Fractional Differential Equations

Practical tracking control of linear motor via fractional-order sliding mode

In this article, in order to optimize the dynamic performance of the permanent magnet synchronous motor (PMSM) speed regulation system, a nonlinear speed-control algorithm for the PMSM control systems using sliding-mode control is developed. First, a sliding-mode control method based on a new sliding-mode reaching law (NSMRL) is proposed. This NSMRL includes the system state variable and the power term of sliding surface function. In particular, the power term is bounded by the absolute value of the switching function, so that the reaching law can be expressed in two different forms during the reaching process. This method can not only effectively suppress the inherent chattering, but also increases the velocity of the system state reaching to the sliding-mode surface. Based on this new reaching law, a sliding-mode speed controller (SMSC) of PMSM is designed. Then, considering the large chattering phenomenon caused by high switching gain, an improved antidisturbance sliding-mode speed controller method, called SMSC + ESO method, is developed. This method introduces an extended state observer to observe the lumped disturbance and adds a feedforward compensation item based on the observed disturbances to the SMSC. Finally, simulation and experimental results both show the validity of the proposed control method.

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A New Reaching Law for Antidisturbance Sliding-Mode Control of PMSM Speed Regulation System

In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes for the trajectory tracking problem are proposed with known or unknown upper bound of the system uncertainty and external disturbances. The developed controllers take the advantage of the NFTSM theory to ensure fast convergence rate, singularity avoidance, and robustness against uncertainties and external disturbances. First, a robust NFTSM controller is proposed which guarantees that sliding surface and equilibrium point can be reached in a short finite-time from any initial state. Then, in order to cope with the unknown upper bound of the system uncertainty which may be occurring in practical applications, a new adaptive NFTSM algorithm is developed. One feature of the proposed control law is their adaptation techniques where the prior knowledge of parameters uncertainty and disturbances is not needed. However, the adaptive tuning law can estimate the upper bound of these uncertainties using only position and velocity measurements. Moreover, the proposed controller eliminates the chattering effect without losing the robustness property and the precision. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed control schemes.

Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems.

Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays

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.

Practical Tracking Control of Linear Motor With Adaptive Fractional Order Terminal Sliding Mode Control

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 Grunwald–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.

Discrete-Time Fractional Order Terminal Sliding Mode Tracking Control for Linear Motor

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 modeled as an underactuated system. By decoupling the underactuated 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 subsliding 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.

Fractional-Order Fuzzy Sliding Mode Control for the Deployment of Tethered Satellite System Under Input Saturation

This paper proposes a dual terminal sliding mode control scheme for tracking tasks of rigid robotic manipulators. As a significant novelty, the presented design technique integrates the individual sliding mode surfaces to achieve the finite time convergence of tracking errors utilizing specially designed construct, and accordingly the convergence time is easily obtained due to the integral design. The underactuated issue and input limitation are specially considered in this paper, i.e., the underactuated issue is solved by introducing the hierarchical methodology into the basic dual sliding mode controller. The proposed method can easily combine with the adaptive technique to eliminate the negative effect caused by the input limitation in the rigorous stability analysis. These newly proposed methods also have the characteristics of nonsingularity and chattering suppression, and the effectiveness and high efficiency are verified by stabilizing the motions of the overhead crane and the tracking tasks of the rigid robotic manipulator. Simulation results validate the theoretical analyses about the proposed method.

Zhiqiang Ma

Papers

Practical tracking control of linear motor via fractional-order sliding mode

Practical Tracking Control of Linear Motor With Adaptive Fractional Order Terminal Sliding Mode Control

Discrete-Time Fractional Order Terminal Sliding Mode Tracking Control for Linear Motor

Fractional-Order Fuzzy Sliding Mode Control for the Deployment of Tethered Satellite System Under Input Saturation

Dual terminal sliding mode control design for rigid robotic manipulator