This paper proposes a practical adaptive fractional order (FO) terminal sliding mode control (SMC) strategy for tracking control of the linear motor. Compared with conventional fast nonsingular SMC, the proposed approach, with a FO integral sliding surface and the adaptive switching input, can obtain higher convergence precision, even though the motion control system suffers from system uncertainties. The adaptive term is designed to guarantee finite-time high-precision convergence of the sliding mode variable, and meanwhile to degenerate the effect of uncertainties by selecting the proper adaptive gain. Moreover, continuous input due to cancelling the sign term ensures that the motion control system is chattering-free. Finally, to further improve precision, we introduce the super-twisting sliding mode disturbance observer for reducing unknown bounded disturbance, i.e., the quantization noise caused by velocity estimation. Experimental results indicate that the control system with the proposed controller is easily implemented, and has higher tracking precision and considerable robustness to uncertainties compared with the existing controllers.

This paper presents a practical discrete-time fractional order terminal sliding mode (DFOTSM) control strategy for high-precision tracking tasks based on a linear motor. In particular, the practical parametric uncertainties involving sliding friction, uncertain payload, and disturbance in tracking tasks are considered in this paper. Combining Grünwald-Letnikov fractional order definition and terminal sliding mode technique, the proposed method synthesizes a novel DFOTSM control law to drive the sliding mode dynamics into the stable region in finite steps theoretically, even though the system is suffering from uncertainties and disturbances, and the motion on the surface can guarantee higher tracking precision than the conventional discrete-time terminal sliding surface by selecting suitable controller parameters. The theoretical analyses give out the guideline of parameter selection, and experiments are carried out on the linear-motor-based test platform to demonstrate that the proposed controller is easily implemented and can achieve high-precision tracking, fast response, and considerable robustness to uncertainties.

In this paper, a novel fractional-order fuzzy sliding mode control strategy is developed to realize the deployment of the tethered satellite system (TSS) with input saturation. The considered TSS is modelled as an under-actuated system. By decoupling the under-actuated system into two subsystems, a fractional-order and a constrained integer-order sliding surfaces are designed for the actuated and unactuated subsystems, respectively. Then, a new hybrid sliding manifold is obtained by coupling the two sub-sliding surfaces. Adaptive fuzzy algorithm is used to regulate the coupling coefficient in the newly proposed hybrid sliding manifold in order to procure satisfactory performance. Meanwhile, the saturation nonlinearity of control input is also considered. The asymptotic stability of the closed-loop system is demonstrated theoretically. With the existence of fractional order, the presented controller can perform faster and more smooth tether deployment when compared with conventional ones. Finally, the effectiveness and superiority of the proposed control approach are validated by illustrative simulations.

This article proposes a variable structure control with neural network and optimized fractional-order selection policy for the sensorless telerobotic system with uncertain time delay, model uncertainty, fractional calculus numerical approximation bias, and external disturbance. Expanded from the integer-order calculus based on the definition of Caputo and the comparison principle, the Riemann–Liouville-based uniformly ultimately bounded stability is introduced to synthesize the sliding mode control with varying order, and the corresponding neural network based force estimation, which is optimized by the specified order based on the greed algorithm. Combined with the mixed-type error, the proposed hybrid integer-order and fractional-order analysis methodology is capable of guaranteeing the Riemann–Liouville-based uniformly ultimately bounded stability of tracking and synchronization errors under time delay. According to Euler difference, the proposed synthesis method can suppress the combined error in the boundedness of approximating double Euler difference errors. Numerical simulation and experiment of the telerobotic system under the control of the proposed method verify the stability analyses.

This article proposes an adaptive neural-network control scheme for a rigid manipulator with input saturation, full-order state constraint, and unmodeled dynamics. An adaptive law is presented to reduce the adverse effect arising from input saturation based on a multiply operation solution, and the adaptive law is capable of converging to the specified ratio of the desired input to the saturation boundary while the closed-loop system stabilizes. The neural network is implemented to approximate the unmodeled dynamics. Moreover, the barrier Lyapunov function methodology is utilized to guarantee the assumption that the control system works to constrain the input and full-order states. It is proved that all states of the closed-loop system are uniformly ultimately bounded with the presented constraints under input saturation. Simulation results verify the stability analyses on input saturation and full-order state constraint, which are coincident with the preset boundaries.