Cable-driven manipulators exhibit strong nonlinearities and low structural stiffness, which make precise control challenging under time-varying uncertainties and external disturbances. This paper presents a time-delay-estimation (TDE)-based adaptive fractional-order nonsingular terminal sliding mode (AFONTSM) control strategy for cable-driven robots. A robust controller is constructed within a TDE-based model-free framework by combining fractional-order nonsingular terminal sliding mode error dynamics with a fast terminal sliding mode reaching law. The main contribution is a new adaptive law that introduces an adaptive exponential term into the update gain to form a nonlinear adaptive mechanism. This design improves adaptive regulation under different operating conditions by suppressing noise-induced chattering during smooth tracking while preserving or enhancing the adaptive gain during trajectory reversal. Lyapunov analysis proves the ultimate uniform boundedness of the tracking error. Experimental results show that, compared with the baseline method, the proposed controller reduces RMSE by 34.52% and 31.11%, ITAE by 33.79% and 32.97%, and ISCT by 6.69% and 17.77% for the two joints, respectively. Further comparisons with recently reported adaptive laws demonstrate that the proposed law provides faster adaptive response, more stable gain evolution, and improved chattering suppression. Additional payload tests further verify the robustness and repeatability of the proposed method.
This paper proposes a new adaptive fractional-order nonsingular terminal sliding mode control scheme integrated with time delay estimation (AFONTSMC–TDE) for cable-driven manipulators. The proposed AFONTSMC–TDE scheme consists of three key elements: time-delay estimation (TDE), a fractional-order nonsingular terminal sliding mode (FONTSM) manifold, and an adaptive variable-gain reaching law. The TDE utilizes intentionally delayed signals to estimate unknown system dynamics, thereby providing a model-free control framework. The FONTSM manifold ensures fast finite-time convergence while inherently avoiding singularity, and the adaptive reaching law dynamically adjusts control gains to achieve rapid response and effective chattering suppression simultaneously. The tracking error is proved to be uniformly ultimately bounded (UUB) via Lyapunov stability analysis. Finally, the superiorities of the proposed AFONTSMC–TDE scheme are validated through experiments on a cable-driven manipulator, demonstrating significant improvements in tracking accuracy over existing fractional-order sliding mode control methods.
Fei Yan, Jianhua Li, Hua-Wei Han et al.· Proceedings of the Instituti...· 0 citations
An adaptive proximate fixed-time terminal sliding mode control (FTTSMC) based on time-delay estimation (TDE) is proposed to ensure high-precision trajectory tracking of robot manipulators subject to unknown dynamics and external disturbances. The controller employs TDE to reconstruct system dynamics online, requiring only the inertia matrix bounds rather than full precise nominal models. Crucially, it replaces the conventional constant bound assumption for the TDE error with a robust state-dependent one, thereby enhancing robustness against discontinuous disturbances. Rigorous Lyapunov stability analysis confirms the fixed-time convergence of the sliding variable and the proximate fixed-time convergence of the tracking error, providing explicit upper bounds on the convergence time. Comparative simulations and experiments on a SCARA robotic platform demonstrate that the developed strategy maintains transient performance comparable to baseline fixed-time approaches while achieving superior steady-state accuracy. Characterized by a compact structure and low computational complexity, the proposed controller exhibits strong potential for high-performance real-time robotic applications.
This paper addresses the path tracking control problem for intelligent vehicles subject to parametric uncertainties, unmodeled dynamics, and external disturbances. A composite learning-based finite-time nonsingular terminal sliding mode control (CL-FNTSMC) strategy is proposed. Unlike conventional adaptive sliding mode controllers that rely solely on tracking errors for parameter update—and thus require the restrictive persistent excitation condition-the proposed scheme incorporates a serial–parallel estimation model to construct prediction errors, which together with tracking errors drive a composite learning law. This mechanism ensures accurate online estimation of unknown parameters under the significantly weaker interval excitation condition. A nonsingular terminal sliding surface, constructed with a continuously differentiable nonlinear function, guarantees finite time convergence while inherently avoiding singularity. Furthermore, a nonlinear disturbance observer is integrated to estimate and compensate for lumped disturbances in real time, substantially enhancing robustness. Rigorous Lyapunov-based analysis establishes the practical finite time stability of the closed loop system. Comprehensive comparative simulations under aggressive disturbances and significant parametric uncertainties demonstrate that the proposed CL-FNTSMC achieves superior tracking accuracy, faster convergence, and markedly improved disturbance rejection compared with conventional NTSMC, adaptive fast NTSMC, and PID controllers. The results confirm that the proposed framework offers an excellent balance of fast transient response, high steady-state precision, and strong robustness.
Piezoelectric actuator-driven nanopositioning systems offer advantages such as fast response and high resolution. However, owing to inherent hysteresis nonlinearities and external disturbances, achieving both high-speed and high-precision trajectory tracking remains challenging for such systems. Therefore, this paper proposes a reaching-phase free recursive terminal sliding mode control (RPF-RTSMC) based on a modified adaptive Hammerstein disturbance observer-based (MAH-DOB) approach. First, the RPF-RTSMC is designed on the basis of a recursive combination of fast terminal and integral sliding modes. Then, through optimization of the initial value configuration, the convergence of the sliding mode is accelerated. This adjustment enables the system to maintain global robustness capability throughout the entire control process. Furthermore, the MAH-DOB approach is integrated into the RPF-RTSMC for the estimation and compensation of lumped disturbances (e.g., rate-dependent hysteresis and uncertainties), thus improving disturbance rejection and mitigating control chattering. A stability analysis of the composite closed-loop system is performed via Lyapunov theory. Finally, experimental results demonstrate that the proposed method outperforms conventional fast nonsingular terminal sliding-mode controller schemes based on a nonlinear disturbance observer in terms of convergence error suppression and disturbance rejection capability.
Zihao Pan, Hui Tang, Chengsi Huang et al.· Nanotechnology and Precision...· 0 citations
This paper addresses the high-precision trajectory tracking control problem for robotic manipulators operating in uncertain environments by proposing a novel fuzzy adaptive gain-tuning sliding-mode control (FAGT-SMC) algorithm. While conventional sliding-mode control offers strong robustness against matched uncertainties, its fixed-gain switching mechanism inevitably induces severe chattering phenomena, causing actuator wear and performance degradation in practical implementations. To overcome this fundamental limitation, this paper designs an intelligent gain adaptation framework that dynamically regulates the sliding-mode switching gain through a fuzzy inference system. The control system structure integrates a nominal equivalent control component derived from the robotic dynamics model with an adaptively tuned discontinuous switching term. Theoretical analysis establishes global stability through Lyapunov-based methods, proving uniform ultimate boundedness (practical stability) of tracking errors under bounded uncertainties and residual fuzzy approximation errors. The proposed FAGT-SMC algorithm effectively balances robustness and control smoothness; therefore, numerical simulations demonstrate effectiveness for advanced robotic applications requiring both precision and adaptability in dynamic operating conditions.
Jianzhen Zhang, Helin Wang, Kun Wei· Processes· 0 citations
Abstract. This paper proposes a composite control strategy combining a radial basis function (RBF) neural network and super-twisting sliding-mode control for high-precision trajectory tracking of the UR10 manipulator under parameter variations, nonlinear friction, and external disturbances. An RBF network is employed to approximate the lumped unknown nonlinear dynamics online, thereby reducing the equivalent disturbance upper bounds. Simultaneously, a super-twisting robust control term is introduced to compensate for approximation residuals and remaining disturbances, which ensures system robustness while effectively suppressing conventional sliding-mode chattering. Furthermore, a projection-based adaptive law is designed to guarantee the strict boundedness of the network weights. Based on Lyapunov theory, the finite-time convergence of the sliding variable and tracking error is proven. Simulations on a 6-degree-of-freedom UR10 manipulator – incorporating mass/inertia perturbations and Coulomb-viscous friction – demonstrate that the proposed method achieves high-precision tracking with small steady-state errors and smooth, chattering-free control torques, verifying its effectiveness and engineering applicability.
Xiaolei Ma, Cheng-Hu Jing, Kun Zhang et al.· Mechanical Sciences· 0 citations
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