Higher Order Sliding Mode Control Research Articles

Higher Order Sliding Mode Control-Based Finite-Time Constrained Stabilization

This brief addresses the problem of finite-time constrained stabilization of nonlinear systems with matched uncertainties. The constrained stabilization refers to designing of higher order finite-time control law such that the output $ {\sigma }$ of the system remains in some prescribed range, i.e., $ {\sigma \in (- c, c)}$ , ${c}$ is chosen as constant while all the higher derivative of the output $ {\sigma }$ satisfy, ${\sigma }=\ddot {\sigma }= \cdots =\dot {\sigma }^{n}=0$ in some finite interval of time. The above problem of relative degree ${n}$ with respect to output $ {\sigma }$ cannot be directly solved by using higher order sliding mode control. Therefore, a new coordinate transformation has been proposed in this brief to reduce the relative degree of such systems by one in some pre-specified range of space. However, in the remaining space, the problem of stabilization can be solved by higher order sliding mode controller having the same relative degree. The segway application is considered as an example to demonstrate the efficacy of the proposed theory.

Robust Tuned Controller Based on Interval Type 2 Fuzzy Logic for Robotic Manipulators Exposed to Perturbations and Parametric Uncertainties

Industrial robotic arms require a reliable ability to operate in the presence of unexpected perturbations. In this paper, control of a robotic arm is contemplated in the presence of parametric uncertainties which are coupled by significant external perturbations. The proposed method is based on tuning of the higher-order sliding mode controller parameters by the interval type 2 fuzzy logic. Initially, the common chattering effect of the classic sliding mode is eliminated by using higher-order SMC and saturation function, which makes it more robust than the classic algorithm. However, the high-order sliding mode still cannot deal with strong external perturbations properly. This issue is addressed by combining the algorithm with fuzzy type 2 membership functions which add the self-tuning feature to the controller. Simulations show the superiority of the proposed controller over the classic and the higher-order sliding mode controllers in dealing with various significant perturbations.

Disturbance observer-based gain adaptation high-order sliding mode control of hypersonic vehicles

In this study, hypersonic vehicle (HV) tracking control in the presence of uncertainties and external disturbance is investigated. As the exact bounds of uncertainties and disturbances are usually unknown during flight, a disturbance observer (DOB)-based gain adaptation high-order sliding mode control (HOSMC) method is proposed for HVs. To mitigate the chattering effect while maintaining strong robustness, a method combining the advantages of the DOB and gain adaptation is introduced into the HOSMC. The DOB is employed to estimate and reject the uncertainties and external disturbance. Additionally, an adaptive control law is developed to compensate for estimation errors. By combining the DOB and the adaptive HOSMC, the unnecessarily large gain for maintaining robustness is reduced; thus, the chattering is mitigated. The effectiveness of the proposed control method is validated via simulation, in which a strong robustness, high tracking performance, and reduced chattering effect are achieved under uncertainties and external disturbance.

Design of higher-order sliding mode controller based on genetic algorithm for a cooperative robotic system

This paper proposes a new control framework for a cooperative robotic system which consists of two manipulators to grasp and handle an object with known geometry. Based on passive decomposition approach, the dynamics of the cooperative system are decomposed into the shape and locked systems, considering uncertainty in the dynamics of the robots. Two higher-order sliding mode controllers are designed for them and are tuned by genetic algorithm in the form of an optimization problem. Using the passivity property of passive decomposition approach, the proposed new higher-order sliding mode controllers ensure passivity of the closed loop system. Stability and convergence of the tracking errors are proved by defining a Lyapunov function and using Barbalat’s lemma. Eventually, the comparative simulation results confirmed that the proposed control scheme works well and as expected, works better than the classical sliding mode controllers.

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.

A novel rooted tree optimization apply in the high order sliding mode control using super-twisting algorithm based on DTC scheme for DFIG

Direct Torque Control (DTC) of the doubly-fed induction generator (DFIG) is receiving increasing attention due to important advantages, such as high performance and low dependence on motor parameters. In this paper, to reduce torque and flux ripples, high order sliding mode control based on the super-twisting (HOSMC-ST) approach is proposed. To improve the performance of this approach, new rooted tree optimization (RTO) algorithm was used in order to search optimal gain of the super-twisting (ST) controller. The simulation experiments demonstrate when using RTO-ST controller can effectively reduce flux and torque ripples with better dynamic performances by compared with performance when used ST traditional.

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.

Sensorless Vector Control of Permanent Magnet Synchronous Linear Motor Based on Self-Adaptive Super-Twisting Sliding Mode Controller

Due to its own structural characteristics, permanent magnet synchronous linear motors (PMSLMs) have unstable motor parameters during operation due to the end effect and the inherent magnetic circuit instability. At the same time, linear motors have the characteristics of reciprocating switching motion and high-speed positioning motion in industrial applications, thus placing high demands on the controller. In order to improve the performance of the PMSLM, this paper firstly studies the linear motor structure, the distribution characteristics of its air gap magnetic field are obtained, and the simulation analysis for the back electromotive force (EMF) of PMSLM of its running process is carried out. Then, a state observer based on the sliding mode state observer (SMO) is built to replace the traditional speed sensor and a super-twisting sliding mode controller is designed. The double-closed loop control of the speed and the use of high-order sliding mode control features effectively reduce the chattering of the system and reduce the impact of the observation error brought by the observer on the system. The adaptive sliding mode control strategy is used to effectively suppress the influence of the boundaryless uncertainty interference on the system and reduce the influence of the observation error brought by the observer on the system. This paper also combines the linear motor experimental platform to further verify the control scheme based on the super-twisting sliding mode non-sensing linear motor. The simulation and experimental results show that SMO has accurate speed and position tracking performance, the system's chattering is significantly reduced, the control precision is excellent, and the introduction of adaptive sliding mode controller enhances the robustness of the system.

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.

Finite-Time Super-Twisting Controller Based on SESO Design for RLV Re-Entry Phase

In this paper, an improved extended state observer (ESO) based on sigmoid function and a finite-time convergence attitude controller are designed for reusable launch vehicle (RLV) in the re-entry phase. First, a control-oriented model (COM) of the RLV is established. According to the singular perturbation theory, the RLV control system is divided into an outer-loop and inner-loop subsystems. Second, a sigmoid function ESO (SESO) is proposed to estimate the model uncertainties and external disturbance caused by the large attitude maneuver and complicated external environment during the RLV re-entry phase. The continuous differentiable sigmoid function has the significant ability in noise suppression. By selecting the proper Lyapunov function, the stability of the SESO is proved. Then, based on the sliding mode control (SMC) theory, an improved multivariable super-twisting high-order sliding mode controller is designed. The finite-time convergence for the whole system is proven by the Lyapunov function technology. Finally, a 6-degree-of-freedom (6-DOF) RLV model is utilized to simulate to verify the effectiveness and robustness of the proposed control scheme.

A strong robust DC-DC converter of all-digital high-order sliding mode control for fuel cell power applications

In the fuel cell power applications, the output voltage and load power are variable which highly depends on the operating conditions. Thus, DC/DC power converters are usually utilized to obtain a constant voltage to match the subsequent power bus. Due to the non-linear characteristics of the fuel cell and load profiles, a stronger robustness design of power converters is required. In order to resolve the above issues, this paper designs a strong robust isolated flyback DC/DC converter for the fuel cell power applications. An all-digital controller based on high-order sliding mode (HSM) control is developed. The super-twisting algorithm of HSM is applied with a digital signal processor (DSP) TMS320F28035 that is used as the control chip. In the experiments, the designed digital HSM controller can achieve a fast convergence with a settling time of less than 0.1 ms and an overshoot of less than 0.1%. A typical incremental PI controller is also designed as the benchmark control method. The effectiveness of the proposed digital HSM controller is demonstrated through several different experiments conducted under large disturbances of load and input voltage.

Trajectory tracking for autonomous underwater vehicle: An adaptive approach

During missions at sea, underwater vehicles are exposed to changes in the parameters of the system and subject to persistent external disturbances. These issues make the design of a robust controller a quite challenging task. This paper focuses on the design of an adaptive high order sliding mode controller for trajectory tracking. The main feature of the proposed control law is that it preserves the advantages of robust control. Moreover, it does not need the knowledge of the upper bound of the disturbance and it is easy to tune in real applications. Using Lyapunov concept, asymptotic stability of the closed-loop tracking system is ensured. The robustness of the proposed controller for trajectory tracking in depth and yaw dynamics is demonstrated through real-time experiments.

Closing Gaps for Aircraft Attitude Higher Order Sliding Mode Control Certification via Practical Stability Margins Identification

In this paper, the conventional aircraft control system certification approach based on phase margin (PM) and gain margin (GM) is extended to higher order sliding mode (HOSM) controllers. The proposed practical stability PM (PSPM) and the practical stability GM (PSGM) are used to quantify the HOSM control system robustness to unmodeled dynamics. The tools/algorithms for the identification of PSPM and PSGM are developed using describing function-harmonic balance method. A design algorithm of a cascade dynamic compensator for a dynamically perturbed HOSM control system is presented and can be used to satisfy required practical stability margins. The theoretical developments are illustrated and validated on controlling the attitude of an F-16 aircraft.

Design and experiment of adaptive modified super-twisting control with a nonlinear sliding surface for a quadrotor helicopter

Quadrotor unmanned aerial vehicle is a nonlinear system of 6-degree-of-freedom motion. In order to handle the nonlinearity that causes undesirable behavior, robustness of flight control has been studied. In this work, we consider the combination of higher order sliding mode control and nonlinear time-varying sliding surface for robustness and accuracy in tracking. An adaptive super-twisting control, a second-order sliding mode control, is utilized to compensate for the uncertainty and perturbation of a quadrotor system. A time-varying sliding surface is designed with a nonlinear function to provide varying properties of closed-loop dynamics and to improve control performance with energy consumption reduction. The proposed control system performance including energy consumption was compared among nonlinear adaptive super-twisting control algorithm, linear adaptive super-twisting control algorithm, and linear super twisting controllers, without and under wind disturbance. The robustness and effectiveness of the proposed control system are demonstrated by several times simulation and experiment using a quadrotor helicopter test bed.

A coordinated high-order sliding mode control of DFIG wind turbine for power optimization and grid synchronization

This paper aims to propose a coordinated high-order sliding mode control (HOSMC) method for power optimization and grid synchronization of a doubly-fed induction generator (DFIG) based wind energy conversion system (WECS). The super-twisting algorithm is employed to maximize the captured wind energy with optimal rotor speed tracking, and regulate the voltage to fulfill the grid requirement. Subsequently, a grid synchronization scheme is proposed, where the wind turbine stator terminal voltage is controlled to synchronize with the grid voltage without employing the current control loop. Meanwhile, a novel reaching law is employed to accelerate the reaching speed. Simulations are carried out to verify the effectiveness of the novel approach, where the first order sliding mode control and the proportional-integral control are considered for comparison. A stepwise wind speed scenario, a variable wind speed condition, and the scenario under parameter perturbations are included in the comparative study. The simulation results fully reveal the robustness, chattering free property and high tracking precision of the proposed method.

Dynamic modelling and design of various robust sliding mode controls for the wind turbine with estimation of wind speed

• Deriving power coefficient of WindPACT 1.5MW wind turbine by FAST and WT-PERF software. • Estimation of wind speed based on ANFIS while training data is obtained by using FAST. • Design and comparison of various sliding mode controls (SMC) to obtain maximum power. • Control of doubly fed induction generator (DFIG) for tracking reference torque. • Robust performance of the high order SMC in the presence of model uncertainties. The main propose of this paper is extracting the maximum efficiency from variable speed wind turbine, which is modelled as an electromechanical system with two masses dynamics. The maximum efficiency can be obtained by tracking the optimal rotor speed, which is controlled by the generator torque as the input. One of the most important information that is required for designing of the control system is the measurement of the effective wind velocity. In this paper, a new ANFIS-based method for estimating the effective wind velocity is developed. The aerodynamic torque has a direct relationship with the power coefficient. So in this paper, power coefficient of WindPACT 1.5 MW turbine as a function of tip speed ratio (TSR) and blade pitch angle is considered. Then, three control methods based on high order sliding mode controllers are examined. The rotor speed and the wind velocity are the only variables required in the design of second and third order sliding mode controllers. FAST (Fatigue, Aerodynamics, Structures and Turbulence) is valid software that offers a fairly complete model of the wind turbine. Results of this paper are validated using FAST. Performance of the designed controllers is compared in terms of the generator torque and desired rotor speed tracking. Finally, the doubly fed induction generator (DFIG) is controlled such that the objectives of reactive power minimization and tracking the desired generator torque are achieved. Two main hindrances in designing the control systems are the uncertainties and the lack of sufficient information on measurements. Therefore robust performance of designed controllers against the model uncertainties is investigated.

Adaptive Quasi-Optimal Higher Order Sliding-Mode Control Without Gain Overestimation

This paper presents an adaptive quasi-optimal higher order sliding-mode control (HOSMC) scheme, which is able to avoid gain overestimation. The overall scheme consists of two elements: 1) a quasi-optimal control law that provides fast finite-time stabilization for a chain of integrators; and 2) an adaptive HOSMC with integration of the quasi-optimal control and the integral sliding-mode concept. The adaptation strategy solves the problem of gain tuning without overestimation and has the advantage of chattering reduction. Moreover, the bounds of the uncertainties are no longer needed in the controller design. Simulation results are provided to demonstrate the effectiveness of the proposed HOSMC algorithm.

Quasi-Continuous MIMO Sliding-Mode Control

High-order sliding-mode (HOSM) control is called quasi-continuous (QC), if it remains continuous everywhere except the HOSM set, where the sliding variables and their derivatives vanish. Such sliding-mode (SM) control features less chattering. Homogeneous QC SM control is designed for the general uncertain multi-input multi-output case and provides any predefined control smoothness level outside of the HOSM set.

Event-Triggered Adaptive Integral Higher-Order Sliding Mode Control for Load Frequency Problems in Multi-area Power Systems

The study proposes a method to design continuous-time event-triggered adaptive integral higher-order sliding mode control for load frequency problems in multi-area power system under load disturbances and parameter uncertainties. Event-triggered strategy reduces the communication burden and lowers the control updating frequency while ensuring high-performance system stability. Event-triggered integral higher-order sliding mode control is used to attain need-based chattering-free control signal compared to event-triggered integral sliding mode control which assures its easy practical implementation. Adaptive estimation of switching gain is used with higher-order integral sliding mode control that eliminates the need of prior knowledge about the system uncertainties. Nonlinear uncertainties in power system like generation rate constraints (GRC) and governor deadband lead to load disturbance that results in deviation of frequency from its nominal value. Robustness of the controller is tested for plant considered with such nonlinearities. System performance without GRC is better; however, proposed controller still ensures finite time convergence of change in frequency under GRC and governor deadband. Proposed controller also guarantees finite time convergence of change in frequency under random varying load disturbances. We have also integrated renewable energy resources in the system and tried to handle relevant output power uncertainty in load frequency problem.