Sliding Mode Function Research Articles

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.

SMC for Discrete-Time Networked Semi-Markovian Switching Systems With Random DoS Attacks and Applications

This article concentrates on the discrete-time sliding mode control (DTSMC) problem for uncertain networked semi-Markovian switching systems (S-MSSs) under random denial-of-service (DoS) attacks. The semi-Markovian kernel (SMK) approach is utilized such that the switching among different modes is mutually governed by the transition probability and the sojourn-time distribution function. Considering randomly occurring DoS attacks, a sliding mode function related to the attack probability is constructed to analyze the impact of malicious attacks. Then, sufficient conditions under the equivalent DTSMC law are derived in view of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> -error mean square stability criterion. Furthermore, the synthesis problem of the proposed DTSMC law ensures that the resulting closed-loop system dynamics can be driven onto the prespecified sliding region within a limited time. Finally, an electronic throttle control system is shown to validate the proposed algorithm.

Finite-Set Quasi-Sliding Mode Predictive Control of $ LC$-Filtered Voltage Source Inverters

Three-phase voltage source inverters (VSIs) with output <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ LC$</tex-math></inline-formula> filter are preferred topologies to provide voltage and frequency support for islanded ac microgrids. This article proposes a finite-set quasi-sliding model predictive control (FS-QSMPC) scheme for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LC$</tex-math></inline-formula> -filtered VSIs to improve the output-voltage quality. By explicitly including a predictive sliding-mode function into the cost function, reduced steady-state ripple and enhanced robustness are achieved compared to typical FS-MPC. Besides, theoretical analysis of stability and robustness for FS-QSMPC is given. Analytical tuning of the weighting factor is also derived to decrease the tuning effort. Comparative simulations and experiments verify the presented approach.

Chattering-free nested adaptive terminal sliding mode control for PEMFC air supply system with event-triggered communication

Aiming at the proton exchange membrane fuel cell air supply system subject to time-varying external load, system uncertainty and limited network communication resources, a chattering-free event-triggered nested adaptive terminal sliding mode controller is first developed to achieve the tracking control of oxygen excess ratio. First, an integral terminal sliding mode function with recursive structure is designed to eliminate the reaching phase of sliding mode control and ensure that the high-frequency switching term only appears in the first derivative of control law. Then, to alleviate the communication burden, an event-triggered control strategy is adopted for the controller-to-actuator channel. Furthermore, a nested dual-layer adaptive law is constructed to adaptively update the robust gain without overestimation, so as to counteract the composite disturbance composed of the lumped system uncertainty and event-triggering error, which does not require priori upper bounds of the composite disturbance and its derivative. Besides, it is theoretically proved that the output tracking error can converge to the origin in finite time and the Zeno behavior can be strictly excluded. Finally, the adaptability and superiority of the proposed event-triggered nested adaptive terminal sliding mode controller are fully validated by a series of numerical simulations and comparative analysis.

Periodic Event-Triggered Sliding Mode Control for Switched Uncertain T-S Fuzzy Systems With a Logistic Adaptive Event-Triggering Scheme

This article investigates the periodic event-triggered sliding mode control problem for switched uncertain Takagi–Sugeno (T-S) fuzzy systems with the external nonlinear disturbance. Firstly, to reduce the utilization of the network bandwidth, a logistic event-triggering scheme is designed, and the triggering threshold can be adaptively adjusted based on the current triggering information. Then, for preventing the controller from using the extra information, an auxiliary function known as the triggering sliding mode function is constructed and added into the triggering condition. The T-S fuzzy event-triggered sliding mode controller and the sampling period are designed simultaneously to deal with structured uncertainty. Then, the sufficient criteria of practical stability and the border of the practical sliding mode region around the specified sliding surface are given, respectively. Finally, the effectiveness of the proposed method is showed by a tunnel diode circuit system model.

Research on model identification and compound control of vibration mirror swing scan system

According to the principle of system identification, the least squares algorithm and MATLAB system identification toolbox is used to identify the model of the test bench of the vibration mirror swing scan system with the step signal and the vibration mirror swing-sweep angular displacement as the input and output quantities. Taking the identification model as the object, a sliding mode variable structures composite controller of fuzzy switching gain adjustment is designed. In the controller, according to the actual conditions achieved by the sliding mode, the switching gain is effectively estimated, so as to eliminate the interference of uncertain factors and high-frequency vibration. At the same time, the sliding mode function and sliding mode controller of the system needs to be designed. The switching hyperplane of the system is designed using the fuzzy switching method and the desired dynamic characteristics of the system, to ensure the smooth transition of the system state from outside the hyperplane to the convergence of the switching hyperplane. The simulation results show that: the new composite control method eliminates the shortcomings of PD series control, improves the response speed and tracking accuracy of the vibration mirror swing scan system, and improves the overall performance of the system. And it has a strong ability to inhibit the adverse effects caused by changes in the parameters of the controlled object.

Reinforcement Learning-Based Sliding Mode Tracking Control for the Two-Time-Scale Systems: Dealing With Actuator Attacks

This brief focuses on the security sliding mode tracking control (SMTC) problem for the two-time-scale systems (TTSs) subjected to actuator attacks. All the system parameters are supposed to be completely unavailable to the defenders, and therefore a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -dependent model-free sliding mode function is designed to cope with such a situation. Then, a new SMTC law, consisting of an optimal tracking controller and an attack compensator, is developed to guarantee the tracking performance of TTSs under actuator attacks. Furthermore, a data-driven SMTC strategy is constructed in a model-free approach. More specifically, the developed SMTC algorithm is implemented by the reinforcement learning method by using the slow and fast sampled data simultaneously. It should be pointed out that both the ill-conditioned numerical issue caused by the coupling of slow-fast dynamics is avoided and the actuator attacks are attenuated. Finally, a networked DC motor example demonstrates the proposed algorithm.

A composite sliding-mode observer with PLL structure for a sensorless SPMSM system

To achieve high-precision speed and position control for the surface-mounted permanent magnet synchronous motor (SPMSM), this paper proposes a sensorless vector control strategy based on a composite sliding-mode observer (SMO) and an improved phase-locked loop (PLL) structure. Different from the existing sensorless methods, the proposed control strategy can further improve the accuracy of observation position and speed. First, a new sliding-mode function and the equivalent control are introduced to weaken the chattering and accelerate the reaching rate. Then, a sliding-mode current observer based on an adaptive law control is designed to observe the back electromotive force (back EMF). Meanwhile, the adaptive law can ensure the stability of the system in different states and reduce the system chattering. Second, an adaptive back EMF observer is presented to accurately observe the estimated back EMF. Furthermore, the stability of the two observers is proved by employing the Lyapunov second method. Next, the variable gain PLL with the signal suppressor is used to obtain an accurate rotor position and speed. Finally, the simulations and experiments are implemented to validate the performance of the proposed control strategy, in terms of speed and position tracking as well as anti-disturbance ability.

On Sliding Mode Control for Singular Fractional-Order Systems with Matched External Disturbances

In this paper, we investigate the problem of sliding mode control for singular fractional-order systems that have matched uncertainties. We design an innovative integral sliding mode function and controller based on the normalizable condition. A strict linear matrix inequality-based sufficient condition is obtained for the system’s stability. The normalizable condition is eliminated by updating and developing the control method, and a sufficient and necessary condition is developed for the admissibility of the system. Lastly, verification of our method’s effectiveness is numerically conducted in two instances.

Event‐triggered switching‐dependent integral sliding mode control for networked switched linear systems with unknown nonlinear disturbance

AbstractThis article investigates the event‐triggered sliding mode control problem for uncertain networked switched systems with the external nonlinear disturbance. First, to reduce the utilization of the network bandwidth, a novel mode‐dependent continuous‐time event‐triggering scheme (ETS) including the state triggering error is proposed. A switching‐dependent auxiliary function called the triggering sliding mode function is constructed, which prevents the controller from using the extra information (the continuous state). Then, a novel switching‐dependent integral‐type switching function that depends on the states of the switching instants and includes an exponential term is proposed. Obtaining the boundary of the sliding mode region benefits from the exponential term for continuous‐time systems. Then, an event‐triggered sliding mode controller is designed, which makes the networked switched systems practical stability, and attains the sliding region around the specified sliding surface. When the constant threshold of the triggering scheme is zero, the system state can converge to zero as time goes to infinity. Moreover, it is proved that the Zeno behavior can be avoided under the proposed continuous‐time ETS. Finally, the effectiveness of the proposed method is shown by a switched Chua's circuit system.

A Novel Robust Super-Twisting Nonsingular Terminal Sliding Mode Controller for Permanent Magnet Linear Synchronous Motors

For accurate position tracking and robust control of permanent magnet linear synchronous motor (PMLSM) servo systems against various uncertainties, such as parameter change, load disturbance, friction force, and so on, this article proposes a novel super-twisting nonsingular terminal sliding mode control method based on a high-order sliding mode observer. First, a dynamic model of PMLSM with uncertainties is established. A novel nonsingular terminal sliding mode function combined with the super-twisting algorithm is then proposed to design a robust super-twisting nonsingular terminal sliding mode controller, which ensures the system convergence to the equilibrium state within a finite time, effectively eliminating the chattering phenomenon and improving the system robustness. To further improve the system tracking performance and anti-interference ability, a high-order sliding mode observer is used to estimate the system uncertainties. The effective tracking performance and robustness of the proposed control method are validated by the experimental results.

Discrete‐time extended state observer‐based model‐free adaptive sliding mode control with prescribed performance

AbstractTo tackle the trajectory tracking problem and achieve high control accuracy in many actual nonlinear systems with unknown disturbance, a novel discrete‐time extended state observer‐ (DESO) based model‐free adaptive sliding mode control strategy with prescribed tracking performance is studied, which only relies on the input/output data of the system rather than explicit model information. Firstly, a compact‐form dynamic linearization method is used to reconstruct the discrete‐time nonlinear process, where the time‐varying parameter linearly connected with the control input is obtained by an adaptive method and the unknown nonlinear term is estimated by a DESO. Then, by considering the prescribed performance and using an unconstrained vector transformed from the constrained tracking error, one model‐free sliding mode controller is designed. In addition, a rigorous stability analysis is presented to show the boundedness of the sliding mode function and the prescribed transient‐state and steady‐state performance of the output tracking error. Finally, the simulations with comparing results verify the effectiveness and superiority of the developed control scheme.

Event-triggered-based adaptive sliding mode control for networked linear control systems

This paper investigates the robust stabilization of the adaptive sliding mode control for a class of linear systems subjected to external disturbance via event-triggered communication (ETC) scheme. First, in order to reduce the bandwidth utilization, a discrete ETC scheme is proposed and the networked sliding mode function is derived using the ETC scheme. Based on the derived sliding mode function, a reduced-order networked sliding mode dynamics with communication delay is established. Second, by constructing a Lyapunov–Krasovskii functional (LKF), asymptotic stability and stabilization criteria of the reduced-order sliding mode dynamics are given in the form of linear matrix inequalities. According to the stabilization result, a novel event-triggered-based adaptive sliding mode controller is designed while guaranteeing the reachability of the sliding surface. Finally, simulation results illustrate the effectiveness and merit of the developed method.

Stabilization of two kinds of nonhomogeneous Markovian jump systems via sliding mode control

AbstractIn this article, the stabilization is addressed for the continuous‐time nonhomogeneous nonlinear Markovian jump system (MJS) with parameter uncertainty and stochastic disturbance via sliding mode control (SMC) technique. By using a piecewise homogeneous Markov chain to describe its time‐varying characteristics, the considered nonhomogeneous MJS is established by two kinds of piecewise homogeneous MJSs. After that, an integral sliding mode function is constructed. Then, by applying the SMC theory, two control schemes are proposed to force the states of the piecewise homogeneous MJSs onto the designed sliding surface. Sufficient conditions are given to assure the stochastic stability of the sliding mode dynamics. In addition, the reachability of the system states under the developed SMC law is discussed via Lyapunov stability theory. Lastly, some simulation results are provided to show the effectiveness of the presented SMC methods.

Fuzzy sliding mode control of piezo-driven stage.

The motion stage with flexible hinges as a guiding mechanism can realize nanometer-level precision positioning. This stage uses a piezoelectric (PZT) actuator as the driving unit. In order to describe the mechanical characteristics of this piezo-driven stage, a double-parallel four-bar mechanism based on eight flexible hinges is analyzed. The natural frequency and modal of this stage are analyzed with the finite element method. In order to reduce the hysteresis influence of the PZT actuator, the model parameters based on the Bouc-Wen hysteresis model are identified by using the particle swarm optimization algorithm, and the boundedness of the hysteresis phenomenon is determined by this model. On this basis, the PZT hysteresis is regarded as a disturbance, and a proportional-integral-differential (PID)-type fuzzy sliding mode control (FSMC) is designed. Taking errors and the derivation in the errors as input and the parameters of the PID sliding surface as the output, the fuzzy sliding mode function is constructed. In addition, taking the absolute value of the sliding mode function as the input and the adjustment factor of the switching control as the output, the fuzzy switching control is constructed. Finally, the effectiveness of the FSMC is verified through several experiments.

Adaptive Neural Network Iterative Sliding Mode Course Tracking Control for Unmanned Surface Vessels

In view of the problem of course tracking control of under‐driven USV under complex external environment, the adaptive control law is designed by constructing an iterative sliding mode function and using Lyapunov stability theory on the basis of the kinetic model of ship motion. The RBF neural network control technology and adaptive control technology are integrated into the control algorithm, and the iterative sliding mode heading tracking controller of the unmanned surface ship adaptive‐neural network is designed. The online reinforcement learning of the RBF neural network is carried out by the reinforcement learning algorithm, which enhances the approximation performance of the network. Besides, the particle swarm optimization with shrinkage factor is applied to the optimization for control parameters to enhance the adaptability and robustness of the control system. The performance experiment verifies the effectiveness and practicability of the adaptive iterative sliding mode control algorithm for unmanned surface ships based on reinforcement learning and particle swarm optimization algorithm; meanwhile, comparative tracking experiments verify that the comprehensive performance of the proposed USV’s course tracking control system is better than that of the genetically optimized neural network sliding mode control system. Therefore, the fusion of multiple algorithms can be applied to improve the performance of the control system.

Research on a New Adaptive Integral Sliding Mode Controller Based on a Small BLDC

A new adaptive saturation Integral Sliding Mode Controller (ADSA-ISMC) is presented to solve the speed fluctuation problem caused by a small brushless DC motor (S-BLDC) under variable load. First, according to the characteristics of S-BLDC and Kalman filter, a Kalman-based S-BLDC load disturbance observer is established, and an adaptive integrated sliding mode controller (AD-ISMC) is constructed based on the motor load obtained by the observer. Then, we introduce the saturation function into the input error link of the traditional integral sliding mode function, to propose a new ADSA-ISMC to improve the windup phenomenon produced by the integral sliding mode controller and prove the stability and convergence of the controller by the Lyapunov method. Finally, the experimental results show that the Kalman load disturbance observer can observe the motor load disturbance well. In addition, when a load of S-BLDC changes, many speed control performance indexes of ADSA-ISMC are significantly better than SMC and AD-ISMC. Theoretical analysis and experimental results show that the ADSA-ISMC proposed in this paper shows excellent control performance in S-BLDC speed control.

Adaptive finite-time disturbance observer-based recursive fractional-order sliding mode control of redundantly actuated cable driving parallel robots under disturbances and input saturation

This paper proposed a novel finite-time disturbance observer-based recursive fractional-order sliding mode control (FTRFOSMC) algorithm under disturbances and input saturation for redundantly actuated cable driving parallel robots (RCDPRs). A recursive fractional-order sliding mode surface composed of the fractional-order non-singular fast terminal sliding mode function and an integral term is constructed, and the fast response convergence and high precision tracking performance can be obtained for the recursive characteristics of the proposed sliding mode surface; meanwhile, an auxiliary system is designed to overcome the adverse effects of the input saturation. Then, to compensate the model uncertainty and external disturbances, an adaptive finite-time disturbance observer is developed, and the estimation error can be stabilized in finite-time for unknown bound of the disturbance and its derivative. The stability of the proposed controller was investigated by the Lyapunov stability theory. Finally, numerical simulations with the software of the MATLAB/Simuink are conducted to verify the effectiveness of the proposed controller.

Robust Continuous Model Predictive Speed and Current Control for PMSM With Adaptive Integral Sliding-Mode Approach

Model predictive control has been considered as a potential alternative method in electrical drives. High reliable predictive model design is a research hotspot. To further improve the performance, a robust continuous model predictive speed and current control for PMSM with an adaptive integral sliding-mode approach are put forward. The prediction model is directly derived from the integral slinging-mode surface. By using the self-regulation method control and the amplitude of the sliding-mode function, an adaptive integral sliding-mode predictive control (AISMPC) is designed. The proposed strategy solves the chattering problem of sliding-mode control and improves the dynamics of the system. AISMPC has been carried out on a digital signal processing hardware system. The experimental results validate the excellent tracking performance of the proposed strategy.

Improved sliding mode dynamic matrix control strategy: Application on spindle loading and precision measuring device based on piezoelectric actuator

Spindle workload simulation and precision measurement are important in evaluating the precision of the spindle under different working conditions. Controlling the loading and measuring system accurately is difficult due to the robustness requirements of the controller, the complex dynamic model of the spindle loading system, the difficulty of obtaining system parameters, and the hysteresis of the piezoelectric actuator (PEA). To overcome this challenge, this study refers to the dynamic matrix control (DMC) method and proposes a highly versatile, robust, improved sliding mode DMC predictive controller (ISLDMC). ISLDMC is a non-inverse model control method with strong stickiness and good tracking characteristics. To help the controller achieve good versatility, this study regards nonlinear links, such as hysteresis of PEA, as an unknown disturbance and collects the step response signals of the piezoelectric system as the model state equation. In consideration of the practical application of the piezoelectric system, the prediction function of the state equation is used at the feedforward end of the controller, and the sliding mode function and incremental output are unified at the output end via weighted form optimization. In the feedback part, a variable correction coefficient is introduced into the state equation of the controller to enhance the tracking characteristics of the controller. This improvement is independently verified in a simulation environment. The design method of the controller is provided, the Schur stability of the closed-loop control system is proven. Moreover, the proposed controller is applied to machine tool spindle workload simulation and a precision-measuring device based on piezoelectric actuators. ISLDMC-based displacement-tracking and force-tracking controllers are designed. The experiment showed that the tracking performance and anti-interference, anti-model mismatch, and linear compensation capabilities of ISLDMC are better than those of the DMC controller, PI controller, and controllers from other studies. Furthermore, the linear compensation and anti-disturbance characteristics of the ISLDMC controller with the step response as the state equation are verified through force tracking experiments, which reveal that ISLDMC has good force tracking performance and anti-disturbance and linear compensation characteristics. The effectiveness of the introduction of dynamic correction coefficients is verified through a separate simulation involving displacement tracking and piezoelectric load experiments. The findings confirm that compared with the DMC controller, the ISLDMC controller improves tracking characteristics to a certain extent and has higher robustness.