Second-order Sliding Mode Control Research Articles

Advanced control scheme of doubly fed induction generator for wind turbine using second sliding mode control

This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator(DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC).Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.

The Second-Order Sliding Mode Control Algorithm for Fixed-Time Stability of Nonlinear Systems

The Second-Order Sliding Mode Control Algorithm for Fixed-Time Stability of Nonlinear Systems

A state-constrained second-order sliding mode control for permanent magnet synchronous motor drives

A state-constrained second-order sliding mode control for permanent magnet synchronous motor drives

Evaluation of control techniques for quadcopter UAV attitude tracking

ABSTRACT This paper evaluates the performance of six controllers used for the attitude tracking of the quadcopter. The evaluation is done by testing the tracking performance and robustness of each controller with respect to unknown dynamics, disturbances, gain variations, and noise. These controllers include the well-known Proportional-Integral-Derivative (PID) controller to establish a baseline, the Linear Active Disturbance Rejection Controller (LADRC), the first-order Sliding Mode Controller (SMC), the second-order Super-Twisting SMC (STSMC), the Backstepping Controller (BSC), and synergetic controller. To ensure a fair and systematic evaluation, the parameters of each control method were optimised using a Particle Swarm Optimizer (PSO), incorporating a penalty term to maintain realistic control signals while minimising error. The paper details the control techniques used and describes the optimisation process. The results suggest the superiority of LADRC over the other controllers. In the conclusion section, the paper presents several prospective strategies aimed at enhancing the discussed control techniques.

Passive Super-Twisting Second-Order Sliding Mode Control Strategy for Input Stage of MMC-PET

When the operating state of the power system changes, a modular multilevel converter power electronic transformer (MMC-PET) based on modular multilevel converters cannot perform efficient energy transfer and power conversion under conventional control strategies. To address the above problems, this paper proposes a passive, second-order super-helical sliding mode control strategy for MMC-PET by combining passive control and second-order super-helical sliding mode control with a stronger anti-interference capability. First, a Euler–Lagrange model based on positive and negative sequence separation is established according to the mathematical model of the MMC; second, the model of the system is passively analyzed, and a passive controller is designed according to its passivity, and the passive controller is further optimized by using the super-helical second-order sliding mode control, which improves the overall robustness and interference immunity; finally, the effectiveness and superiority of the super-twisting second-order sliding mode passive control strategy is demonstrated by verifying it through the construction of the MMC-PET simulation model and testing it under various non-ideal working conditions.

Fixed-time second-order sliding mode control for uncertain nonlinear systems subject to non-vanishing mismatched terms

The traditional second-order sliding mode (SOSM) algorithms can only achieve the finite-time regulation for standard integrator sliding mode systems and the convergence time of which is dependent on the system’s initial values and grows as the initial values grow. In this paper, we propose a novel fixed-time SOSM controller whose settling time is bounded by a fixed time independent of the system’s initial values. First, a new sliding mode system subjects to a non-vanishing mismatched term is developed to reduce the input uncertainties and relax the well-defined relative degree assumption. Second, a Lyapunov criterion for practical fixed-time stability with a less conservative convergence time estimation is introduced, based on which a practical fixed-time SOSM controller is designed for the new sliding mode system. Finally, a strict Lyapunov analysis demonstrates that the closed-loop system is globally practically fixed-time stable (GPFxTS). Particularly, if the mismatched term is vanishing, global fixed-time convergence of the sliding variable to zero can be achieved. Buck converter is given as an application.

A novel robust nonlinear optimal second-order sliding mode control scheme for power optimization of wind energy conversion systems

In this article, we propose a novel robust nonlinear optimal second-order sliding mode controller using the homotopy perturbation method (RNOSOSMC-HPM) to maximize wind power capture and minimize the mechanical stress on the drive train. To design the nonlinear optimal controller, the homotopy perturbation method (HPM) is applied to compute the approximate solution of the partial differential Hamilton-Jacobi-Bellman (HJB) equation. Next, the nonlinear optimal controller is combined with a second-order sliding mode controller to create robustness and eliminate chattering. The RNOSOSMC-HPM controller can provide safe wind turbine operation under uncertainties and create a good trade-off between maximizing the wind power captured and attenuating the mechanical loads by minimizing the control input. To investigate the effectiveness of the presented the RNOSOSMC-HPM controller, we compare the results of the proposed method with some existing control schemes in two different scenarios. The results indicate that the RNOSOSMC-HPM controller furnishes desired responses.

Deep reinforcement learning based active surge control for aeroengine compressors

This study proposes an active surge control method based on deep reinforcement learning to ensure the stability of compressors when adhering to the pressure rise command across the wide operating range of an aeroengine. Initially, the study establishes the compressor dynamic model with uncertainties, disturbances, and Close-Coupled Valve (CCV) actuator delay. Building upon this foundation, a Partially Observable Markov Decision Process (POMDP) is defined to facilitate active surge control. To address the issue of unobservability, a nonlinear state observer is designed using a finite-time high-order sliding mode. Furthermore, an Improved Soft Actor-Critic (ISAC) algorithm is developed, incorporating prioritized experience replay and adaptive temperature parameter techniques, to strike a balance between exploration and convergence during training. In addition, reasonable observation variables, error-segmented reward functions, and random initialization of model parameters are employed to enhance the robustness and generalization capability. Finally, to assess the effectiveness of the proposed method, numerical simulations are conducted, and it is compared with the fuzzy adaptive backstepping method and Second-Order Sliding Mode Control (SOSMC) method. The simulation results demonstrate that the deep reinforcement learning based controller outperforms other methods in both tracking accuracy and robustness. Consequently, the proposed active surge controller can effectively ensure stable operation of compressors in the high-pressure-ratio and high-efficiency region.

Practical Event-Triggered Finite-Time Second-Order Sliding Mode Controller Design.

This article proposes a novel event-triggered second-order sliding mode (SOSM) control algorithm using the small-gain theorems. The developed algorithm has global event property in aspects of the triggering time intervals. First, an SOSM controller is designed related to the sampling error of states, and it is proved that the closed-loop system is finite-time input-to-state stable (FTISS) with the sampling error via utilizing the small-gain theorems. Second, combined with the constructed SOSM controller, a new triggering mechanism is proposed depending on the sampling error by designing the appropriate FTISS gain condition. Third, the practical finite-time stability of the closed-loop system is verified. It is shown that the minimum triggering time interval is always a positive value in the whole state space. Finally, the simulation results demonstrate the effectiveness of the developed control method.

Research on Super-Twisting Sliding Mode Voltage Regulation Control of Electric Spring

The traditional control of electric spring (ES) is too complex and lack of robustness, as well as the chattering phenomenon and control accuracy of traditional sliding mode control, a second-order terminal sliding mode control based on super twisting algorithm is proposed. In this paper, the phase plane method is used to establish the mathematical model of ES, solve the state space equation, and regard the AC power supply as a simplified error analysis. Then a second-order sliding mode controller is proposed. The controller parameters are solved to obtain the second-order sliding mode control rate, and the stability is verified. Finally, three groups of comparative simulation experiments were set up by Matlab/Simulink, and the effectiveness of the model was verified by considering the voltage mutation caused by the change of power supply and circuit parameters. Compared with the traditional control method, the proposed control strategy not only ensures the voltage stability, but also improves the control accuracy and the performance of suppressing sliding mode chattering, and has better dynamic response ability.

Trajectory Following Control of an Unmanned Vehicle for Marine Environment Sensing.

An autonomous surface vehicle is indispensable for sensing of marine environments owing to its challenging and dynamic conditions. To accomplish this task, the vehicle has to navigate through a desired trajectory. However, due to the complexity and dynamic nature of a marine environment affected by factors such as ocean currents, waves, and wind, a robust controller is of paramount importance for maintaining the vehicle along the desired trajectory by minimizing the trajectory error. To this end, in this study, we propose a robust discrete-time super-twisting second-order sliding mode controller (DSTA). Besides, this control method effectively suppresses the chattering effect. To start with, the vehicle's model is discretized using an integral approximation with nonlinear terms including environmental disturbances treated as perturbation terms. Then, the perturbation is estimated using a time delay estimator (TDE), which further enhances the robustness of the proposed method and allows us to choose smaller controller gains. Moreover, we employ a genetic algorithm (GA) to tune the controller gains based on a quadratic cost function that considers the tracking error and control energy. The stability of the proposed sliding mode controller (SMC) is rigorously demonstrated using a Lyapunov approach. The controller is implemented using the Simulink® software. Finally, a conventional discrete-time SMC based on the reaching law (DSMR) and a heuristically tuned DSTA controller are used as benchmarks to compare the tracking accuracy and chattering attenuation capability of the proposed GA based DSTA (GA-DSTA). Simulation results are presented both with or without external disturbances. The simulation results demonstrate that the proposed controller drives the vehicle along the desired trajectory successfully and outperforms the other two controllers.

Adaptive Second-order Sliding Mode Control of Electrical Throttles Based on Online Zero-crossing Checking

Adaptive Second-order Sliding Mode Control of Electrical Throttles Based on Online Zero-crossing Checking

Direct yaw moment control of eight-wheeled distributed drive electric vehicles based on super-twisting sliding mode control

This paper proposed a novel direct yaw moment control (DYC) system to enhance vehicle stability and handling performance in various driving conditions and overcome the chattering problem of traditional sliding mode control. Accordingly, a DYC strategy is developed for eight-wheeled DDEVs by utilizing a super-twisting sliding mode (STSM) algorithm. Initially, a three-degrees-of-freedom model, nonlinear tire model, and motor model are established for vehicles. Subsequently, the reference yaw rate is obtained based on the reference model of the vehicle to serve as a control target. The DYC strategy is then established using the error between the actual yaw rate and the reference yaw rate as the input. Moreover, a traditional sliding mode (SM) controller is developed to enhance vehicle stability. A second-order SM controller is designed by incorporating a STSM control algorithm to address the chattering problem associated with traditional SM controllers. The algorithm adaptively adjusts the sliding surface and controls the gains based on the dynamic state of the vehicle. The effectiveness of the proposed control strategy is validated via hardware-in-the-loop simulations.

A generalized super-twisting algorithm-based adaptive fixed-time controller for spacecraft pose tracking

Abstract A generalized super-twisting second-order sliding mode adaptive fixed-time control law, which is used for spacecraft pose tracking in the presence of internal and external uncertainties, is proposed. Lie group SE(3) (for special Euclidean group), which is the configuration space for rigid body motion, is used for modeling the six-degrees-of-freedom dynamics of spacecraft. A fixed-time sliding mode surface is proposed and applied to design an generalized super-twisting sliding mode control law. A novel dual-layer adaption law for the controller is proposed to the ensure the gains varying rapidly with the disturbance. The adaptive second-order sliding mode controller guarantees a uniform exact convergence for the closed-loop tracking control system with less energy consumption. Numerical simulations are performed to demonstrate the excellent performances of the control law.

A Barrier-Function-Based Second-Order Sliding Mode Control With Optimal Reaching for Full-State and Input-Constrained Nonlinear Systems

This paper considers the design of a minimum-time Second Order Sliding Mode Control (SOSMC) method for a class of full state and input constrained nonlinear systems. In this study, to enable the handling of the state and input constraints, a barrier function-based state transformation method is employed to convert the original control problem to an unconstrained control problem. Using the new representation of the system dynamics and the input-state linearization technique, a novel sliding manifold is proposed. Relying on the proposed sliding manifold on the concept of the Robust Fuller's Problem, a second order sliding mode controller is developed to achieve optimal reaching time in the presence of the considered constraints. Furthermore, as a tool for computing the reaching time of the proposed minimum-time SOSMC, a new computational method is developed. To quantify the effects of the constraints on the optimal reaching time, the reaching time of the proposed SOSMC and the unconstrained minimum-time SOSMC methods are compared. Numerical simulations verify the efficacy of the proposed control method making reference, as an illustrative example, to the Duffing oscillator.

Composite Second-Order Sliding Mode and Backstepping Control for Power Pulsation Suppression in Dynamic Wireless Charging

Composite Second-Order Sliding Mode and Backstepping Control for Power Pulsation Suppression in Dynamic Wireless Charging

First-and Second-Order Sliding Mode Control Design for Networked 2-D Systems Under Round-Robin Protocol.

This article investigates the sliding mode control (SMC) problem for a class of uncertain 2-D systems described by the Roesser models with a bounded disturbance. In order to reduce the communication usage between the controller and the actuators, it is supposed that only one actuator node can gain the access to the network at each sampling time along horizontal or vertical direction, where a proper 2-D round-robin protocol is designed to periodically regulate the access token and a set of zero-order holders (ZOHs) is employed to keep the other actuator nodes unchanged until the next renewed signal arrives. Based on a novel 2-D common sliding function, a token-dependent 2-D SMC scheme with first-order sliding mode is appropriately constructed to cope with the impacts from the periodic scheduling signal and the ZOHs. Furthermore, a novel super-twisting-like 2-D SMC scheme with second-order sliding mode is designed to improve the robustness against the bounded disturbance. By resorting to token-dependent Lyapunov-like function, sufficient conditions are obtained to guarantee the ultimate boundedness of the horizontal and vertical states as well as the 2-D common sliding function. For acquiring the optimized gain matrices, two searching algorithms are formulated to solve two optimization problems arising from finding optimized control performance. Finally, two comparative examples are exploited to demonstrate the effectiveness and the advantageous of the proposed first-and second-order 2-D SMC design schemes under round-robin scheduling mechanism.

Design and implementation of a redundant control system for variable speed hydro generators

Hydro plant control system (HPCS) has gained a high level of attention in recent years because of their flexibility, reliability, and easy-to-use. This paper analyzes the performance of a 250 MW doubly-fed induction machine (DFIM) under different speed sensor faults (omission, gain, and saturation) that will clarify the need for technically feasible redundancy. The control redundancy, which consists of fault detection, speed estimation, and reconfiguration circuit, is implemented to enhance the permanence and reliability of the DFIM. The logic-based fault detection technique is implemented to detect the speed sensor fault. A second-order sliding mode controller (SOSMC) based model reference adaptive system (MRAS) estimator is implemented to estimate the rotor speed. The proposed redundancy circuit is modeled for a 250 MW hydrogenerating unit using the MATLAB/Simulink environment. It is observed that the proposed redundancy circuit is robust against uncertainty in the machine parameters. Experimental validation is performed in a scaled-down laboratory prototype. The simulation and experimental results demonstrate the efficacy of the proposed redundancy circuit. Fault detection and reconfiguration of the control redundancy circuit are performed within 20 ms.

Prescribed performance sliding mode control for the PAMs elbow exoskeleton in the tracking trajectory task

PurposeThis study discusses the tracking trajectory issue of the exoskeleton under the bounded disturbance and designs an useful tracking trajectory control method to solve it. By using the proposed control method, the tracking error can be successfully convergence to the assigned boundary. Meanwhile, the chattering effect caused by the actuators is already reduced, and the tracking performance of the pneumatic artificial muscles (PAMs) elbow exoskeleton is improved effectively.Design/methodology/approachA prescribed performance sliding mode control method was developed in this study to fulfill the joint position tracking trajectory task on the elbow exoskeleton driven by two PAMs. In terms of the control structure, a dynamic model was built by conforming to the adaptive law to compensate for the time variety and uncertainty exhibited by the system. Subsequently, a super-twisting algorithm-based second-order sliding mode control method was subjected to the exoskeleton under the boundedness of external disturbance. Moreover, the prescribed performance control method exhibits a smooth prescribed function with an error transformation function to ensure the tracking error can be finally convergent to the pre-designed requirement.FindingsFrom the theoretical perspective, the stability of the control method was verified through Lyapunov synthesis. On that basis, the tracking performance of the proposed control method was confirmed through the simulation and the manikin model experiment.Originality/valueAs revealed by the results of this study, the proposed control method sufficiently applies to the PAMs elbow exoskeleton for tracking trajectory, which means it has potential application in the actual robot-assisted passive rehabilitation tasks.

Quadrotor Position and Attitude Tracking Using Advanced Second-Order Sliding Mode Control for Disturbance

Although sliding mode control (SMC) provides powerful control performance, it exhibits chattering phenomena that can lead to operational issues in quadrotor systems when certain thresholds are reached. To address this limitation, this study introduces second-order sliding mode control (SOSMC), which significantly reduces chattering. Furthermore, a modified version of the SOSMC, called advanced second-order sliding mode control (ASOSMC), is proposed by incorporating an additional term to enhance its control capabilities. The ASOSMC exhibits a stability higher than that of traditional SOSMC during quadrotor flight. We established the stability of the ASOSMC system using a more powerful strict Lyapunov stability analysis instead of the conventional Lyapunov stability employed in SMC. This paper presents the design and performance evaluation of the ASOSMC via simulation and compares it with those of conventional SMC (CSMC) and SOSMC. The simulation results confirm that the ASOSMC offers superior control performance in quadrotor systems.