Fixed-Time-Convergent Sliding Mode Control with Sliding Mode Observer for PMSM Speed Regulation.

This paper focuses on the speed control of a permanent magnet synchronous motor (PMSM) for electric drives with model uncertainties and external disturbances. Conventional sliding mode control (CSMC) can only converge asymptotically in the infinite domain and will cause unacceptable sliding mode chattering. To improve the performance of the PMSM speed loop in terms of response speed, tracking accuracy, and robustness, a hybrid control strategy for a fixed-time-convergent sliding mode controller (FSMC) with a fixed-time-convergent sliding mode observer (FSMO) is proposed for PMSM speed regulation using the fixed-time control theory. Firstly, the FSMC is proposed to improve the convergence speed and robustness of the speed loop, which can converge to the origin within a fixed time independent of the initial conditions. Then, the FSMO is used as a compensator to further enhance the robustness of the speed loop and attenuate sliding mode chattering. Finally, simulation and experimental results show that the proposed method can effectively improve the dynamic performance and robustness of the PMSM speed control system.

A Tube Model Predictive Control Method for Autonomous Lateral Vehicle Control Based on Sliding Mode Control.

This paper aims to enhance the lateral path tracking control of autonomous vehicles (AV) in the presence of external disturbances. While AV technology has made significant strides, real-world driving scenarios often pose challenges such as slippery or uneven roads, which can adversely affect the lateral path tracking control and reduce driving safety and efficiency. Conventional control algorithms struggle to address this issue due to their inability to account for unmodeled uncertainties and external disturbances. To tackle this problem, this paper proposes a novel algorithm that combines robust sliding mode control (SMC) and tube model predictive control (MPC). The proposed algorithm leverages the strengths of both MPC and SMC. Specifically, MPC is used to derive the control law for the nominal system to track the desired trajectory. The error system is then employed to minimize the difference between the actual state and the nominal state. Finally, the sliding surface and reaching law of SMC are utilized to derive an auxiliary tube SMC control law, which helps the actual system keep up with the nominal system and achieve robustness. Experimental results demonstrate that the proposed method outperforms conventional tube MPC, linear quadratic regulator (LQR) algorithms, and MPC in terms of robustness and tracking accuracy, especially in the presence of unmodeled uncertainties and external disturbances.

Sliding Mode Fault Tolerant Control for Unmanned Aerial Vehicle with Sensor and Actuator Faults.

The unmanned aerial vehicle (UAV) has been developing rapidly recently, and the safety and the reliability of the UAV are significant to the mission execution and the life of UAV. Sensor and actuator failures of a UAV are one of the most common malfunctions, threating the safety and life of the UAV. Fault-tolerant control technology is an effective method to improve the reliability and safety of UAV, which also contributes to vehicle health management (VHM). This paper deals with the sliding mode fault-tolerant control of the UAV, considering the failures of sensor and actuator. Firstly, a terminal sliding surface is designed to ensure the state of the system on the sliding mode surface throughout the control process based on the simplified coupling dynamic model. Then, the sliding mode control (SMC) method combined with the RBF neural network algorithm is used to design the parameters of the sliding mode controller, and with this, the efficiency of the design process is improved and system chattering is minimized. Finally, the Simulink simulations are carried out using a fault tolerance controller under the conditions where accelerometer sensor, gyroscope sensor or actuator failures is assumed. The results show that the proposed control strategy is quite an effective method for the control of UAVs with accelerometer sensor, gyroscope sensor or actuator failures.

Design and Control of a Polycentric Knee Exoskeleton Using an Electro-Hydraulic Actuator.

An exoskeleton robot helps the wearer with mechanical forces by identifying the wearer's intentions and requires high energy efficiency, sufficient load capacity, and a comfortable fit. However, since it is difficult to implement complex anatomical movements of the human body, most exoskeleton robots are designed simply, unlike the anatomy of real humans. This forces the wearer to accept the robot's stiffness entirely, and to use energy inefficiently from the power source. In this paper, a simple 1 degree of freedom (DoF) structure, which was mainly used in the knees of exoskeleton robots, was designed with a polycentric (multi-axial) structure to minimize the misalignment between wearer and robot, so that torque transfer could be carried out efficiently. In addition, the overall robot system was constructed by using an electro-hydraulic actuator (EHA) to solve the problems of the energy inefficiency of conventional hydraulic actuators and the low load capacity of conventional electric actuators. After the configuration of the hardware system, the sliding mode controller was designed to address the EHA nonlinear models and the uncertainty of the plant design. This was configured as Simulink for the first verification, and the experiment was conducted by applying it to the actual model to demonstrate the performance of the sliding mode control. In this process, an optical rotary encoder was used as the main feedback sensor of the controller. The proposed polycentric knee exoskeleton robot system using the EHA was able to reach the desired target value well despite the presence of many model uncertainties.

Periodic event-based sliding mode tracking control of Euler-Lagrange systems with dynamic triggering.

In this article, we propose the design of a robust tracking controller of perturbed Euler-Lagrange systems (ELSs) based on dynamic event-triggered (DET) sliding mode control (SMC) with periodic evaluation of triggering rule. To ensure robustness, we employ the SMC technique and introduce a dynamic periodic event-triggering strategy to reduce communication frequency significantly. This strategy involves the incorporation of an auxiliary dynamic variable to formulate the event-triggering condition, leading to the generation of sparser triggering instants. An upper bound of the sampling period is also obtained in this design to facilitate the periodic assessment of the event-triggered strategy, alleviating the need for continuous verification of the event condition. This technique is more economical with respect to communication resources and practical than its continuous counterpart due to the relaxation of continuous measurements. The stability of the closed loop system is established using Lyapunov analysis within the dynamically triggered event-based SMC framework. The necessary switching gain for maintaining the stable motion of the sliding variable is derived with the help of Lyapunov analysis. The tracking error is shown to be ultimately bounded, and Zeno-behaviour is excluded to ensure finite sampling. A comparative analysis based on simulation results is included to highlight the effectiveness of the proposed scheme, especially in reducing the network usage in the transient phase of the response while achieving comparable steady-state behaviour. Ultimately, we validate the effectiveness of the proposed algorithm by simulating a two-link manipulator and experimentally implementing it with a one-link manipulator.

Adaptive fractional-order nonsingular terminal sliding mode control and sequential quadratic programming torque distribution for lateral stability of FWID-EVs with actuator constraints.

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes.

A composite sliding mode control with the first-order differentiator and sliding mode observer for permanent magnet synchronous machine.

This paper proposes a composite sliding mode control (SMC) to optimize the tracking performance and the anti-disturbance performance of permanent magnet synchronous machine (PMSM) speed regulation systems. The differential term in the control law can magnify the measurement noise, resulting in more discontinuity. To filter out the high frequency noise and make the control law smoother, the first-order differentiator (FOD) is employed to estimate the speed error and its derivative. Since the feedforward compensation can improve the robustness of the system, a disturbance observer (DOB) based on the sliding mode observer (SMO) is designed to reinforce the dynamic performance under disturbance variation. Under the effect of the feedforward compensation, chattering can be further weakened by decreasing the switching gain appropriately. Finally, the effectiveness of the proposed methods is confirmed by various experimental results.

Fractional-order finite-time sliding mode control for uncertain teleoperated cyber-physical system with actuator fault.

The stability of the teleoperated cyber-physical system with model uncertainty, external disturbance, and actuator fault is addressed in this study by using a suitable fractional-order sliding mode control (SMC) strategy. First, the sliding surface is designed to ensure the better tracking performance of the system. Second, the suggested control method combines SMC with an adaptive strategy to ensure that the system is stable in finite time. Third, neural network (NN) and fuzzy logic system (FLS) are used to estimate the model uncertainty, time-varying delay, external disturbance and unknown coefficient matrices of sliding mode surface, respectively. Finally, the advantages of the proposed control scheme are confirmed by the simulation example.

Design and analysis of ELM-based predefined time sliding mode adaptive controller for PMLM position control under physical constraints.

Achieving accurate position tracking for robotics and industrial servo systems is an extremely challenging task, particularly when dealing with control saturation, parameter perturbation, and external disturbance. To address these challenges, a predefined time convergent sliding mode adaptive controller (PTCSMAC) has been proposed for a permanent magnet linear motor (PMLM). A novel sliding mode surface (SMS) with predefined time convergence PDTC has been constructed, which ensures that the error converges to zero within the prescribed time. The system not only meets the expected performance standards but also has a uniformly bounded motor speed. The trajectory tracking error in SMS is proven to converge to zero within the predefined time. This predefined time stability of the closed-loop system has been demonstrated by using the Lyapunov stability criterion with PDTC. The convergence time (CT) can be arbitrarily set, and the upper bound of it is not affected by the initial value and control parameters of the system. A new updated version of extreme learning machine (ELM) is introduced to approximate the uncertain part of the system based on PDTC. The ELM is also provided with the hyperbolic tangent function to estimate the saturation constraint. This is done by converting the function into a linear function concerning the unconstrained control input variable. Then, based on established stability, a novel sliding mode adaptive controller (PTCSMAC) with predefined time convergence is designed. The convergence time (CT) of the controller is unaffected by the initial conditions as well as the control parameters. The rigorous numerical simulations on the PMLM model with complex disturbances verify the strong robustness and high-precision tracking characteristic of the proposed control law.

Nonlinear robust sliding mode - Backstepping hybrid control for WECS -theoretical design and experimental evaluation.

This paper proposes a new contribution in the field of optimizing control techniques for wind systems to enhance the quality of the energy produced in the grid. Although the Sliding Mode control technique, whether classical or involving the use of artificial intelligence, has shown interesting results, its main drawback lies in the oscillation phenomenon commonly referred to as "chattering." This phenomenon affects the accuracy and robustness of the system, as well as the parametric variation of the system. In this work, we propose a solution that combines two nonlinear techniques based on the Lyapunov theorem to eliminate the chattering phenomenon. It is a hybrid approach between the Backstepping strategy and the Sliding Mode, aiming to control the active and reactive powers of the doubly fed induction generator (DFIG) connected to the electrical grid by two converters (grid side and machine side). This hybrid technique aims to improve the performance of the wind system in terms of precision errors, stability, as well as active and reactive power. The proposed solution has been validated in the Matlab & Simulink environment to assess the performance and robustness of the proposed model, as well as experimentally validated on a test bench using the DSPACE 1104 card. The obtained results are then compared with other techniques, demonstrating a significant improvement in performance.

Nonsmooth funnel transformation function-based discrete-time sliding-mode control with deterministic performance margin for servo systems.

This paper proposes a nonsmooth funnel transformation function-based discrete-time sliding-mode control strategy for the discrete-time servo systems with unknown frictions and disturbances. For obtaining a more accurate discrete-time system model, a filter-based adaptive identification algorithm (FAIA) is introduced, where the unknown measurement noises are considered. Based on the identified system model and a novel discrete-time nonsmooth funnel transformation function (improving the tracking performances), a discrete-time sliding-mode surface is designed to confine the tracking error to a smaller funnel region compared with the predefined one, which has a deterministic performance margin related to the upper bound of the lumped disturbance. Furthermore, selections of steady-state funnel boundary and sliding-mode surface parameter can be guided theoretically according to the upper bound of the lumped disturbance. Experimental results show that the tracking error is guaranteed in the predefined funnel with a deterministic performance margin by using the proposed control strategy.

Sliding-mode anti-disturbance speed control of permanent magnet synchronous motor based on an advanced reaching law.

In order to improve the performance of a permanent magnet synchronous motor (PMSM) speed controller, an advanced reaching law sliding mode control (ASMC) strategy is proposed in this study. The advanced sliding mode reaching law (ASMRL) introduces a power term of the system state and a checkmark function term about the sliding mode function based on the traditional constant-proportional rate reaching law(TSMRL) , and replaces the sign function with a hyperbolic tangent function. A detailed theoretical analysis of the characteristics of the ASMRL is then presented. The theoretical analysis shows that the ASMRL converges to the sliding mode surface more quickly and with less chattering than the TSMRL. In addition, a sliding mode disturbance observer (SMDO) is designed to estimate the total disturbance of the system, and the estimated disturbance is compensated to ASMC. Then the stability of the system with ASMC and the stability of the system with ASMC+SMDO is proved by Lyapunov's theorem. Finally, the proposed control strategy is validated on an experimental platform of PMSM. The experimental results show that the ASMC has a faster convergence speed, smaller chattering, better disturbance rejection performance than the traditional constant-proportional rate reaching law sliding mode control(TSMC), and better performance with the addition of SMDO.

Research on robust fuzzy logic sliding mode control of Two-DOF intelligent underwater manipulators.

This study investigates the independent motion control of a two-degree-of-freedom (Two-DOF) intelligent underwater manipulator. The dynamics model of two-DOF manipulators in an underwater environment is proposed by combining Lagrange's equation and Morison's empirical formulation. Disturbing factors such as water resistance moments, additional mass force moments and buoyancy forces on the intelligent underwater manipulator are calculated exactly. The influence of these factors on the trajectory tracking of the intelligent underwater manipulator is studied through simulation analysis. Based on the design of the sliding mode surface of the PID structure, a new Fuzzy-logic Sliding Mode Control (FSMC) algorithm is presented for the control error and control input chattering defects of traditional sliding mode control algorithm. The experimental simulation results show that the FSMC algorithm proposed in this study has a good effect in the elimination of tracking error and convergence speed, and has a great improvement in control accuracy and input stability.

Self-learning sliding mode control based on adaptive dynamic programming for nonholonomic mobile robots.

This paper proposes a self-learning sliding mode control (SlSMC) strategy with stability guarantee for the trajectory tracking of nonholonomic mobile robots (NMRs) under matched uncertainties, which improves the control performance of NMRs by optimizing the reaching law and the sliding mode surface of SMC as well as retaining the finite-time convergence and the robustness to uncertainties. In the presence of adverse factors such as skidding, slipping and environmental noise, the kinematic model of NMRs is reconstructed and an integral terminal sliding mode controller is designed for the trajectory tracking of NMRs. Then, based on the sliding mode controller, the proposed control strategy formulates the optimization of the SMC's reaching law and the sliding mode surface under stability constraints as two asynchronous optimal control problems with control constraints. Meanwhile, an online continuous-time receding-horizon optimization mechanism based on an actor-critic algorithm is proposed to solve the optimal problems asynchronously and improve online learning efficiency. The stability and the convergence of the proposed strategy are validated both in theory and simulations. Furthermore, extensive contrastive simulation results illustrate that the proposed receding horizon learning-based control strategy outperforms three recent methods in control performance. Finally, experiments of the proposed self-learning SMC strategy are carried out based on a real intelligent vehicle, and the experimental results also verify that the proposed method can meet the actual control needs of NMRs.

Nonlinear adaptive control of magnetic levitation system using terminal sliding mode and integral backstepping sliding mode controllers.

Magnetic levitation (MagLev) system is an unstable, highly non-linear and dynamically fast. These characteristics make it challenging task to design a suitable controller to ensure any object to stay at a certain distance from the electromagnet with negligible error. It can be achieved by generating the required flux with the help of a control input. This suspension of ferromagnetic object in air is achieved by balancing the forces of attraction of gravity and electromagnetic. This makes the system highly vulnerable to external disturbances and parametric uncertainties. The controller must be able to adapt the changing electrical resistance and be robust if the mass of the levitating object for MagLev changes. In this paper, three nonlinear controllers: adaptive terminal sliding mode control (AT-SMC), adaptive backstepping sliding mode (ABS-SMC) and adaptive integral backstepping sliding mode (AIBS-SMC) based controllers have been proposed for tracking the air gap to desired value while maintaining the momentum and flux to desired values. Lyapunov theory has been used for proving the global asymptotic stability of the proposed controllers. For performance analysis, simulations have been carried out using Matlab/Simulink environment, where the proposed controllers have been compared with each other. Among the proposed controllers, AT-SMC gives better performance in terms of transient and overall dynamical response. The effect of parametric variations/uncertainties on all of the proposed controllers has also been examined by varying parametric values, by adding noise and disturbance in the system. Moreover, simulation results for the proposed controllers have also been compared with recently proposed controllers in literature. The physical realization of proposed AT-SMC has been examined with the help of a comparison between simulation results and the controller hardware in loop (C-HIL) experimental results.

Hyperbolic uncertainty estimator based fractional order sliding mode control framework for uncertain fractional order chaos stabilization and synchronization.

This paper formulates a new fractional order (FO) integral terminal sliding mode control algorithms for the stabilization and synchronization of N-dimensional FO chaotic/hyper-chaotic systems, which are perturbed with unknown uncertainties. In order to render closed loop robustness, a novel efficient double hyperbolic functions based uncertainty estimator is developed for the estimation and mitigation of unknown uncertainties. Moreover, a double hyperbolic reaching law comprising of tangent hyperbolic and inverse sine hyperbolic functions is incorporated in the presented control techniques for the practical convergence of various chaotic system states and tracking errors to infinitesimally close to equilibrium. Examples such as FO Lu, FO Chen and FO Lorenz systems are taken to investigate robustness, finite time convergence, tracking accuracy and closed loop stability properties of the devised methodologies. Last but not least, comparative analysis is also carried out between the proposed and prior control techniques through various time domain performances such as settling time, error indices and measure of control energy.

Formation-containment control of multiple underactuated surface vessels with sampling communication via hierarchical sliding mode approach.

The formation-containment control problem of multiple underactuated surface vessels (USVs) is investigated in this paper. A hierarchical sliding mode control strategy is proposed to solve this problem under sampling communication. The proposed control comprises two layers: a local sliding model control layer and a distributed coordination layer. The local control layer is designed to drive each USV tracking the reference trajectories, and the distributed coordination layer is proposed to generate the reference trajectories satisfying the control objective of formation-containment control. To achieve the formation-containment control of the closed-loop multiple USVs, a sufficient condition is obtained by utilizing the Lyapunov stability and eigenvalue analysis. Finally, a simulation result is provided to show the effectiveness of the proposed hierarchical sliding mode approach.

Two-dimensional event-triggered sliding mode control for Roesser model with time delays.

This paper is concerned with the event-triggered sliding mode control (SMC) strategy for the discrete-time two-dimensional (2-D) systems represented by Roesser model with time delays. Firstly, the linear sliding surface functions combined with the event-triggered scheme are constructed for the 2-D Roesser model. Then sufficient conditions are established for the asymptotic stability of the reduced-order sliding mode dynamics and the existence of linear sliding surface functions in terms of linear matrix inequality. Subsequently, the event-triggered sliding mode control law is designed by the Lyapunov function approach to drive the state trajectories of the resultant closed-loop system into a bounded region and maintain there for subsequent time. Finally, a numerical example is given to illustrate the effectiveness of the proposed SMC design method.

An improved method combined SMC and MLESO for impedance control of legged robots' electro-hydraulic servo system.

The electro-hydraulic servo system (EHSS) drives the hydraulic quadruped robot, which has the advantages such as high load capacity, fast response velocity, and powerful motion ability. EHSS of single leg consists of three sets of hydraulic drive unit (HDU), which is the joint driver. As a result, HDU control is the fundamental control of the hydraulic quadruped robot, and it controls the robot's motion performance directly. In order to improve the control accuracy and adaptability to different working conditions of impedance control for HDU, a composite control method combining sliding mode control (SMC) and model-based linear extended state observer (MLESO), which is called SMC-MLESO, is designed in this paper. Firstly, the chattering problem of SMC is improved by designing a novel composite reaching law and adding total disturbance to sliding mode control law. Secondly, the parameters of sliding mode surface are calculated by the optimal control. The parameters of MLESO are calculated by the bandwidth of the controller. And the known model of the system is added to observer to reduce the influence of sensor noise. Finally, comparative experiments show that SMC-MLESO has a good control effect. The maximum error of using SMC-MLESO is 0.101 mm and the biggest change of the maximum error is 36.5% under different working conditions, which is better than PI+Gcp and PI+Gcp+Gfp(The two controllers were designed by the author's previous research, which was published by Journal of the Franklin Institute).

Linear active disturbance rejection control of servo systems via IMC principle with active damping and sliding mode techniques.

In this paper, a new linear active disturbance rejection control (LADRC) is proposed for servo systems based on active damping (AD), internal model control (IMC) and sliding mode control (SMC). The IMC rules are applied to tune the controller gains for a prescribed tracking performance. The AD method injects a virtual damping force into the motion system to actively attenuate disturbances. By deriving the sliding dynamics of IMC, a boundary layer solution of SMC is employed to enhance the robustness of control system. As the improved robust IMC scheme is applied as the controller of LADRC, the uncompensated disturbance of linear extended state observer can be better suppressed. With this method, a higher tracking control accuracy is expected to be obtained in the presence of uncertain dynamics. Theoretical stability was analyzed based on the Lyapunov method. Comparative experiments were conducted on a permanent magnet synchronous motor to validate the superiority of the proposed approach.