed to be related to the negative magnitude of sliding variables. It helps to enhance the system stability while providing a fast convergence rate from the W-ASG. A nonsingular terminal sliding variable is applied to the proposed WS-ASMC. It has strong attractivity and hence improves the convergence rate in the sliding phase. Additionally, as it exhibits a synergistic effect with the S-ASG, it is a solution to mitigate the problem of the insufficient control torque generated by applying this sliding variable. Based on these benefits, the proposed WS-ASMC can provide precise tracking performance with robustness owing to the synergistic effects of the enhanced reaching and sliding phases. It is shown that the tracking errors are uniformly ultimately bounded. The effectiveness of the proposed control is clearly demonstrated through the simulation of robot manipulators and is compared with that of existing control approaches.

We present a practical adaptive sliding-mode control approach, namely, the strong and stable adaptive sliding-mode control (SS-ASMC), in this paper. There is a significant effort towards addressing the technical challenges associated with the switching gains with two adaptive laws, which are called parent and child adaptive laws. A parent adaptive law helps achieve strong switching gains through fast adaptation rate when sliding variable moves away from the sliding manifold. A child adaptive law updates the parameter of the parent adaptive law, which helps to achieve the switching gains with fast and stable adaptation rate in the vicinity of the sliding manifold. Such switching gains with two adaptive laws provide remarkably precise tracking performance while enhancing the robustness. Besides, to yield desirable closed-loop poles and simplicity of control approach structure, the proposed SS-ASMC approach employs a combination of time-delayed estimation and pole-placement method, which makes it unnecessary to have a rather complete system dynamics. It is shown by the bounded-input-bounded-output stability through the Lyapunov approach, and thus the tracking errors are also proved to be uniformly ultimately bounded. The effectiveness of the proposed SS-ASMC approach is illustrated in simulations with robot manipulators, which is compared with that of the existing control approaches.