Second-order Sliding Mode Control Research Articles

Sensor Effects in LCL-Type Grid-Connected Shunt Active Filters Control Using Higher-Order Sliding Mode Control Techniques.

The effects of measuring devices/sensors on improving the power quality (PQ) of electric networks are studied in this paper. In this context, improving the performance of an LCL-type grid connected to a three-phase three-wire shunt active filter (SAF) in the presence of voltage perturbations is studied. In order to ensure the high-quality performance of LCL-SAF in the presence of voltage perturbations, the robust continuous second-order sliding mode controller (2-SMC), including twisting and super-twisting controllers, and continuous higher-order sliding mode controller (C-HOSMC)-based approaches are employed. These controllers, whose outputs are processed by pulse-width modulation (PWM), allow minimization of the phase shift and prevent the generation of discontinuous chattering commands, which can severely damage the VSI components. Moreover, an integration of a generalized instantaneous power identification algorithm with an advanced phase locked loop (PLL) was proposed and experimentally tested to validate the effective performances of SAF under severe perturbations. Additionally, the studied approaches were tested via simulations taking into account a conventional nonlinear industrial load in a real textile factory environment, using measurements provided by power quality analyzers. Finally, the effects of the measuring devices, including the current and voltage sensors, on the accuracy and reliability of the SAF and, consequently, on the PQ of the electric power grid were studied via simulations and experimentally. The results of this study support the validity of the recently published patent.

A composite position control of flexible lower limb exoskeleton based on second-order sliding mode

Aiming at the problem that the trajectory tracking error of flexible lower limb exoskeleton robot is too large under the condition of external disturbance and parameters uncertainty, a composite position control method based on second-order sliding mode control was proposed. Firstly, the flexible lower limb exoskeleton robot is modeled by Lagrange function. Secondly, considering that the system is affected not only by matched disturbance but also by unmatched disturbance, two finite time state observers are used to observe and compensate the two disturbances in real time. The super-twisting method is employed in the position control section to ensure that the trajectory tracking error of the knee joint converges to zero in finite time. Finally, the Lyapunov function proves the stability of the suggested control technique. The experimental findings reveal that the suggested control approach has a better trajectory tracking effect and resilience than classic PD control and sliding mode control, indicating its superiority.

Design and Analysis of Rate Predictive Fractional-Order Sliding Mode Controller (RP-FOSMC) for MPPT and Power Regulation of DFIG-based Wind Energy Conversion System (WECS)

Now a days, maximum power point tracking (MPPT), power regulation and transient load reduction are the major issues in the WECSs. To overcome these challenges and to cope with WECS nonlinearity and MIMO nature, nonlinear predictive control algorithms based on Tip-Speed Ratio MPPT (TSR-MPPT) and Rate Predictive Control (RPC) strategies are proposed for the variable speed DFIG-based WECS. The designed control system consists of a FOSMC that is based on fractional-order PID sliding surface model and super-twisting control algorithm (STA) for MPPT through Optimal Torque Control (OTC) algorithm and a Nonlinear-RPC (N-RPC) that is designed based on STA and RPC strategies for power regulation via pitch angle control. FOSMC based on STA improve the dynamics of the controlled system by increasing the degrees of freedom of the sliding surface, minimizing the effects caused by imperfect modelling of nonlinear systems and provide chattering free response of the system and the stability of the designed STA based FOSMC law was proven by Lyapunov criterion. N-RPC is a novel adaptive model-less feedback control algorithm that addresses the limitations of MPC and PID controllers. It limits the power production above rated wind speed and ensure the transient load reduction. The proposed cascaded control algorithms are implemented in a MATLAB/Simulink environment. In this work, the system parameters of Sany SE7715 wind turbine that is installed in Adama-II wind farm, Ethiopia with generating capacity of 1.5 MW is used. The simulation result confirms that the proposed control algorithms achieve optimum power extraction as compared to second-order SMC (2-SMC) and excellent stress reduction in the drive train under variable wind speed. Moreover, they are effective and robust regarding to the application of different external disturbance and sensor noise (i.e., Gaussian & non-Gaussian) and perfectly achieved the required objectives of our investigation.

Distributed time cooperative control of multi-missile systems via second-order sliding mode

Aiming at intercepting hidden aerial targets, a distributed time cooperative system of decoy-attacker heterogeneous missiles is provided. The decoy missiles of the system constrain a hidden target to maneuver. After the target is fully exposed, the decoy missiles will cooperate with the attacker missiles to achieve cooperative interception via sliding mode time cooperative guidance law. Then, a super-twisting second-order sliding mode control eliminates the chattering problem of sliding mode control, and the attacking time convergence of guidance law is verified by the Lyapunov function. Finally, simulation results show that the cooperative system can completely distribute time cooperation in expected conditions and has a good performance in cooperative attacks with an effective interception.

Enhanced Second-Order Sliding Mode Control Technique for a Five-Phase Induction Motor

Recently, several research papers have addressed multiphase induction motor (IM) drives, owing to their several benefits compared to the three-phase motors, including increasing the torque pulsations frequency and reducing the rotor harmonic current losses. Thus, designing a robust controller to ensure the proper operation of such motors became a challenge. The present study reports the design of an effective second-order sliding mode control (SO-SMC) approach for a five-phase IM drive. The proposed control approach finds its strongest justification for the problem of using a law of nonlinear control robust to the system uncertainties of the model without affecting the system’s simplicity. The formulation of the proposed SO-SMC approach is a prescribed process to ensure the stability and proper dynamics of the five-phase IM. A detailed stability analysis is also presented for this purpose. To validate the effectiveness of the proposed controller, the five-phase IM drive is tested under different dynamic situations, including load changes and system uncertainties. The presented numerical results prove the ability of the designed SO-SMC to handle high system nonlinearities and maintain high robustness against uncertainties.

Position and Attitude Tracking of MAV Quadrotor Using SMC-Based Adaptive PID Controller

A micro air vehicle (MAV) is physically lightweight, such that even a slight perturbation could affect its attitude and position tracking. To attain better autonomous flight system performance, MAVs require good control strategies to maintain their attitude stability during translational movement. However, the available control methods nowadays have fixed gain, which is associated with the chattering phenomenon and is not robust enough. To overcome the aforementioned issues, an adaptive proportional integral derivative (PID) control scheme is proposed. An adaptive mechanism based on a second-order sliding mode control is used to tune the parameter gains of the PID controller, and chattering phenomena are reduced by a fuzzy compensator. The Lyapunov stability theorem and gradient descent approach were the basis for the automated tuning. Comparisons between the proposed scheme against SMC-STA and SMC-TanH were also made. MATLAB Simulink simulation results showed the overall favourable performance of the proposed scheme. Finally, the proposed scheme was tested on a model-based platform to prove its effectiveness in a complex real-time embedded system. Orbit and waypoint followers in the platform simulation showed satisfactory performance for the MAV in completing its trajectory with the environment and sensor models as perturbation. Both tests demonstrate the advantages of the proposed scheme, which produces better transient performance and fast convergence towards stability.

Design and control of PV integrated qZS-CMI system with meta heuristic assisted artificial neural network

“Quasi-Z source cascaded multilevel inverter (qZS-CMI) is a rising topology in photovoltaic (PV) power system. This resolves the drawbacks of traditional CMI-oriented PV systems as it has better balanced dc-link voltage”. However, limited works are there for revealing controller design and modeling of qZS-CMI-oriented systems. This work introduces a controller model for a 3-phase qZS-CMI design. Two different phases are exploited in this work. In Phase I, an optimized “Second order Sliding Mode Controller (SoSMC)” is introduced to determine the PV voltage. For current regulation, Phase II uses an "Optimized Proportional Resonant (PR) controller with Artificial Neural Network (ANN)." A new "Fitness Enabled-Rider Optimization Algorithm (FE-ROA)" is used to optimize control gains in both phases. By using the FE-ROA convergence is improved. In Phase II, the suggested FE-ROA is used to train the ANN. The primary goal of phase I is to minimize the discrepancy between the reference and PV voltage, whereas phase II aims to minimize the error between computed and link grid current. As a result, the introduced model achieves "grid-connected current injection," and system-level management improves "Maximum Power Point Tracking (MPPT)." Finally, the effectiveness of chosen methodology is demonstrated using a variety of measures.

The application of a optimal controller for the flexible joint robot

This paper describes the operation of a single Degree of Freedom (DOF) flexible robotic arm by the optimal controller. The derived model is based on Euler- Lagrange approach, while the first and second-order (super twisting) Sliding Mode Control (SMC) is proposed as a nonlinear control strategy. Exploration of a flexible robotic arm with using state-of-the-art controllers is essential for practical applications. This is even more refreshing when these arms have joints that work independently of each other to create a smooth connection between the joints, but it still ensures the natural properties like a real human arm. This system has many similarities with the flexible link system of the MIMO model in its operational state analysis. Control laws must be followed by logical rules in a coherent whole. The next step is to design a controller to fit the structure of the system. The author also compared the use of the above controller with a system without using any controller to determine the effectiveness of using the above controller.

Direct yaw moment control and state observer design for four in-wheel motor drive electric vehicles based on super-twisting algorithm

In order to improve the handling stability for four in-wheel motor drive electric vehicles (4IWMD EVs), a novel direct yaw moment control (DYC) strategy is proposed in this paper. To begin with, the problem formulation is stated by considering modeling errors and external disturbance. To obtain direct yaw moment output, a direct yaw moment controller is given by using conventional sliding mode theory at first. In order to deal with large gains of sign function, which brings severe chattering problem in conventional first-order sling mode (FOSM) control, an improved adaptive second-order sliding mode control strategy is proposed based on super-twisting algorithm (STA) to estimate vehicle model errors and external lumped disturbance. In addition, taking the cost problem in practice into account, an integral sliding mode observer (ISMO) is constructed to estimate and calculate the actual values of sideslip angle indirectly on the basis of STA. Furthermore, a composite control strategy is proposed according to stability analysis, combining adaptive second-order sliding mode controller with ISMO. Eventually, comparative simulations are conducted in Carsim and Simulink. The results show that proposed control strategy can achieve superior tracking performance under the premise of tackling chattering phenomenon, and the response curves are smoother. Meanwhile, the influence of uncertain disturbance proves to be weakened significantly with STA-based scheme while performances of other control strategies are seriously affected, which verifies the robustness and effectiveness of proposed control strategy.

SOSM Controller Design for Output Constrained Systems Subject to Disturbances With Unknown Magnitudes

This brief aims to develop a new second-order sliding mode (SOSM) control method for nonlinear systems subject to output constraints and disturbances with unknown magnitudes. First of all, the problem of output constraint can be solved by proposing a novel barrier Lyapunov function. Then, in order to handle disturbances with unknown magnitudes, we establish an integral dynamics. Based on these, the SOSM control algorithm can be constructed by using the technique of adding a power integrator step by step. The proposed SOSM controller can not only guarantee that the output variable keeps staying within the preset boundary but also deal with disturbances with unknown magnitudes. Finally, the validity of the control scheme is verified through an academic example.

Adaptive Intelligent High-Order Sliding Mode Fractional Order Control for Harmonic Suppression

A second-order sliding mode control (SOSMC) with a fractional module using adaptive fuzzy controller is developed for an active power filter (APF). A second-order sliding surface using a fractional module which can decrease the discontinuities and chattering is designed to make the system work stably and simplify the design process. In addition, a fuzzy logic control is utilized to estimate the parameter uncertainties. Simulation and experimental discussion illustrated that the designed fractional SOSMC with adaptive fuzzy controller is valid in satisfactorily eliminating harmonic, showing good robustness and stability compared with an integer order one.

Tracking and synchronization control strategy of vehicle dual-motor steer-by-wire system via super-twisting SOSMC and MDCS

This paper proposes a novel vehicle dual-motor steer-by-wire (SBW) system to improve the reliability and safety of traditional SBW system. However, the dual-motor SBW system is a strongly coupled, nonlinear and multivariable system, whose biggest challenge is the tracking and synchronization control. In order to improve the tracking and synchronization control performance of dual-motor SBW system, a tracking and synchronization control strategy of vehicle dual-motor SBW system via super-twisting second-order sliding mode control (SOSMC) and mean deviation coupling structure (MDCS) is proposed. Firstly, the steering motor model, rack and pinion model and vehicle dynamics model are established. Then, the angle tracking controller based on super-twisting SOSMC is designed to ensure the robustness and tracking performance of each motor. Next, the MDCS and the angle synchronization controller based on super-twisting SOSMC are proposed to compensate the synchronization error between dual-motor caused by mismatched driving force, external interference and parameter uncertainty. Finally, the simulation analysis is carried out by using Carsim/Simulink and the hardware-in-the-loop experiment is implemented based on the dual-motor experimental platform. The simulation and experimental results verify the effectiveness of the proposed control strategy.

Super‐spiral sliding mode controller design for single‐winding bearingless switched reluctance motor

The strong coupling effect between the torque system and the suspension system of the single-winding bearingless switched reluctance motor (SWBSRM) would result in continuous interference to the system and bring difficulties to the design of the control system. Moreover, strong external disturbances will further reduce the stability of the control system. To improve the anti-disturbance ability and enhance the robustness of the control system of SWBSRM, a design method of the entire control system based on the second-order sliding mode (SOSM) controllers is proposed. The strongly coupled SWBSRM torque system and suspension system are linearised and decomposed through the feedback linearisation method to benefit the design of SOSM controllers. Then, combined with a super-spiral algorithm, the super-spiral sliding mode controllers in the outer loop for torque and suspension system are designed separately. The design of controllers considers the interference caused by the coupling effect and the influence of external disturbance. The range of gain, which can ensure the finite time convergence of the control system is determined through proof of stability. Simulation and experiment results show that the second-order sliding mode controllers have faster response speed and control precision when suppressing coupled interference and strong external disturbance.

Adaptive prescribed performance second-order sliding mode tracking control of autonomous underwater vehicle using neural network-based disturbance observer

For trajectory tracking control problem of autonomous underwater vehicle (AUV) with model uncertainties, unknown nonlinear external disturbances, and input saturation, an observer-based adaptive second-order sliding mode control scheme with prescribed performance is proposed. Firstly, a finite time performance function (FTPF) is constructed to constrain the tracking error to the prescribed precision within the preset finite time, and achieve the prescribed dynamic convergence performance and tracking accuracy. Then, a neural network-based disturbance observer (NNDO) is designed to deal with model uncertainties and external disturbances, respectively. Based on prescribed performance control and sliding mode control technique, an adaptive prescribed performance second-order sliding mode control strategy was proposed. In addition, we construct an auxiliary system to overcome the effect of thrust saturation. Lyapunov method is applied to demonstrate the stability of the closed-loop system. Finally, the validity of the proposed control law is verified by numerical simulations.

Research on the Trajectory Tracking of Adaptive Second-Order Sliding Mode Control Based on Super-Twisting

This article focuses on the trajectory tracking problem in the actuation control section of autonomous vehicles. Based on a two-degrees-of-freedom dynamics model, this paper combines adaptive preview control with a second-order sliding mode control method to develop a new control method. By designing an objective function based on lateral deviations, road boundaries, and the corresponding characteristics of the overall vehicle motion, the method adaptively adjusts the preview time to obtain the ideal yaw rate and then uses a second-order sliding mode control algorithm named Super-Twisting to calculate the steering wheel angle. Combining the low-pass filter with this controller can effectively suppress the chattering caused by the switching of the sliding mode plane while proposing a concept of smoothing based on gradient derivative, the smoothness after filtering is one-seventeenth of that before filtering, whereas the phase plane is used to prove its effectiveness and stability, it can be seen from the phase diagrams that all the state points are in the stable region. A joint simulation model of Matlab/Simulink and Carsim was built to verify the control effectiveness of the controller under the double-shift road, and the simulation results show that the designed controller has good control effect and high tracking accuracy. Meanwhile, the simulation model is also used for other simulations, firstly, simulation comparison tests were carried out with the Model Predictive Control algorithm at speeds of 36 and 54 km/h, compared to the MPC controller, the tacking accuracy of the ST controller has improved to 64.42% and 51.02% at 36 and 54 km/h; secondly, taking simulation of the designed controller against a conventional sliding mode controller based on isokinetic law of convergence, compared to the CSMC controller, the tracking accuracy of the ST controller has improved 41.78% at 54 km/h, and the smoothness of the ST controller is one-nineteenth of that of the CSMC controller; thirdly, carrying out simulations on parameter uncertainties, and replacing parameter uncertainty with Gaussian white noise, the maximum tracking error at 36 and 54 km/h did not exceed 0.3 m, and tracking remains good. Small fluctuations in the steering wheel angle do not affect the normal actuation of the actuator.

Modeling and Second-Order Sliding Mode Control for Lateral Vibration of High-Speed Train With MR Dampers

The lateral vibration of high-speed train reduces the ride stability and passenger comfort. Semi-active suspension system is often adopted to suppress the lateral vibration of trains due to its low cost and low energy consumption in control, where magnetorheological (MR) damper is the main vibration absorber. In this paper, a full model of the controlled system that consists of the 3-degree of freedom train model and the hysteretic MR damper model is first built. Then, a second-order sliding mode (SOSM) controller is designed for the suppression of lateral vibration of train, where the hysteresis and non-hysteresis nonlinearities are addressed simultaneously and rigorously. Finally, comparative simulations are conducted under the excitation of the German low-interference track spectrum. The results show that the proposed controller can suppress the lateral vibration of high-speed train efficiently in the sense that, compared with the passive control, the internal model-based resonant control and repetitive learning control, the suspension ratio of root-mean-square of lateral acceleration is reduced by 96.98%, 35.70% and 10.54%, respectively.

Design and real-time implementation of a robust fractional second-order sliding mode control for an electromechanical system comprising uncertainties and disturbances

The present article evaluates the design, analysis, and implementation of a novel fractional second-order sliding mode control scheme for an uncertain second-order system. The developed controller comprises a fractional-order proportional integral derivative sliding surface. The closed-loop stability analysis is performed by using the Lyapunov theorem. The proposed equivalent and switching control signals have been mathematically evaluated at various scenarios comprising uncertainties and disturbances. Several simulations are investigated by including model uncertainties, measurement noises, and disturbances. In addition, various real-time experiments are conducted with different operating conditions. To this end, a real-time reduced-order approximated model of an electromechanical system is constructed. The controller performance has been compared with a number of control techniques to illustrate the promising features of the proposed fractional-order controller. It can be reported that the transient response of the system, control signals applicability, and disturbance rejection capability are quite satisfactory when compared to recently presented control schemes. As a consequence, it is evident that the control scheme has the ability to reduce the chattering phenomenon and increase the system’s robustness.

Review on Floating Offshore Wind Turbine Models for Nonlinear Control Design

This article proposes a review of the modeling approaches for floating offshore wind turbines (FOWTs) for nonlinear control design. The aerodynamic, hydrodynamic and mooring line dynamic modules for the FOWT have been reviewed to provide an overview of several modeling approaches with their respective features. Next, three control-oriented models from the literature are revisited by presenting their methodological approaches to modeling and identification. These three models cover the three most popular types of FOWTs. Then, the performances of these models are validated with the open fatigue, aerodynamics, structures, and turbulence (OpenFAST) code, and their performances are evaluated according to several criteria. Finally, one of the three models is used to illustrate a nonlinear second-order sliding mode control based on the twisting algorithm to optimize the performance of the FOWT in terms of energy extraction and reduction in the platform pitch oscillation.

Frequency Regulation of Nonlinear Power Systems using Neural Network Observer-Based Optimized Resilient Controller

This study introduces a resilient frequency controller for nonlinear interconnected power systems to counteract endogenous/exogenous system disturbances. A neural network-based observer (NNO) is intended to estimate lumped system disturbances, such as unmodelled dynamics and unknown disturbances. The estimated NNO’s output is incorporated with a second-order sliding mode controller (SOSMC) to minimize chattering in the control effort and improve the nominal performance of the undertaken plant. The design parameters of SOSMC have been optimally identified by applying Harris hawk optimization (HHO), exercising integral error-based objective function. HHO has demonstrated superior tuning capabilities than other well-known optimization methodologies in terms of convergence rate and transient measurements of system outputs. The asymptotic convergence of estimated error and overall stability of the system has been established employing the Lyapunov argument. System outputs are compared with the results reported in the literature to validate the efficacy of the proposed resilient frequency controller. Presented results showcase the mastery of the applied NNO-based SOSMC over its counterparts in weaker chattering, fast disturbance rejection, and a high degree of robustness against endogenous/exogenous disturbances.

Adaptive Second-Order Sliding Mode Control of Buck Converters with Multi-Disturbances

In this paper, a novel adaptive second-order sliding mode (2-SM) control approach, based on online zero-crossing detection, was proposed to solve the problems of the chattering and fixed control gain for buck converters with multi-disturbances. In modeling, the possible parameter perturbations and external disturbances of the converter system were contained. Instead of the traditional first-order sliding mode (1-SM), the twisting algorithm with 2-SM was adopted for the controller design, which could overcome the chattering problem and realize control continuity. Meanwhile, a novel adaptive mechanism was introduced to replace the conventional fixed control gain by time-varying control gain, the idea of which is to calculate the number of the zero-crossing points of the sliding surface online. As a result, the control magnitude of the improved controller could be reduced to a minimal admissible level, and the steady error of the output voltage could converge to the expected value. Furthermore, the robust stability of the converter system with multi-disturbances wads investigated. Comparative simulations and experiments validated the advantages of this paper as offering better robustness and control performance.