Super Twisting Control Algorithm Research Articles

The Design and Processor-In-The-Loop Implementation of a Super-Twisting Control Algorithm Based on a Luenberger Observer for a Seamless Transition between Grid-Connected and Stand-Alone Modes in Microgrids

The abrupt transfer from grid-connected (GC) to stand-alone (SA) operation modes is one of the major issues that may threaten the stability of a distributed generation (DG) system. Furthermore, if the islanding mode happens, it is vital to take into consideration the load voltages or load current waveforms as soon as feasible. This paper develops an advanced control technique based on a super-twisting sliding mode controller (ST-SMC) for a three-phase inverter operating in both the GC and SA modes. This control scheme is proposed to ensure a smooth transition from the GC to SA mode and enhance the load voltage waveforms under the islanding mode. In addition, to minimize the operational costs of the system and the complexity of the studied model, a digital Luenberger observer (DLO) with a proper design is adopted for estimating the inverter-side current. The control scheme of the whole system switches between a current control mode during the GC mode and a voltage control mode during the SA mode. The super-twisting control algorithm is applied to the outer voltage control loop involved in the cascaded voltage/current control scheme in the SA mode. Simulation tests of a three-phase inverter are performed for the purpose of assessing the suggested control performance by using the PowerSim (PSIM) software and comparing it with a classical PI controller. Furthermore, a processor-in-the-loop (PIL) implementation in a DSP board TMS32F28335 while debugging is conducted using code composer studio 6.2.0. The obtained results show efficient control properties, such as a smooth transition among the microgrid (MG) operating modes, as well as effectiveness and robustness during both the GC and SA operation modes.

Novel adaptive law for super-twisting controller: USV tracking control under disturbances

A novel adaptive super-twisting control algorithm, for Unmanned Surface Vehicles (USV) tracking control is presented. The proposed adaptive law is obtained using a Lyapunov approach, to analyze the system closed-loop stability. Furthermore, several conditions are given to guarantee robustness in presence of unknown bounded disturbances/uncertainties, chattering mitigation and the finite-time convergence. This adaptive control strategy has the advantage that the controller gains, which are in terms of a single control parameter, requires adjusting a small number of parameters compared with other adaptive strategies, moreover and its dynamics is smooth, improving the controller performance. To assess the proposed control methodology effectiveness, a trajectory tracking control is designed and implemented on an unmanned surface vehicle under the action of bounded unknown uncertainties and external perturbations. Numerical simulations and experimental results conducted with a vessel prototype demonstrate the performance and advantages under payload variations and external environmental conditions. Finally, a comparative study between the proposed approach with other adaptive super-twisting works has been conducted.

Super-Twisting Sliding Mode Control for the Stabilization of a Linear Hyperbolic System

This letter deals with the stabilization of a linear hyperbolic system subject to a boundary disturbance. Our feedback design relies on a super-twisting control algorithm, which leads to a feedback that is continuous with respect to the state, in contrast with the classical sliding mode design. Our first result is the existence of solutions of the closed-loop system. Moreover, the global asymptotic stability, that is our second result, is proved together with the guarantee that the disturbance is rejected.

Echo State Network-Enhanced Super-Twisting Control of Passive Gait Training Exoskeleton Driven by Pneumatic Muscles

In this article, a robust trajectory tracking control method is proposed for the passive gait training exoskeleton system driven by pneumatic muscles (PMs). Conventional model-based controllers suffer from limitations with respect to model uncertainties and external disturbances caused by PMs and complex robotic systems. An echo state network (ESN) is used in this study to approximate the model uncertainties and external disturbances of the exoskeleton system. Based on the approximation of ESN, a super-twisting control (STC) algorithm is designed to guarantee accurate tracking control at both hip and knee joint levels. Because there are both weight error and global approximation error in neural network approximation, a standard quadratic form cannot be obtained which plays an important role in the stability analysis of the traditional super twisting algorithm. To solve this issue, a dedicated positive definite matrix is constructed in this article, which bridges the ESN and STC by providing a parameter selection criteria. The stability with respect to the tracking problem of the exoskeleton system is then guaranteed according to the Lyapunov theorem. Both numerical simulations and experimental results present better tracking accuracy and robustness compared with the traditional sliding mode control and STC.

Design and Analysis of Rate Predictive Fractional-Order Sliding Mode Controller (RP-FOSMC) for MPPT and Power Regulation of DFIG-based Wind Energy Conversion System (WECS)

Now a days, maximum power point tracking (MPPT), power regulation and transient load reduction are the major issues in the WECSs. To overcome these challenges and to cope with WECS nonlinearity and MIMO nature, nonlinear predictive control algorithms based on Tip-Speed Ratio MPPT (TSR-MPPT) and Rate Predictive Control (RPC) strategies are proposed for the variable speed DFIG-based WECS. The designed control system consists of a FOSMC that is based on fractional-order PID sliding surface model and super-twisting control algorithm (STA) for MPPT through Optimal Torque Control (OTC) algorithm and a Nonlinear-RPC (N-RPC) that is designed based on STA and RPC strategies for power regulation via pitch angle control. FOSMC based on STA improve the dynamics of the controlled system by increasing the degrees of freedom of the sliding surface, minimizing the effects caused by imperfect modelling of nonlinear systems and provide chattering free response of the system and the stability of the designed STA based FOSMC law was proven by Lyapunov criterion. N-RPC is a novel adaptive model-less feedback control algorithm that addresses the limitations of MPC and PID controllers. It limits the power production above rated wind speed and ensure the transient load reduction. The proposed cascaded control algorithms are implemented in a MATLAB/Simulink environment. In this work, the system parameters of Sany SE7715 wind turbine that is installed in Adama-II wind farm, Ethiopia with generating capacity of 1.5 MW is used. The simulation result confirms that the proposed control algorithms achieve optimum power extraction as compared to second-order SMC (2-SMC) and excellent stress reduction in the drive train under variable wind speed. Moreover, they are effective and robust regarding to the application of different external disturbance and sensor noise (i.e., Gaussian & non-Gaussian) and perfectly achieved the required objectives of our investigation.

Control of Multistability in an Erbium-Doped Fiber Laser by an Artificial Neural Network: A Numerical Approach

A recurrent wavelet first-order neural network (RWFONN) is proposed to select a desired attractor in a multistable erbium-doped fiber laser (EDFL). A filtered error algorithm is used to classify coexisting EDFL states and train RWFONN. The design of the intracavity laser power controller is developed according to the RWFONN states with the block control linearization technique and the super-twisting control algorithm. Closed-loop stability analysis is performed using the boundedness of synaptic weights. The efficiency of the control method is demonstrated through numerical simulations.

Real-time implementation of a super twisting control algorithm for an upper limb wearable robot

This paper proposes a robust nonlinear controller for an active orthosis. The system is composed of the upper limb orthosis worn by the arm, which can be represented by a nonlinear second-order dynamical model. A robust control strategy is developed to guarantee an accurate and precise movement that encounter important issues such as unknown disturbance torque, inertial and viscous and the parameter uncertainties. A novel control strategy is proposed based on the Super Twisting Algorithm (STW). The stability analysis is performed based on the Lyapunov theory. For further dissemination of the proposed method, a wearable robot arm was built and the exoskeleton building process includes the following parts: mechanical design, mechanical components, electronic circuit design, robot assembly, programming of closed-loop control algorithms in the microprocessor. Hardware-in-the-loop is being implemented by a DAQ-Advantech, PCI-1716 AE, and PC to test the super twisting control algorithm. An experimental prototype, including the arm wearable exoskeleton, is designed and implemented. Experimental results indicate the proposed controller is able to reach high tracking accuracy.

A 6-DOF sliding mode fault tolerant control solution for in-orbit autonomous rendezvous

The goal pursued by this article, is to evaluate the potential of sliding-mode control and estimation techniques, to address fault tolerance against a large class of actuator faults, including loss of controllability of the faulty actuator, for autonomous rendezvous between a chaser spacecraft and a passive spacecraft on a circular orbit. The proposed solution is based on the dual quaternion formalism, to describe in a single equation, rotational and translational spacecraft dynamics, solar array flexible modes, propellant sloshing, the most dimensioning space disturbances, and their coupling. Such a modelling formalism enables to propose a six degree-of-freedom fault tolerant control architecture, which relies on the generalized super-twisting control algorithm nested with a nonlinear fault estimator. An anti-windup strategy based on polytope algebra is applied to the control algorithm, to prevent instability due to actuator saturation when faults occur. Asymptotic stability of the proposed fault-tolerant control scheme is formally proved with respect to a wide variety of faults, providing that the first derivatives of the fault estimation error versus time and the sliding surface, are bounded. Intensive simulations from a functional engineering simulator that accurately simulates the rendezvous mission, are presented in the paper, as well as capture-oriented criteria. The presented results demonstrate that the proposed fault-tolerant solution is able to cover any kind of thruster faults, including total loss of controllability of the faulty thruster, as well as solar array flexible modes, propellant sloshing, gravity gradient, the second zonal harmonic, atmospheric drag and magnetic disturbances.

Control of Vehicle’s Mixed Longitudinal and Lateral Stability with Engine Dynamics Using Super Twisting Control Algorithm

Vehicle stability control is one of the most important subjects in the control engineering field. Many research activities have been done to develop more comfort and safe travel for passengers. In this paper, vehicle mixed stability in longitudinal and lateral motion has been investigated. Four-wheel seven degrees of freedom model of vehicle is considered to extract the dynamic equations and closed-loop system simulation. Dugoff’s nonlinear model has been used to simulate the behavior of tires and road, and Cho’s engine model with two state variables has been used for vehicle power system simulation, so it makes the input torque to wheels to be more realistic. Because of the good robustness properties of sliding mode control, the second-order sliding mode with a super-twisting algorithm has been used for calculation of control inputs. This method is proved to be so appropriate and useful in the case of uncertainty in a complicated vehicle dynamic model and multiple disturbances in vehicle motion. Engine throttle angle and yaw moment have been considered as a longitudinal system and lateral system control inputs respectively. The longitudinal slip coefficient and yaw rate are considered as system output. Simulation results show the effectiveness of the proposed method.

Finite-Time Cooperative Guidance Strategy for Impact Angle and Time Control

In this article, two cooperative guidance schemes with impact angle and time constraints are proposed for multiple missiles cooperatively intercepting a maneuvering target in the presence or absence of a leader missile. First, cooperative interception with impact angle constraint is formulated based on the relative motion equation between the interceptors. Subsequently, the design of the guidance law is divided into two stages. In the first stage, based on finite-time consensus theory and the super-twisting control algorithm, the cooperative guidance law in the direction of the line of sight (LOS) is derived to control the impact time so that all missiles can simultaneously intercept the target in finite time. Then, based on finite-time sliding mode control and the super-twisting control algorithm, a finite-time convergence cooperative guidance law in the normal direction to the LOS is developed to control the intercept angle and the LOS angle rate so that each missile can accurately hit the target at a desired angle. Finally, by controlling the consensus error of flight time in the presence of a leader missile, a finite-time cooperative guidance method in the “leader–follower” scenario is derived for simultaneous arrival at the target. The proposed methods can effectively suppress chattering and ensure fast convergence in finite time. Simulation experiments are conducted to verify the effectiveness of the proposed cooperative guidance schemes.

Super-twisting control using higher order disturbance observer for control of SISO and MIMO coupled systems

In this paper, accuracy of the existing disturbance observer (DO) for disturbance estimation is increased by increasing its order. Stability of the proposed higher order disturbance observer (HODO) is analysed. Furthermore, a new HODO based super-twisting control (STW) algorithm is presented for the system with the bounded matched disturbances. A HODO based sliding mode control (SMC) algorithm with the integral sliding surface is proposed where the controller gains depend on the disturbance estimation error bound instead of the disturbance magnitude. Therefore, controller gains required in the proposed approach for the disturbance rejection are lesser as compared to the STW. As a result of which, with the proposed control, substantial chattering attenuation better than the STW is achieved. The proposed control technique is successfully applied to the single-input single-output (SISO) Industrial Emulator system with matched disturbance and the multi-input multi-output (MIMO) coupled 2-DOF Helicopter system with complex disturbances. The simulation and experimental outcomes illustrate the effective implementation of the proposed control strategy for tracking desired input, achieving stabilization and robustness of the system in the existence of bounded complex matched disturbances.

A fractional super-twisting control of electrically driven mechanical systems

The Super Twisting Control Algorithm (STA) constitutes a powerful and robust technique for control and observation problems. The structure of the STA allows inducing second-order sliding modes, such that the sliding variable and its derivative remain at zero after some finite time. However, the STA requires the strong differentiability of the sliding variable and the weak differentiability of disturbances. Thus, the sliding variable should become from an adequate design, ensuring its strong differentiability. Nonetheless, in the more general case of not necessarily integer-order differentiable disturbances, a typical case in electromechanical systems due to non-smooth effects, alternative control methods need to be considered. For that reason, this paper proposes a structural modification of the STA, allowing the integral of the discontinuous function to assume a fractional order to compensate not necessarily integer-order differentiable disturbances. An experimental assessment is conducted, and comparisons to other sliding mode based controllers are presented to demonstrate the reliability of the proposed method.

Adaptive Super-Twisting Control for Mobile Wheeled Inverted Pendulum Systems

Recently, the mobile wheeled inverted pendulum (MWIP) has gained an increasing interest in the field of robotics due to traffic and environmental protection problems. However, the MWIP system is characterized by its nonlinearity, underactuation, time-varying parameters, and natural instability, which make its modeling and control challenging. Traditionally, sliding mode control is a typical method for such systems, but it has the main shortcoming of a “chattering” phenomenon. To solve this problem, a super-twisting algorithm (STA)-based controller is proposed for the self-balancing and velocity tracking control of the MWIP system. Since the STA is essentially a second-order sliding mode control, it not only contains the merits of sliding mode control (SMC) in dealing with the uncertainties and disturbances but can also be effective in chattering elimination. Based on the STA, we develop an adaptive gain that helps to learn the upper bound of the disturbance by applying an adaptive law, called an adaptive super-twisting control algorithm (ASTA). The stability of the closed-loop system is ensured according to the Lyapunov theorem. Both nominal experiments and experiments with uncertainties are conducted to verify the superior performance of the proposed method.

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.

Adaptive higher order super-twisting control algorithm for a flexible air-breathing hypersonic vehicle

A novel adaptive higher order super-twisting control algorithm (AHOSTC) is proposed for a flexible air-breathing hypersonic vehicle (FAHV). Firstly, the nonlinear control-oriented model (COM) is processed using input/output feedback linearization method. Therefore, significant flexible effects aroused by slender fuselage and strong coupling between propulsion and aerodynamic of FAHV could be considered during the application of model-based control techniques. Secondly, an adaptive control gain L is incorporated into normal higher order super-twisting algorithm (HOSTA) via dilation rescaling to improve speed of response and attenuate chattering, in the meanwhile, the matched disturbances can be compensated and the finite-time convergence can be achieved. In addition, gain L could be adjusted by the presented novel adaptive law automatically, especially when Lipschitz constants of disturbances are unknown and time-varying. Furthermore, the stability of adaptive law is analyzed via Lyapnuov criteria. Ultimately, compared with normal HOSTA, the proposed AHOSTC is able to enhance robustness and respond speed, while minimizing effects of chattering efficiently. Simulations on longitudinal model of FAHV are carried out to compare AHOSTC with normal HOSTA. The results demonstrate the superiority and effectiveness of AHOSTC under different simulation conditions, external disturbances and parametric uncertainties.

Higher Order Sliding Mode Control for Blood Glucose Regulation of Type 1 Diabetic Patients

Type 1 diabetes mellitus (T1DM) treatment depends on the delivery of exogenous insulin to obtain near normal glucose levels. This article proposes a method for blood glucose level regulation in type 1 diabetics. The control strategy is based on comparing the first order sliding mode control (FOSMC) with a higher order SMC based on the super twisting control algorithm. The higher order sliding mode is used to overcome chattering, which can induce some undesirable and harmful phenomena for human health. In order to test the controller in silico experiments, Bergman's minimal model is used for studying the dynamic behavior of the glucose and insulin inside human body. Simulation results are presented to validate the effectiveness and the good performance of this control technique. The obtained results clearly reveal improved performance of the proposed higher order SMC in regulating the blood glucose level within the normal glycemic range in terms of accuracy and robustness.

Super twisting sliding mode control algorithm for developing artificial pancreas in type 1 diabetes patients

Diabetes mellitus is one of the most common disease in the world. Specifically, juvenile diabetes in which pancreas of patient does not produce insulin that results in high concentration of glucose in the blood plasma for longer periods of time. High concentration of the glucose can cause many complications and may lead to the death. For this purpose optimal control of the blood glucose concentration is required in type 1 diabetes patients. In this research work closed loop control algorithm is proposed based on the sliding mode control (SMC) for type 1 diabetes patient. Bergmans minimal model is presented for studying dynamical behaviour of the glucose and insulin inside human body. Control mechanism based on classical SMC is designed and compared with the super twisting control algorithm which is based on the higher order SMC. A common drawback of classical SMC is the high frequency chattering in control signal which is minimized by using super twisting SMC approach. Super twisting SMC controller is designed and subjected to external disturbances for verifying the required robustness of the closed loop. A comparative analysis of the classical SMC and super twisting SMC is given in results section. Meal disturbance to diabetes patient is also explicitly explained and is given in simulation results. Numerical simulation results are provided to show the superiority and the advantages of the proposed controller such as robustness to external disturbances, no chattering, less control effort and accurate output tracking, thus proposed controller can be considered as a suitable choice for designing automatic insulin pumps for diabetes patients.

Adaptive Super Twisting control design for manufactured diesel engine air path

In this paper, we design a higher order sliding mode controller for the purpose of regulating the diesel engine air path. The proposed controller is based upon the Super Twisting control algorithm (STA) which is well known for its ability to reduce the so-called chattering phenomenon which affects the classical sliding mode controllers. The proposed controller is an Adaptive Super Twisting (ASTA) controller which incorporates an adaptive mechanism for tuning the control gains. This mechanism allows the controller to deal with unknown bounds on the uncertainties and the actuator faults that may affect the engine. Theoretical conditions on the control gains are provided in order to ensure the convergence of the ASTA controller. The simulations on a recently validated experimental air path diesel engine model show good results for actuator failures conditions even in the presence of uncertainties on model parameters.

Gain-scheduled continuous higher-order sliding mode control for uncertain nonlinear system

This paper proposes a gain-scheduled continuous higher-order sliding mode control scheme for a class of minimum phase uncertain nonlinear system. Higher-order sliding mode control is equivalently represented as finite time stabilization of all-dimension integrator chains with bounded uncertainties. After carried out state feedback control, the control law is composed of two parts. One part achieves finite time convergence of pure integrator chains. The other part, gain-scheduled super-twisting control algorithm, is employed to overcome the uncertainties without obtaining the upper bounds in advance. This control approach features that the whole control input is continuous, control chattering is puny, and over-estimated gain is not existent. Finite time convergence of the closed-loop control system is formally proved based on quadratic form Lyapunov function. Simulation results for an academic example and the ship heading control verify the effectiveness and applicability of the proposed approach.

Finite‐time‐convergent fault‐tolerant control for dynamical systems and its experimental verification for DTS200 three‐tank system

This study presents a fault-tolerant continuous super-twisting control algorithm for dynamical systems, subject to Lipshitzian and non-Lipshitzian bounded disturbances. The conditions of finite-time convergence of the entire system state to the origin are obtained. An experimental verification of the designed fault-tolerant algorithm is conducted for a DTS200 three-tank system through varying fault sources, disturbances, input conditions and inter-tank connections.