Higher Order Sliding Mode Research Articles

First and High Order Sliding Mode Control of a DFIG-Based Wind Turbine

Wind energy has many advantages, because it does not pollute and is an inexhaustible source of energy. In this paper, we study the dynamical behavior of the Horizontal Axis Wind Turbine (HAWT) with MPPT (Maximum Power Point Tracking) algorithm and a pitch control, using a Doubly Fed Induction Generator (DFIG). The DFIG stator is directly linked to the grid; the rotor is connected via a back-to-back converter. To ensure a maximal power extraction, we use the MPPT algorithm combined with a PI controller to generate the maximum power and to force the system to work at the maximum operation point. The pitch control is used to protect the Wind Turbine (WT) against high wind speed. Field Oriented Control (FOC) based on a Sliding Mode (SM) first order and high order (super-twisting) are compared. These schemes control the stator active and reactive powers as well as the stator power factor and improve the power quality injected in the grid. Simulations illustrate the active and reactive power control of the HAWT by adjusting the rotor voltages of the DFIG. We choose the two rotor currents to define the sliding surfaces, in order to avoid the measurement of the electromagnetic torque and stator active and reactive powers. Adequate simulations results with Matlab-Simulink of the whole system including the MPPT algorithm, pitch control and SM controllers are presented and discussed.

High Order Sliding Mode Backstepping Control for a Class of Unknown Pure Feedback Nonlinear Systems

This paper aims at addressing the problem of finite time exact tracking control for a class of unknown nonlinear systems in pure feedback form while guaranteeing the closed-loop stability. The uncertain nonlinear system considered in this paper is not only in completely non-affine form but also explicitly dependent on the time and therefore, can cover a general class of nonlinear systems. By incorporating high order sliding mode controller into backstepping design procedure, a new robust control scheme with novel integrators is proposed, which is able to steer the tracking error to zero. Moreover, the closed loop stability can be proved with the help of the constructed integrators in every design step. Two simulation examples are presented to illustrate the correctness and effectiveness of the proposed control scheme.

High-Order Sliding Modes Based On-Line Training Algorithm for Recurrent High-Order Neural Networks

Abstract This work presents a discrete on-line training algorithm for recurrent high-order neural networks (RHONN). The proposed training algorithm is based on the arbitrary order differentiators of high-order sliding modes (HOSM) theory. Due to HOSM-based differentiators can approximate derivatives in finite time, the proposed training algorithm avoids the compute of the derivatives, unlike conventional training algorithms. The proposed HOSM-based algorithm is implemented for the training of a RHONN identifier, and its performance is compared with the results using the extended Kalman filter (EKF) training algorithm. Results of a implementation of the identifier for the Lorenz system and an implementation of the identifier for a tracked robot using experimental data are presented.

Robust Output-Feedback Control in a Dynamic Positioning System via High Order Sliding Modes: Theoretical Framework and Experimental Evaluation

Despite being an established and mature technology, Vessel Dynamic Positioning Systems are always in focus for the development of novel control applications in order to increase their operational capacities. Rapid and robust transient response without loss of control accuracy is, for instance, a requirement for autonomous operations. Standard technologies currently applied by the industry lack such properties. Emerging methods, such as nonlinear robust control techniques, may help to achieve this goal. This paper proposes using a Super-Twisting Controller, allied with a High Order Sliding Mode Observer to perform the Dynamic Positioning Task. This method provides the robustness of standard Sliding Modes Controllers while keeping accuracy and chattering suppression. A novel nonlinear sliding manifold and wave-frequency filtering is proposed for the Dynamic Positioning problem. The efficacy of this control structure is demonstrated in a series of experimental tests, whereby the subject vessel is controlled while disturbed by wave action.

Globally Fixed-Time High-Order Sliding Mode Control for New Sliding Mode Systems Subject to Mismatched Terms and Its Application

High-order sliding mode (HOSM) control is used for output regulation of uncertain systems with known relative degree. Yet, the traditional HOSM algorithm can only achieve finite-time output regulation for standard integrator sliding mode systems, whose settling time depends on system initial conditions. In this article, first, we extend the standard sliding mode system to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the uncertainties in input channel and/or relax the well-defined relative degree assumption. Second, the conventional constant upper bounds assumption is relaxed to time-varying functions, which enables us to obtain a globally convergent controller. Finally, for the new sliding mode system under the new global assumption, we propose a novel fixed-time HOSM controller whose settling time can be predefined and is free of system initial conditions. In addition, strict Lyapunov analysis is provided to show that the new sliding mode system under the proposed controller and the new global assumption is globally fixed-time stable. An application to buck converter is given to show the effectiveness of the proposed controller.

Higher Order Sliding Mode Control Using Discontinuous Integral Action

In this article, we propose a novel family of higher order sliding mode (HOSM) controllers with discontinuous integral term for a class of single-input–single-output (SISO) nonlinear systems. They belong to a recently introduced class of controllers, named continuous HOSM since they are able to compensate exactly and in finite-time perturbations/uncertainties using a continuous control signal. They are obtained by introducing a discontinuous integral action at the input of the plant. Here, continuously differentiable Lyapunov functions are used to rigorously prove the stability of the closed-loop system. We also investigate an approximation of this strategy, where a continuous integral term replaces the discontinuous one. The robustness properties of the closed-loop controller with continuous and discontinuous integral term are studied.

Global High-Order Sliding Mode Controller Design Subject to Mismatched Terms: Application to Buck Converter

This paper studies the high-order sliding mode (HOSM) control for a general class of uncertain nonlinear systems. Firstly, the standard sliding mode system is extended to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the system uncertainties in the control channel and relax the well defined relative degree assumption. Secondly, the conventional constant upper bounds assumption is relaxed to time-varying positive functions, which enables us to obtain a global result. For the new sliding mode system under the new global assumption, a novel HOSM controller, that has a simple relay polynomial form, is then proposed. By introducing a new continuous component in the controller, the discontinuous component of the controller only needs to be selected to suppress the uncertainties and thus a controller with minimal discontinuous component magnitude can be implemented. Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented.

Robustness vs Chattering-effect study for the Sliding Mode Control

In Sliding Modes control literature, a popular paradigm says that the so called “chattering-effect” (undesirable mechanical vibrations on the plant under control) can be reduced or even removed at all without affecting the control robustness. Nevertheless, results of practical implementations support that this is not necessarily true. In this work, the actual behaviour of a class of high order Sliding Modes used as the control law for a Multiple-Input Multiple-Output system is presented, where the real performance of system robustness is studied when the chattering-effect change in magnitude. In this study, to achieve the chattering reduction, the Super-Twisting algorithm is used, and the plant to control is a 3-DoF robot arm. The results of this work show that when techniques to reduce the chattering-effect are utilized, the corresponding reduction in system robustness should also be taken into account, and that achievements of theoretical concepts must be bounded when they are implemented in practical applications.

A New Class of Uniform Continuous Higher-Order Sliding Mode Controllers

Abstract This paper proposes a new class of uniform continuous higher-order sliding mode algorithm (UCHOSMA) for the arbitrary relative degree systems. The proposed methodology is a combination of two controllers where one of the components is a uniform super-twisting control which acts as the disturbance compensator and the second part gives the uniform finite time convergence for the disturbance free system. This algorithm provides uniform finite time convergence of the output and its higher derivatives using an absolutely continuous control signal and thus alleviating the chattering phenomenon. The attractive feature of the proposed controller is that irrespective of the different initial conditions, the control is able to bring the states of the system to the equilibrium point uniformly in finite time. The effectiveness of the proposed controller has been demonstrated with both simulation and experimental results.

High-order sliding mode control of DFIG under unbalanced grid voltage conditions

This paper proposes a novel high-order sliding mode (HOSM) based control methodology for direct power control (DPC) of doubly-fed induction generator (DFIG) wind turbine which is operating under unbalanced grid voltage conditions. Firstly, a set power quality enhancement strategies are presented, incorporating six power compensation schemes corresponding to six selective control targets in both steady and variable speed conditions. Meanwhile, the DFIG output powers are regulated with the proposed HOSM-DPC scheme, wherein a super-twisting algorithm is employed to cope with the chattering phenomenon and simplify the controller structure. The Lyapunov function method is utilized to decide the stability region of the controller parameters. Experiments and simulations are conducted to prove the validity and the performance of HOSM-DPC, where the DPC method with lookup table and the first order sliding mode based DPC are incorporated for comparison purpose. The experimental tests fully reveal the effectiveness of HOSM-DPC in power quality improvement subjected to unbalanced grid voltage conditions, and the superior performance of HOSM-DPC in dynamic response, chattering phenomenon elimination and variable wind speed operation are also validated.

Data fusion based improved HOSM observer for smart structure control

The benefit of data fusion in improving the performance of Higher Order Sliding Mode (HOSM) observer is brought out in this paper. This improvement in the performance of HOSM observer, resulted in the improvement of active vibration control of a piezo actuated structure, when controlled by a Discrete Sliding Mode Controller (DSMC). The structure is embedded with two piezo sensors for measuring the first two vibrating modes. The fused output of sensors is applied to the HOSM observer for generating state estimates, these states generated are applied to the DSMC, designed for the fourth order linear time invariant model of the structure. In the simulation study, the structure is excited at the first and second mode resonance. It is found that better vibration suppression is obtained, when the states generated by the fused output of sensors is applied as controller input, than the vibration suppression obtained by applying the states generated by using individual sensor output. The closed loop performance of DSMC obtained with HOSM observer is compared with the closed loop performance obtained with the conventional observer. Results obtained shows that better vibration suppression is obtained when the states generated by HOSM observer is applied as controller input.

Generalized Model Reference Adaptive Control by Means of Global HOSM Differentiators

In this paper, we combine a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains with classical model reference adaptive control (MRAC) schemes to solve the relevant and yet open problem of trajectory tracking via output feedback of uncertain plants with arbitrary relative degree in a simple-closed form for the control design. The gains of the differentiator are adapted through state-norm observers for the unmeasured state, whereas the control parametrization explores the input–output filters commonly used in the MRAC design. Global asymptotic stability and robust exact tracking are rigorously demonstrated. Simulations highlight the claimed properties as well as the remarkable simplicity of the proposed adaptive control system using robust exact differentiators when compared to more involved alternatives found in standard approaches. The theoretical results are also illustrated with an application to bilateral teleoperation.

A New Control Strategy of 5-Phase PM Motor under Open-Circuited Phase Based on High Order Sliding Mode and Current References Real-Time Generation

The high quality of electrical power in high power and high reliability applications is a crucial necessity even under fault mode function. However, in these conditions, the quality of the torque is a key feature. To overcome this problem, the multiphase permanent magnet (PM) motors seems to be a very attractive choice. In order to highlight the robustness and reliability of this technology, this paper investigates the control of a five-phase PM motor under an open circuited phase fault conditions. Moreover, a High Order Sliding Mode (HOSM) controller combined to an optimal reference current generation is tested and compared to a PID controller under fault mode conditions. This original control strategy is proposed for faulted conditions. Compared to classical fault tolerant control, this strategy allows a better dynamic tracking of the non-sinusoidal reference currents and leads to a smooth torque with minimal losses even in severe fault conditions. To validate the proposed control strategy, simulation, and experimental results are presented and discussed.

Vision-Based CubeSat Closed-Loop Formation Control in Close Proximities

Abstract A vision based formation and attitude controller has been derived and simulated for the formation keeping of two 3U CubeSats. Four markers are installed on the leader CubeSat. Two cameras are installed on the follower CubeSat. An efficient vision based pose estimation method is used to estimate the pose of the follower with respect to the leader. A Higher-Order Sliding Mode (HOSM) exact differentiator with finite-time convergence is derived to estimate the rate of the follower’s pose parameters. The follower’s pose and its time rate are fedback to HOSM formation and attitude controllers to correct any gradual drift in formation and pose of the follower. The simulations show the effectiveness of the approach, and its feasibility on existing hardware.

Omnidirectional mobile robot robust tracking: Sliding-mode output-based control approaches

This work deals with the robust position tracking control problem for an omnidirectional mobile robot. To this aim, four continuous Sliding-Mode Control strategies are presented. The position and orientation of the platform are assumed to be the only available information about the system. To implement the controllers as output-feedback controllers, a High-Order Sliding-Mode Observer is implemented for each output signal. The proposed robust control strategies are able to deal with some classes of external disturbances. The closed-loop stability of each controller is proved by means of Lyapunov functions and homogeneity concepts. Simulations and experiments validate the applicability of the proposed controllers.

On the renovation and analysis of high order sliding mode approaches with application to robotic systems

Variable structure control (VSC) approaches have been widely used to study nonlinear or ill-defined systems. While sliding mode methods can enhance the system robustness, a chattering phenomenon degrades system performances. In order to reduce this phenomenon appearing on the control law, several concepts have been proposed, particularly those called high order sliding mode (HOSM) approaches. In this paper, a renovated theorem of HOSM based on high order procedures has been presented, aiming to improve and to simplify the implementation of HOSM controllers. As the stability of dynamical systems is a fundamental requirement for its practical value, an original proposal for developing general forms of the Lyapunov equation matrices has been demonstrated for high orders of sliding modes, which are essential for the HOSM stability analysis-based Lyapunov theory. Simulation results present control comparisons between motion control behaviours of a robotic system controlled by the proposed HOSM approaches.

High-order sliding mode control for variable speed PMSG wind turbine based disturbance observer

This paper introduces a model-based control system for variable speed wind energy conversion system (VSWECS)-based permanent magnet synchronous generator (PMSG). Comparing to traditional wind turbines operating methods, these variable speed systems have the advantages of increasing the energy capture and reducing the mechanical stress. In order to exploit this latest advantage, a high order sliding mode (HOSM) control strategy has been developed to enhance system performances, ensure the maximum power point tracking (MPPT) and track the generator reference speed. Moreover, for the WT system, the turbine torque is considered as an immeasurable disturbance. Therefore, using a modified disturbance observer will allow direct tracking of the maximum power point. The stability analysis of the system has been proved using the Lyapunov theory. Finally, simulation results have been presented to verify the proposed approach efficiency.

High-order sliding mode control for variable speed PMSG-wind turbine-based disturbance observer

This paper introduces a model-based control system for variable speed wind energy conversion system (VSWECS)-based permanent magnet synchronous generator (PMSG). Comparing to traditional wind turbines operating methods, these variable speed systems have the advantages of increasing the energy capture and reducing the mechanical stress. In order to exploit this latest advantage, a high order sliding mode (HOSM) control strategy has been developed to enhance system performances, ensure the maximum power point tracking (MPPT) and track the generator reference speed. Moreover, for the WT system, the turbine torque is considered as an immeasurable disturbance. Therefore, using a modified disturbance observer will allow direct tracking of the maximum power point. The stability analysis of the system has been proved using the Lyapunov theory. Finally, simulation results have been presented to verify the proposed approach efficiency.

A Novel Robust Finite-Time Trajectory Control With the High-Order Sliding Mode for Human–Robot Cooperation

Human-robot cooperation is the major challenges in robot manipulator control, as the controller has to couple the complicated motion of the human arm and the robot end-effectors. To improve the human-robot coordination, this paper proposed a novel robust finite-time trajectory control based on the nonsingular fast terminal sliding mode and the high-order sliding mode. The proposed method is able to quickly reach the global convergence and minimize motion errors. Based on the nonsingular fast terminal sliding surface, the proposed control method employed a super-twisting algorithm to eliminate the chattering issues to enhance the control robustness. Also, the simplified robust control term does not require the first derivative of the sliding variable. To validate the proposed controller, theoretical analysis and simulation were conducted and the results demonstrated the effectiveness of the proposed method.

Combining Homogeneous High Order Sliding Mode and Nonlinear Dynamic Inversion for fixed wing aircraft attitude and speed control

Abstract This paper addresses the problem of robust flight control for fixed wing aircrafts. Such systems are generally of Multi-Input Multi-Output (MIMO) form, tightly coupled and highly nonlinear whereby the nonlinearity resides both in the dynamic equations and in the aerodynamic coefficients. Consequently, we propose to combine Homogeneous High Order Sliding Mode (HHOSM) and Nonlinear Dynamic Inversion (NDI) approaches in order to deal with the piloting controller. The overall controller is designed so as to ensure the tracking of desired longitudinal velocity and attitude angles. The dynamics inversion uses nonlinear full-state feedback to globally linearize the dynamics of the selected controlled variables so that a linear controller can then be applied to regulate these variables with a desirable closed-loop behavior. To handle the nonlinearity, the desired closed-loop dynamics are given by an HHOSM controller. Simulations are carried out on a real-time virtual simulation platform for the development of Aircraft Control Systems (ACS). The obtained results demonstrate the effectiveness of the proposed controller. It is shown that HHOSM-NDI autopilot delivers a high dynamic tracking performance and can alleviate the chattering effect. Moreover, finite time convergence to the origin is ensured.