Second-order Sliding Mode Control Scheme Research Articles

Fuzzy logic based sliding surface adjustment of second-order sliding mode controllers

<p>This research work designs a variant of second-order sliding mode control scheme, making use of varying sliding surface inferred using a fuzzy inference system. The varying sliding surface is an effective strategy to improve controller performance. A surface with a relative degree of two is first built by accounting for the uncertainties and perturbances of the system. Thereafter, in order to enhance the dynamics of the system being controlled, a varying sliding surface based on a straightforward double input-single output fuzzy logic inference architecture is proposed. The controller ensures system's reaching conditions, and also the stability and robustness. The designed control scheme is studied in comparison with a sliding mode controller of second order having a constant surface of sliding using SIMULINK based simulation for a nonlinear system. The comparison shows that the proposed strategy exhibits an improved dynamic performance than the conventional sliding mode control of second order having a constant surface of sliding.</p>

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.

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.

A New Efficient Cuckoo Search MPPT Algorithm Based on a Super-Twisting Sliding Mode Controller for Partially Shaded Standalone Photovoltaic System

The impact of Partial Shading Conditions (PSCs) significantly influences the output of Photovoltaic Systems (PVSs). Under PSCs, the Power-Voltage (P-V) characteristic of the PVS unveils numerous power peaks, inclusive of local maxima and a global maximum. The latter represents the optimum power point. Traditional Maximum Power Point Tracking (MPPT) algorithms struggle to track the Global Maximum Power Point (GMPP). To address this, our study emphasizes the creation of a novel algorithm capable of identifying the GMPP. This approach combines the Cuckoo Search (CS) MPPT algorithm with an Integral Super-Twisting Sliding Mode Controller (STSMC) using their benefits to enhance the PVS performance under PSCs in terms of high efficiency, low power losses, and high-speed convergence towards the GMPP. The STSMC is a second-order Sliding Mode Control strategy that employs a continuous control action that attenuates the “chattering” phenomenon, caused when the first-order SMC technique is employed. Indeed, the proposed CS-STSMC-MPPT algorithm consists of two parts. The first one is based on the CS algorithm used for scanning the power-voltage curve to identify the GMPP, and subsequently generating the associated optimal voltage reference. The second part aims to track the voltage reference by manipulating the duty cycle of the boost converter. The proposed CS-STSMC-MPPT algorithm is featured by its strength against uncertainties and modeling errors. The obtained simulation results underline a high convergence speed and an excellent precision of the proposed method in identifying and tracking the GMPP with high efficiency under varying shading scenarios. For comparative purposes, this method is set against the hybrid CS-Proportional Integral Derivative, the conventional CS, the Particle Swarm Optimization, and the Perturb and Observe algorithms under different PSCs, including zero, weak, and severe shading. Simulation conducted in the Matlab/Simulink environment confirms the superior performance of the proposed CS-STSMC-MPPT algorithm in terms of precision, convergence speed, efficiency, and resilience.

Neural network-based adaptive second-order sliding mode control for uncertain manipulator systems with input saturation

In order to solve the trajectory tracking problem for robotic manipulators with dynamic uncertainty, external disturbance and input saturation, a novel second-order sliding mode control scheme based on neural network is proposed in this paper. First of all, a model-based second-order non-singular fast terminal sliding mode controller (SONFTSMC) is designed to overcome the chattering problem under the consideration of uncertain parameters. Then attention is focused on the scenario that all those nonlinear uncertainties are unknown, and a new fuzzy wavelet neural network (FWNN) is designed to estimate those unknown uncertainties via lumping them into one compounded uncertainty. In addition, all parameters in FWNN are adjusted autonomously by using an adaptive method. The proposed second-order non-singular fast terminal sliding mode (SONFTSM) control method not only improves the convergence speed and tracking accuracy of the robotic manipulator, but also enhances its robustness. Finally, the advantages of SONFTSM control strategy over existing sliding mode control methods are verified with comparative simulations.

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.

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.

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.

Multiphase-Based Optimal Slip Ratio Tracking Control of Aircraft Antiskid Braking System via Second-Order Sliding-Mode Approach

This article addresses a novel multiphase-based real-time optimal slip ratio tracking control problem of an aircraft antiskid braking system (ABS) based on the second-order sliding-mode approach. First, a comprehensive dynamic model of an aircraft ABS is established, in which the coupling mechanism of the longitudinal, the vertical, and the pitching dynamics of the aircraft are thoroughly considered. Second, for the aircraft ABS with high nonlinearity, since the measurements of aircraft velocity and acceleration cannot be transmitted to the aircraft ABS in time, the second-order sliding-mode differentiator (SMD) will be designed to estimate them simultaneously. Then, the optimal slip ratio signal, which formulates the maximum friction coefficient, will be updated based on the static friction coefficient model with real-time measured and estimated signals. Furthermore, a novel multiphase-based slip ratio regulation algorithm integrated with the second-order sliding-mode control strategy is proposed on the basis of runway characteristics to track the optimal slip ratio signal, which can not only stop the aircraft faster but prevent the mainwheel from final locking. Finally, the simulation results are presented to demonstrate that the aircraft antiskid braking algorithm proposed in this article can effectively prevent the mainwheel from locking under different runway conditions, and significantly improve the braking efficiency.

Sliding mode observer-based fractional-order proportional–integral–derivative sliding mode control for electro-hydraulic servo systems

This paper proposes an observer-based sliding mode control method for electro-hydraulic servo systems with uncertain nonlinearities, external disturbances, and immeasurable states. The mathematical model is built based on the principle of electro-hydraulic servo systems. Owing to its highly robustness and finite time properties, the sliding mode observer is chosen and designed to estimate the velocity and the equivalent pressure online only using the position feedback. Then, in order to tackle the chattering problem of conventional sliding mode control and increase the control accuracy, a novel second-order sliding mode control scheme is proposed based on the fractional-order proportional–integral–derivative sliding surface and the state observer. The stability of the overall system is proved by Lyapunov theory. Finally, the detailed simulations are conducted, which include the comparative analysis of control performance with other methods and the study of observation performance.

Second-Order Sliding Mode Controller Design with a Larger Domain of Attraction

In this paper, by combining a second-order sliding mode (SOSM) algorithm with the saturation technique, a novel SOSM control scheme has been presented. The feature of the proposed SOSM controller lies that there is a saturation function imposed on the sliding variable, which could significantly enlarge the domain of attraction for the closed-loop system. The geometric method has been utilized to prove that all the sliding variables will be steered to the origin in a finite time. Meanwhile, the relation between the control parameters and the shape of the phase trajectory has also been discussed. Finally, the proposed method has been applied to the tracking control problem for a robotic manipulator.

Cascade Second Order Sliding Mode Control for Permanent Magnet Synchronous Motor Drive

This paper presents a cascade second-order sliding mode control scheme applied to a permanent magnet synchronous motor for speed tracking applications. The control system is comprised of two control loops for the speed and the armature current control, where the command of the speed controller (outer loop) is the reference of the q-current controller (inner loop) that forms the cascade structure. The sliding mode control algorithm is based on a single input-output state space model and a second order control structure. The proposed cascade second order sliding mode control approach is validated on an experimental permanent magnet synchronous motor drive. Experimental results are provided to validate the effectiveness of the proposed control strategy with respect to speed and current control. Moreover, the robustness of the second-order sliding mode controller is guaranteed in terms of unknown disturbances and parametric and modeling uncertainties.

Finite-time stability of an underactuated tethered satellite system

The tethered satellite system has been extensively studied due to its widespread applications for space missions. However, the tether's oscillation draws back the performance of the system, and furthermore this oscillation is governed by an uncontrollable state. In this paper, an adaptive hierarchical second-order sliding mode control scheme is proposed to suppress the oscillation of space tether, and disturbance as well. Based on the dynamics equations, system energy of the tethered satellite system is further studied. A reference sliding variable is addressed to strengthen the coupling between the controllable and uncontrollable state. The proposed second-order sliding control scheme can suppress the oscillation and disturbance effectively, and meanwhile can weaken the control chattering. The closed-loop stability with the addressed references sliding variable is strictly verified via Lyapunov function. Finally, the proposed controller is verified by numerical simulations of both deployment and retrieval. With the comparison of other control scheme shows that the sub-satellite can be deployed and retrieved quickly and stably under the proposed scheme. Furthermore, the simulations in presence of disturbance prove the robustness of the proposed controller.

Extended Second Order Sliding Mode Control for Mismatched Uncertain Systems with Only Output Measurable

Most existing Second Order Sliding Mode Control (SOSMC) approaches are achieved under assumptions that 1) all of state variables must be accessible; 2) the second derivative of all state variables must exist, even though mathematical model of systems uses the first order equations. In this paper, a new adaptive SOSMC scheme is proposed for mismatched uncertain systems in which these above assumptions are required. In this proposed method, only output variables are used in the sliding surface and controller design. The advantage of no need of all state variables in controller design makes the method more useful and realistic since it can be applied to a wider class of systems. Finally, a vertical take-off and landing aircraft at the nominal airspeed of 135~knots is simulated to demonstrate the advantages and effectiveness of the proposed approach.

Development of an adaptive radial basis function neural network estimator-based continuous sliding mode control for uncertain nonlinear systems

In this paper an adaptive neural network (NN)-based nonlinear controller is proposed for trajectory tracking of uncertain nonlinear systems. The adopted control algorithm combines a continuous second-order sliding mode control (CSOSMC), the radial basis function neural network (RBFNN) and the adaptive control methodology. First, a second-order sliding mode control scheme (SOSMC), which is published recently in literature for linear uncertain systems, is extended for nonlinear uncertain systems. Second, an adaptive radial basis function neural network estimator-based continuous second order sliding mode control algorithm (CSOSMC-ANNE) is adopted. In CSOSMC-ANNE control methodology, a radial basis function neural network with adaptive parameters is exploited to approximate the unknown system parameters and improve performance against perturbations. Also, the discontinuous switching control of SOSMC is supplanted with a smooth continuous control action to completely eliminate the chattering phenomenon. The convergence and global stability of the closed-loop system are proved using Lyapunov stability method. Numerical computer simulations, with dynamical model of the nonlinear inverted pendulum system, are presented to demonstrate the effectiveness and advantages of the presented control scheme.

Projective synchronization in fixed time for complex dynamical networks with nonidentical nodes via second-order sliding mode control strategy

This paper is concerned with the global projective synchronization in fixed time for complex dynamical networks (CDNs) with nonidentical nodes in the presence of disturbances. Firstly, in order to realize the fixed-time projective synchronization of CDNs with matched disturbances, the second-order sliding mode is established, and the global fixed-time reachability of sliding manifolds is analyzed. The fixed-time stability of the sliding mode dynamics is also proved analytically based on Lyapunov stability theory. Moreover, the fixed convergence time of both reaching and sliding mode phases can be adjusted to any desired values in advance by the choice of the designable parameters. Secondly, in order to realize the fixed-time projective synchronization of CDNs with mismatched disturbances, a super-twisting-like (STL) controller, which does not require the information of the derivative of the sliding variable, is designed, and the synchronization condition is addressed in terms of linear matrix inequalities (LMIs). By the proposed controllers, continuous control signals can be provided to reduce the chattering effect and improve the control accuracy. Finally, two numerical examples are given to demonstrate the validity of the theoretical results and the the feasibility of the proposed approaches.

Maximum Wind Power Tracking of Doubly Fed Wind Turbine System Based on Adaptive Gain Second-Order Sliding Mode

This paper proposes an adaptive gain second-order sliding mode control strategy to track optimal electromagnetic torque and regulate reactive power of doubly fed wind turbine system. Firstly, wind turbine aerodynamic characteristics and doubly fed induction generator (DFIG) modeling are presented. Then, electromagnetic torque error and reactive power error are chosen as sliding variables, and fixed gain super-twisting sliding mode control scheme is designed. Considering that uncertainty upper bound is unknown and is hard to be estimated in actual doubly fed wind turbine system, a gain scheduled law is proposed to compel control parameters variation according to uncertainty upper bound real-time. Adaptive gain second-order sliding mode rotor voltage control method is constructed in detail and finite time stability of doubly fed wind turbine control system is strictly proved. The superiority and robustness of the proposed control scheme are finally evaluated on a 1.5 MW DFIG wind turbine system.

Finite-Time Attitude Trajectory Tracking Control of Rigid Spacecraft

In this paper, we investigate the finite-time attitude tracking control problem for a rigid spacecraft on the special orthogonal group ( $SO(3)$ ). The exponential coordinates, derived from the exponential and logarithmic maps of Lie group, are utilized to describe the attitude tracking error on $SO(3)$ almost globally unique except for a zero measure set on which the logarithmic map is double valued. To avoid this issue, a novel nonsingular sliding surface is designed to guarantee that the attitude tracking error will never reach the zero measure set and provide fixed-time stability during the sliding phase. Then, a novel continuous second-order sliding mode control scheme is developed to force the system state to reach the desired sliding surface in finite time. The salient feature of the proposed control scheme is that it significantly suppresses the chattering phenomenon. In addition, to address the lack of angular velocity measurements, a finite-time observer is proposed to recover the unknown angular velocity information in finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed control scheme.

Decentralized Sliding Mode Control of Islanded AC Microgrids With Arbitrary Topology

This paper deals with modeling of complex microgrids and the design of advanced control strategies of sliding mode type to control them in a decentralized way. More specifically, the model of a microgrid including several distributed generation units (DGUs), connected according to an arbitrary complex and meshed topology, and working in islanded operation mode, is proposed. Moreover, it takes into account all the connection line parameters and it is affected by unknown load dynamics, nonlinearities and unavoidable modeling uncertainties, which make sliding mode control algorithms suitable to solve the considered control problem. Then, a decentralized second-order sliding mode control scheme, based on the suboptimal algorithm is designed for each DGU. The overall control scheme is theoretically analyzed, proving the asymptotic stability of the whole microgrid system. Simulation results confirm the effectiveness of the proposed control approach.

Outer synchronization of small-world networks by a second-order sliding mode controller

In this paper, we investigate outer synchronization of two small-world dynamical networks via second-order sliding mode control strategy. In particular, based on the coupling feature of the nodes, a message feedback chain is established. And then, the synchronization will be analyzed via pinning some nodes. By means of the second-order sliding mode theory, we propose the effective controller to realize outer synchronization between two small-world networks with a lower cost. Finally, we present some simulations to illustrate the theoretical results.