Second-Order Sliding Mode Research Articles

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.

Three-dimensional line-of-sight-angle-constrained leader-following cooperative interception guidance law with prespecified impact time

To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight (LOS) angles in Three-Dimensional (3D) space, this paper proposes a 3D leader-following cooperative interception guidance law. First, in the LOS direction of the leader, an impact time-controlled guidance law is derived based on the fixed-time stability theory, which enables the leader to complete the interception task at a prespecified impact time. Next, in the LOS direction of the followers, by introducing a time consensus tracking error function, a fixed-time consensus tracking guidance law is investigated to guarantee the consensus tracking convergence of the time-to-go. Then, in the direction normal to the LOS, by combining the designed global integral sliding mode surface and the second-order Sliding Mode Control (SMC) theory, an innovative 3D LOS-angle-constrained interception guidance law is developed, which eliminates the reaching phase in the traditional sliding mode guidance laws and effectively saves energy consumption. Moreover, it effectively suppresses the chattering phenomenon while avoiding the singularity issue, and compensates for unknown interference caused by target maneuvering online, making it convenient for practical engineering applications. Finally, theoretical proof analysis and multiple sets of numerical simulation results verify the effectiveness, superiority, and robustness of the investigated guidance law.

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

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.

Wave Energy Optimal Control Structure With Second-Order Sliding Mode Tracking: Hardware-in-the-Loop Assessment

Wave Energy Optimal Control Structure With Second-Order Sliding Mode Tracking: Hardware-in-the-Loop Assessment

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.

Perturbed Unicycle Mobile Robots: A Second-Order Sliding-Mode Trajectory Tracking Control

This paper contributes to the design of a second–order sliding–mode controller for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy takes into account the design of two particular sliding variables, which ensure the convergence of the tracking error to the origin in a finite time despite the effect of some external perturbations. The straightforward structure of the controller is simple to tune and implement. The global, uniform and finite–time stability of the closed–loop tracking error dynamics is demonstrated by means of Lyapunov functions. Furthermore, the performance of the proposed approach is validated through some experiments using a QBot2 unicycle mobile robot.

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

Data-driven Second-order Sliding Mode Fault-Tolerant Control for a Class of Discrete-time Nonlinear Systems

The current paper presents a data-driven discrete-time integral second-order sliding mode fault-tolerant control (DISSM-FTC) strategy for a category of discrete-time nonlinear systems. The characteristic of the presented control strategy can be easily implemented because it only employs the system's input and output data model through a partial form dynamic linearization (PFDL) approach. At the same time, the fault diagnosis mechanism employs a time-varying threshold with prescribed performance to decide whether a fault occurs or not. Then, the DISSM-FTC method is presented, and a theoretical analysis ensures the stability of the presented strategy. Finally, the efficiency of the presented approach is confirmed through numerical simulations. In contrast to the previous works, the merits of the DISSM-FTC strategy are: 1) the fault-tolerant control problem is solved for the PFDL data model; 2) a novel fault diagnosis mechanism with prescribed performance is proposed; and 3) a data-driven DISSM-FTC method is first proposed.

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 Novel Selective Harmonic Mitigation PWM Technique With THD Minimization Using Second-Order Sliding Modes

A Novel Selective Harmonic Mitigation PWM Technique With THD Minimization Using Second-Order Sliding Modes

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

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.

Discrete Second Order Sliding Mode Control for Fractional Order Hammerstein System

This study explores the control of discrete fractional order Hammerstein systems using first-order sliding mode control (FOSMC) and improves its performance by integrating second-order sliding mode control (2SMC). Two simulation examples are presented to assess the effectiveness of these techniques. Results indicate that 2SMC performs better than FOSMC, demonstrating its superiority in controlling these complex systems and offering promising advancements in control strategies.

A Composite Super-Twisting Sliding Mode Approach for Platform Motion Suppression and Power Regulation of Floating Offshore Wind Turbine

The floating platform motion of an offshore wind turbine system can exacerbate output power fluctuations and increase fatigue loads. This paper proposes a new scheme based on a fast second-order sliding mode (SOSM) control and an adaptive super-twisting extended state observer to suppress the platform motion and power fluctuation. Firstly, an affine nonlinear model of the floating wind turbine pitch system is constructed. Then, a fast SOSM pitch control law is adopted to adjust the blade pitch angle, and a new adaptive super-twisting extended state observer is constructed to achieve total disturbance observation. Finally, simulations are conducted under two cases of wind and wave conditions based on FAST (fatigue, aerodynamics, structures, and turbulence) and MATLAB/Simulink. Compared with the traditional proportional integral (PI) control scheme and standard super-twisting control scheme, the platform roll under the proposed scheme is reduced by 13% and 4%, and pitch is reduced by 16% and 3% in Case 1. Correspondingly, the roll is reduced by 9% and 15%, and pitch is reduced by 7% and 1% in Case 2. For the tower top pitch and yaw moment, load reductions of 7% and 3% or more are achievable compared with those under the PI control scheme. It is indicated that the proposed scheme is more effective in suppressing floating platform motion, stabilizing output power of the wind turbine system, and reducing tower loads.

PSO Tuning of a Second-Order Sliding-Mode Controller for Adjusting Active Standard Power Levels for Smart Inverter Applications

In recent years, due to their ability to supply electricity in isolated places where building electrical transmission networks are expensive, Microgrids (MGs) have gained much attention. A new technology called smart inverters (SIs) is currently implemented in inverter-based MGs. SIs are designed to regulate energy under given standards for connecting inverters to the grid. The closed-loop control of SIs technology is still under study and improvement due to several challenges in fields such as stability and reliability. This paper proposes a DQ control for active power regulation on a single-phase voltage source inverter (SPVSI) using a second order sliding mode control (SMC-2) for addressing the abovementioned concerns. The SMC-2 tuning is performed by a metaheuristic algorithm known as particle swarm optimization (PSO). Moreover, to simulate domestic MGs, the SPSVI operation for tracking active power values is performed by ramp rate references based on standard IEEE Std 1547-2018 for inverters connected to the grid. The SMC-2 was appropriately tuned by a PSO algorithm through MATLABTM and the system simulation through PSCADTM. The results show that the algorithm performed better compared to a classical algorithm such as proportional-integral control in terms of integral absolute error (IAE) and integral square error (ISE).

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.

Cascade Control of Grid-Connected NPC Converters via Sliding Mode Technique

This paper proposes a two-stage control strategy including an adaptive sliding mode control (ASMC) and a nonlinear high-gain observer (HGO) for the three-level neutral-point-clamped (NPC) converter in dc microgrids. In the outer loop, an ASMC is utilized to regulate the dc-link voltage. By introducing an adapted gain, the tradeoff between the chattering and dynamic performance of the classic sliding mode control is overcome, thus the transient response of the NPC converter can be further enhanced without increasing the chattering. In addition, a nonlinear HGO is cooperated with the ASMC method to reject exogenous disturbance for the NPC converter, which not only assures a high disturbance rejection capacity but also accommodates the inevitable measurement noise in the actual applications. For the inner loop, in consideration of the parameter uncertainty, a high-gain observer-based second-order sliding mode (SOSM) control is adopted to assure the steady state performance and the robustness of the NPC converter. Finally, a set of comparative experimental results confirm the effectiveness and superiority of the proposed control scheme implemented in the NPC converter. Additionally, the robustness under parameter variation of the proposed method is also validated.