Higher Order Sliding Mode Control Research Articles

Prescribed-Time High-Order Sliding Mode Control Subject to Mismatched Terms With Unknown Gain Functions

Prescribed-Time High-Order Sliding Mode Control Subject to Mismatched Terms With Unknown Gain Functions

Multi-motor average deviation coupling control strategy based on hyperbolic convergence law high-order sliding mode control using extended state sliding mode observer

This paper aims to develop a multi-motor synchronous drive control system for the direction of the width of the lifting arm of a catamaran. Firstly, we establish a mathematical model of permanent magnet synchronous motor and introduce the composition of AC servo control systems. We then analyze the sources of control interference in multi-motor drive systems. Based on the mean deviation coupling control strategy of multi-motor synchronous control, we design a speed tracking controller and a speed synchronization controller using hyperbolic convergence law high-order sliding mode control. Then, we design an extended state sliding mode observer to estimate the unmodeled dynamics of the system in real time. We prove the global stability of the controller using Lyapunov stability theory. Finally, the control model is simulated, and the results confirm the effectiveness of the multi-motor synchronization control method based on the hyperbolic convergence law of higher-order sliding mode control. The control method effectively mitigates the jitter associated with traditional sliding mode control and demonstrates improved synchronization and tracking performance.

UOWC Integration with ROVs: A Fiber-Optic Approach for Enhanced Underwater Exploration

Underwater Optical Wireless Communication (UOWC) revolutionizes underwater exploration, leveraging seawater's unique property—reduced absorption of blue-green light. This offers superior advantages over traditional communication methods, providing higher bandwidth and lower latency. This paper explores the integration of UOWC with Remotely Operated Vehicles (ROVs), enhancing data exchange and command capabilities in challenging underwater environments. Seawater's unique properties empower UOWC to outperform acoustic and RF methods, crucial for real-time applications. The study utilizes advanced techniques like Fiber-Optic Communication, High Order Sliding Mode Control, and Hybrid Blockage Detection for ROV integration and control. While the abstract focuses on theory and design, it sets the stage for empirical validations, emphasizing the need for future research to quantify improvements in real-world underwater scenarios

Real-Time HIL Simulation of Nonlinear Generalized Model Predictive-Based High-Order SMC for Permanent Magnet Synchronous Machine Drive

The dynamics of the permanent magnet synchronous motor (PMSM) are described by nonlinear equations, which present challenges. Variations in external factors such as unidentified disturbances (loads) and evolving motor properties add complexity to control efforts. To tackle these intricacies and limitations, a nonlinear control approach is essential. Recent attention has turned to employing predictive control techniques for nonlinear multivariable systems, offering an intriguing avenue for research. In this context, this study introduces a novel hybrid control approach that addresses nonlinearity, parametric fluctuations, and external disturbances. The method combines two essential components: first, the outer loop utilizes high-order sliding mode control (HSMC) to optimize torque and trajectory speed, mitigating chattering phenomena while preserving the PMSM’s convergence and robustness traits. The inner loop, known as the current control, employs the newly developed nonlinear robust generalized predictive control (RNGPC) technique. Importantly, this strategy circumvents the need for direct measurement and observation of external disturbances and parameter uncertainties. The proposed strategy follows a two-phase process. Initially, the reference quadratic current is designed using the electromagnetic torque computed via HSMC, subsequently determining the necessary current to achieve the desired torque. The second phase involves computing the controller law through the robust generalized nonlinear predictive control technique. The approach’s strength lies in its ability to maintain stability and convergence in the face of external disturbances and parameter fluctuations, without necessitating precise measurements or knowledge of the disturbances. To validate the proposed control approach, simulation and experimental tests have been conducted across various operational scenarios. The obtained results demonstrate the method’s robustness against external disturbances and parameter changes while ensuring rapid convergence and reliable performance.

High-order sliding mode control with hyperbolic evaluation function for improving performances of a squirrel-cage induction motor fed by a two-level inverter

High-order sliding mode control with hyperbolic evaluation function for improving performances of a squirrel-cage induction motor fed by a two-level inverter

Passivity and higher-order sliding mode control for doubly-fed induction generation wind power system

To simplify the model of DGIG and improve the robustness, the variable speed and constant frequency (VSCF) DFIG wind power generation systems from the perspective of energy and robustness were studied. It was based on passivity and sliding mode control (SMC) theory. Firstly, the model of DFIG based on Euler-Lagrange (EL) equations was established, so the original DFIG wind turbine system is divided into electrical and mechanical subsystems. For two subsystems, the electrical subsystem was designed. In contrast, the mechanical subsystem is an energy-consuming system and is stable through selecting suitable design parameters. Hence, the system control algorithm is simplified. A high-order terminal SMC was designed to get a faster speed and better robustness for the speed loop. Simulation results show that the proposed controller is simple and effective. It can guarantee the wind power system outputs constant frequency. The motor speed can also track the reference speed quickly, so the performance of the wind turbine system is improved.

Designing a High-Order Sliding Mode Controller for Photovoltaic- and Battery Energy Storage System-Based DC Microgrids with ANN-MPPT

This paper introduces a robust proportional integral derivative higher-order sliding mode controller (PID-HOSMC) based on a double power reaching law (DPRL) to enhance large-signal stability in DC microgrids. The microgrid integrates a solar photovoltaic (SPV) system, an energy storage system (ESS), and DC loads. Efficient DC-DC converters, including bidirectional and boost converters, are employed to maintain a constant voltage level despite the lower SPV output power. An artificial neural network (ANN) generates the optimal reference voltage for the SPV system. The dynamical model, which incorporates external disturbances, is initially developed and based on this model, and the PID-HOSMC is designed to control output power by generating switching gate pulses. Afterwards, Lyapunov stability theory is used to demonstrate the model’s closed-loop stability, and theoretical analysis indicates that the controller can converge tracking errors to zero within a finite time frame. Finally, a comparative numerical simulation result is presented, demonstrating that the proposed controller exhibits a 58% improvement in settling time and an 82% improvement in overshoot compared to the existing controller. Experimental validation using processor-in-the-loop (PIL) confirms the proposed controller’s performance on a real-time platform.

Hierarchical control combined with higher order sliding mode control for integrating wind/tidal/battery/hydrogen powered DC offshore microgrid

Due to the intermittent nature of renewable energy sources, energy storage devices play a key role in achieving power balance for microgrid. To reduce the overall carbon footprint, this paper considers fuel cells and batteries as auxiliary sources with wind and tidal energy as primary sources. A two-stage control system has been designed, which has been subdivided into system-level and local-level control systems. The system-level control includes an energy management system that optimizes load distribution, minimizes system cost, and meets battery state of charge and hydrogen level constraints. To make the microgrid independent and minimize transportation costs, on-site hydrogen production has been deployed using an electrolyzer system. At the local level, a fast reaching law-based terminal sliding mode controller has been implemented for accurate and robust tracking of the references provided by the system-level control. The stability of the proposed framework has been validated using the Lyapunov stability criteria. The proposed 600 V and 400 kW microgrid structure has been realized using MATLAB/Simulink simulations. Furthermore, the effectiveness of the proposed control scheme has been compared with PID and ITSMC in terms of accuracy and robustness under both power deficit and surplus modes. Finally, the real-life efficacy has been validated by utilizing controller hardware-in-loop experiments.

Finite-time high-order sliding mode control of supercavitating vehicle based on perturbation observer

High precision control is one of the most important problems in the research of supercavitating vehicle. Specific motion mode and complicated environmental factors lead to some great challenges in control, such as model uncertainties, strong coupling and nonlinearity, and unknown external disturbances. Under the influence of these factors, effectively ensuring the integrated control of the depth and attitude of the supercavitating vehicle has become a research hotspot. In this paper, a high-order sliding mode control method based on a finite-time convergence perturbation observer is proposed for depth and attitude coordinated control of the longitudinal dynamics model of the supercavitating vehicle. A special sliding mode surface and a novel high-order sliding mode reaching law solve the problem of depth and attitude integrated modeling and control model coupling respectively. For the total perturbation of the system generated by the cavitation shape, the planing force and the wetted rate of the tail fins and unknown external disturbances, a finite-time convergence perturbation observer is designed to observe and compensate it in the control law. The system can be converged in a finite time by the Lyapunov stability method. The simulation results indicate that the supercavitating vehicle can accurately track the depth and attitude command using the proposed control law under the uncertainty, which verifies the robustness of the control system.

Higher Order Sliding Mode Control of MIMO Induction Motors: A New Adaptive Approach

In this paper the objective is to force the outputs of nonlinear nonaffine multi-input multi-output (MIMO) systems to track those of a linear system with the desired properties. The approach is based on designing higher order sliding mode controller (HOSMC) with the definition of a new proportional-integral (PI) sliding surface. To this end, a linear state feedback with an adaptive switching gain (ASG) is applied to the nonlinear MIMO systems. Therefore, the switching gain can increase or decrease based on the system conditions. Then, the chattering is completely removed using a combination of HOSMC and ASG. Moreover, the proposed procedure is independent from the upper bound of the matched uncertainty, which is in the direction of system inputs. The finite time convergence to the sliding surface is also proved, which provides an invariance property in finite time. Note that invariance is the most important property of SMC. Finally, the general model of MIMO induction motors (IM) is used to address and to verify the proposed controller.

Sliding mode control with higher order strategy for buck converter in the presence of dynamic load

The combination of DC-to-DC converters with DC machines for smooth beginning of DC drives has various practical applications. The Buck converter provides smooth start of the DC motor by applying desired voltage in accordance with the control signal. This paper proposes a Higher Order Sliding Mode (HOSM) based control algorithm for the speed control of Permanent Magnet DC (PMDC) motor with Buck converter under different loaded conditions. This control algorithm minimizes the initial peak current and provides smooth speed control with load changes. The performance of proportional integral derivative sliding surface is compared with classical sliding surface for constant load torque through Matlab simulation. In proportional integral derivative sliding surface (PIDSS), the integral component aids in the elimination of steady-state errors in the variable under control. This is especially useful for systems where it is essential to maintain zero steady-state error. Simulation results indicate the performance of the proposed HOSM control algorithm in achieving the required speed and load variations in finite time.

Trajectory tracking of autonomous underwater vehicle under disturbance based on time-delay adaptive high-order sliding mode control

This paper introduces an innovative adaptive generalized super twisting algorithm (AGSTA) controller combined with a time-delay estimator (TDE) to address the trajectory-tracking issue in autonomous underwater vehicles (AUVs) impacted by disturbances. AUVs utilized in underwater exploration often carry sensors, such as Doppler velocity logs, for position and speed determination. However, owing to instrument precision limitations and other factors, these sensors suffer from a slow sampling speed. Furthermore, manual tuning requirement, conventional GSTAs do not provide substantial benefits in real-world applications, adversely affecting AUV position control. To rectify this issue, we proposed a TDE founded on delayed sensor data to estimate the vehicle fluid dynamics, integrated with an AGSTA, to enhance the controller performance. A comprehensive stability analysis of the control system was carried out under these parameters. The effectiveness of the proposed method was demonstrated through simulation results.

Design of sliding mode control with state varying gains for a Benchmark Twin Rotor MIMO System in Horizontal Motion

In this paper, a sliding mode control (SMC) with state-varying gains is proposed to control the yaw orientation of the Twin Rotor MIMO System (TRMS). This proposed SMC algorithm reduces the chattering effect without affecting the properties of the robustness of the sliding modes. The salient feature of this control is that the magnitude of the variable gains depends on the absolute values of the states and tracking error. This design exhibits a relation between first-order and higher-order sliding mode control algorithms. Besides, the developed control strategy does not overestimate disturbances. Hence, the energy utilized by the control effort is reduced significantly. The stability analysis is accomplished by considering the TRMS model in the horizontal plane to illustrate the asymptotic stability condition. Further, a comparison between the twisting algorithm and the proposed control law is highlighted. However, it is evinced that the proposed variable gain SMC is a combination of a twisting algorithm and conventional SMC. Simulations studies are carried out to highlight the efficacies of the proposed controller using MATLAB/Simulink environment.

Event-Triggered Second-Order Sliding Mode Controller Design and Implementation

The paper presents an event-triggered higher-order sliding mode controller design. The event-triggering technique is the alternative approach to real-time controller execution, unlike the classic time-triggering technique, which is not time-dependable and is governed by the triggering policy. The technique is suitable for system resource relaxation in case of computation burden or network usage mitigation. The paper describes the stability analysis of the super-twisted sliding mode controller based on input-to-state stability notation. The stability analysis introduces a triggering policy related directly to the ultimate boundness of the system states and preselected sliding variables. The controller time execution with the selected triggering condition prevents the exhibition of the Zeno phenomena, where the minimal inter-event time of the controller has a positive non-zero lower bound. The minimal value of the inter-event time is related directly to the controller parameters and triggering bound, the selection of which is given with the derived stability conditions regarding the designer’s objective. Preventing the fast nonlinear controller execution, especially close to the sliding manifold, also alleviates the chattering phenomena effectively, which is a primal drawback, and limits the usage of the controller on various systems. The method’s efficiency is verified with the hardware-in-the-loop system, where the dynamic and robustness of the triggering approach are compared to the standard time-triggered execution technique.

High order sliding mode control for restoration of a population of predators in a Lotka-Volterra system.

Human-induced extinction and rapid ecological changes require the development of techniques that can help avoid extinction of endangered species. The most used strategy to avoid extinction is reintroduction of the endangered species, but only 31% of these attempts are successful and they require up to 15 years for their results to be evaluated. In this research, we propose a novel strategy that improves the chances of survival of endangered predators, like lynx, by controlling only the availability of prey. To simulate the prey-predator relationship we used a Lotka-Volterra model to analyze the effects of varying prey availability on the size of the predator population. We calculate the number of prey necessary to support the predator population using a high-order sliding mode control (HOSMC) that maintains the predator population at the desired level. In the wild, nature introduces significant and complex uncertainties that affect species' survival. This complexity suggests that HOSMC is a good choice of controller because it is robust to variability and does not require prior knowledge of system parameters. These parameters can also be time varying. The output measurement required by the HOSMC is the number of predators. It can be obtained using continuous monitoring of environmental DNA that measures the number of lynxes and prey in a specific geographic area. The controller efficiency in the presence of these parametric uncertainties was demonstrated with a numerical simulation, where random perturbations were forced in all four model parameters at each simulation step, and the controller provides the specific prey input that will maintain the predator population. The simulation demonstrates how HOSMC can increase and maintain an endangered population (lynx) in just 21-26 months by regulating the food supply (hares), with an acceptable maximal steady-state error of 3%.

Robust discrete-time super twisting formation protocol for a 6-DOF Quadcopter swarm

This paper contains a discrete-time higher-order sliding mode control for achieving the formation of a 6-Degrees of Freedom (DOF) Quadcopter swarm using the concept of a discrete Multi-agent system (DMAS). A graph theory is used to represent the communication between the Quadcopters and a leader-follower approach of DMAS is used to design the discrete super-twisting (DST) protocol for the formation of a 6-DOF Quadcopter swarm. The DST protocol not only ensures robustness but also reduces the convergence time and the chattering during the formation process of Quadcopters in a swarm. The stability condition of the formation is also derived using the Lyapunov function. The protocol is validated for the formation of 5 Quadcopters in the given pattern. The simulation results show that the formation is achieved in a finite time. Further to show the efficacy of the DST formation protocol, the results are compared with the first-order discrete-time sliding mode controllers designed by switching type reaching law and non-switching type of reaching law. As the first-order discrete-time sliding mode controllers have a significant amount of quasi-sliding mode band (QSMB) in the sliding surface during the operations, the DST protocol of higher-order discrete-time sliding mode control is preferred. From the comparative analysis, it is inferred that the DST protocol performs better for the formation of a 6-DOF Quadcopter swarm.

Integrated optimal control of distributed in-wheel motor drive electric vehicle in consideration of the stability and economy

From the perspective of handling stability and economy, this paper brings forward an integrated optimal control scheme of distributed in-wheel motor drive electric vehicles (IWMDEV). A linear quadratic regulator (LQR) controller is presented according to nominal model and ideal motions firstly. To tackle the uncertain parameters and random disturbance, a novel robust optimal (RO) control strategy is further proposed to design the top level controller by employing the combination of optimal control and high order sliding mode control. By virtue of the integral and terminal sliding mode surface, the resulting robust optimal control method can not only achieve better performance, but also converge in finite time without chattering phenomenon. As for the bottom level controller, an optimal algorithm is developed to determine the weights for each term in objective function of torque allocation dynamically and coordinate the relationship between driving safety and energy-saving performance timely. Finally, joint simulations are carried out. In comparison with LQR control strategy, the results demonstrate that the proposed control scheme could ensure the robustness and effectiveness in the presence of parametric perturbation and external disturbance. Moreover, the torque allocation algorithm, which considers both handling stability and energy consumption, proves to be an effectual approach.

A Discrete-Time Event-Driven Near-Optimal Second-Order SMC for Multirobotic System Formation Prone to Network Uncertainties.

In this article, we propose a novel stochastic event-driven near-optimal sliding-mode controller design for addressing the consensus of a multiagent system in a network. The system is prone to external disturbances and network uncertainties, such as losses and delays of data packets. The randomness of network uncertainties introduces stochasticity in the system. The design starts with the formulation of control-affine dynamics based on a single integrator robot model, formation error, and sliding surface dynamics. An event-triggering condition is then derived for an update of control input for each agent. These input updates guarantee desired consensus in finite time with reaching time of each agent's sliding surface having an upper bound. The admissibility of event-driven near-optimal control updates is also ensured for each agent. The near-optimal control design for each agent has achieved through neural-network-based actor-critic architecture. The implementation of Pioneer P3-DX mobile robots illustrates threefold efficacy of the proposed design: 1) advantages of event-driven approach and higher order sliding mode controller; 2) robustness to network uncertainties; and 3) near-optimality in system performance.

A Passive Decomposition Based Robust Synchronous Motion Control of Multi-Motors and Experimental Verification.

Recently, with the trend of redundancy design, the importance of synchronous motion control of multiple motors has been emphasized in various fields such as automotive, construction, and industrial engineering. Therefore, this paper proposed a novel passive decomposition-based robust synchronous control strategy for a multi-motor system, guaranteeing that both the tracking error of each motor and the synchronous error between motors are ultimately and synchronously bounded, even under the presence of parametric uncertainty and unstructured external disturbance. Specifically, a passive decomposition is used to obtain the locked and shape systems from the original system, and then a sliding mode control system along with robust compensations is designed for each decomposed system to achieve the precise synchronous motion control of the n number of motors. Here, the controller for the locked system reduces the tracking errors of motors for a given desired trajectory, while the controller for the shaped system decreases the synchronous errors between motors. Furthermore, the control system is generally and conveniently formulated to adopt the arbitrary n number of motors that must track a given desired trajectory and be synchronized. Compared to other related studies, this work especially focused on increasing the robustness of the entire system using both high-order sliding mode control and two separate compensation terms for model uncertainty and unstructured external disturbance. Finally, to validate the effectiveness of the proposed synchronous control strategy, the extensive experimental studies on two/three/four-geared BLDC motors with a high dead-zone effect were conducted, and we also compared the synchronous control performance of the proposed control strategy with the other representative control approaches, a master-slave control scheme and an independent one to address the superiority of the proposed control system. Regardless of the number of motors, due to the robustness of the control system, it is found that the proposed control ensures the tracking and synchronous errors are less than 1 degree for the sine-wave trajectory while it guarantees that the errors are below 1.5 degree for the trapezoidal trajectory. This control approach can be widely and generally applied to the multiple motor control required in various engineering fields.

Design of Adaptive Fuzzy Fixed-Time HOSM Controller Subject to Asymmetric Output Constraints

This paper is concerned with the control design of adaptive fuzzy fixed-time high-order sliding mode (HOSM) under asymmetric output constraints. The main objective of the paper is to construct a control scheme to build the HOSM in a fixed time and fulfill the pre-set constraint condition. For this purpose, initially to conquer this obstacle regarding the output constraint, a barrier Lyapunov function is developed to keep the output variable within the predefined constraint during operation. Then, the unknown functional bounds of uncertainties in the considered system are modeled by invoking fuzzy logic systems. With the integrated use of adaptive fuzzy control and backstepping-like techniques, a novel protocol for the fixed-time HOSM control with asymmetric output constraints is developed. Through the strictly theoretical clarification, the HOSM is fixed-time established under the suggested control strategy. The effectiveness of the derived results is eventually testified by some comparative simulation results.