Super-twisting Sliding Mode Control Research Articles

A Nonlinear Backstepping Controller Design for High-Precision Tracking Applications with Input-Delay Gimbal Systems

This paper proposes a novel nonlinear control approach for a two-axis gimbal to achieve accurate real-time tracking performance in maritime surveillance applications. For this objective, the control system must overcome system complexities and limitations, including nonlinear dynamics, coupled Euler angle-based measurements, and delay time constraints. The nonlinear backstepping controller was designed, taking into consideration the nonlinearities and system couplings to preserve the system stability. Then, an extra backstep was incorporated to minimize the control errors due to the delay time. The proposed control scheme enhances the tracking performances and expands the system’s bandwidth, which is validated in the simulations and experimental studies in comparison with a super-twisting sliding mode controller introduced in a previous study.

A Moving Target Tracking Control of Quadrotor UAV Based on Passive Control and Super-Twisting Sliding Mode Control

A novel asymptotic tracking controller for an underactuated quadrotor unmanned aerial vehicle (UAV) is proposed to solve a moving target tracking problem. Firstly, the control system is decoupled into the position control system and the attitude control system. Secondly, a method combined artificial potential field with passivity control (APF&PC) is introduced for the positioning system to achieve high-precision tracking of moving target at a fixed distance. Thirdly, a super-twisting sliding mode (STSM) method with an improved reaching law for the attitude system is applied to ensure that the attitude converges to the desired value. Furthermore, the stabilities of two subsystems are proved, and sufficient stability conditions are derived based on the passive method and Lyapunov method, respectively. Finally, simulation results of the moving target tracking verify the superiority and robustness of the proposed control method in the presence of parameter uncertainties and external disturbances.

Sensor-less Speed and Flux Control of Dual Stator Winding Induction Motors Based on Super Twisting Sliding Mode Control

This paper proposes a direct speed and flux control system for Dual Stator Winding Induction Machines (DSWIMs) based on Super Twisting Sliding Mode Control (STSMC). The proposed nonlinear controller which has finite time convergence of error to zero, is designed such that the Lyapunov stability condition is satisfied. Furthermore, a novel torque-sharing algorithm is introduced for DSWIMs. This algorithm enables them to operate in a wide speed region, including zero speed, such that the required electromagnetic torque is supplied by two winding sets based on their power ratings. In addition, a Sliding Mode Control (SMC) based full order observer is proposed for DSWIMs. This observer, which is able to estimate the winding fluxes, flux angles and rotor speed with high-accuracy, guarantees the optimal flux condition. The functionality of the proposed sensor-less DSWIM drive scheme is evaluated through some experimental tests performed on a 3.3 kW DSP-based DSWIM drive system. The experimental results confirm the effectiveness of the proposed control method, torque sharing algorithm and the full order observer in various speed regions.

시간지연을 갖는 2축 짐벌시스템의 강인한 추종제어계 설계에 관한 연구

This paper presents a novel target tracking control design method for 2-axis gimbal system. Especially, the delay time raised from control signal calculation, sensing signal transducing and transmitting, affects the system stability and degrades the control performance. To overcome these issues, in this study, the authors propose a new tracking system design method based on robust control framework. The designed control system can preserve the system stability and control performance simultaneously in spite of time delay. The developed control method was applied to a 2-axis gimbal system. A STSMC (super-twisting sliding mode control) scheme was provided for a comparison study. Finally, the simulation results were presented for validating the usefulness of the method.

Development of a force actuator for hybrid model tests using super-twisting sliding mode control

Hybrid model testing is a solution to overcome the limitations of small-scale model testing, such as scaling conflict or infrastructure limits, still retaining the real physical phenomena’ complexity. In hybrid model testing, the physical and numerical substructures interact with each other through a network of sensors and actuators. So, to apply the desired effects in the physical substructure, precise control of the actuators is necessary. In this paper, a robust control technique will be employed (super-twisting sliding mode control) to design the force actuator controller for hybrid model testing of vessels in a wave tank. First, the force actuator system dynamics is detailed, consisting of a servomotor controlling the force in a line attached to the vessel model. The methodology and design for the super-twisting sliding mode controller are described, taking into account the uncertain friction torque, the vessel motion and the system delays. Finally, the proposed actuator’s performance is validated experimentally in a simpler environment: The servomotor is mounted on a linear guideway to simulate the vessel’s horizontal displacement in waves. We analyzed the force actuator step response and frequency response (0.1–2.0 Hz) with disturbance motions varying from 0.5 to 1.5 Hz. The developed actuator showed good results (mean absolute error inferior to 0.1 N in all tests), where the high-frequency error spikes (up to 0.33 N) should not have a significant effect on the hybrid model tests’ slow dynamics. We conclude that the force actuator will be a valuable tool for hybrid model testing.

Super-twisting sliding mode control with defined boundary layer for chattering reduction of permanent magnet linear synchronous motor

The super-twisting algorithm (STA, a class of second-order sliding mode control (SOSMC)) is widely used in permanent magnet linear synchronous motor (PMLSM) systems for its least amount of information and simplest calculations among the SOSMC algorithms. Due to the discretization and sign function of the STA, the chattering problem may be induced. In this paper, we propose an STA method with a defined boundary layer (called δSTA) to further reduce chattering in high-precision positioning system. With the δSTA method, when the sliding variable crosses the zero point, the speed is adjusted via two different saturation functions, instead of discontinuous sign functions of the STA. The proposed control law was proven to be stable, ensuring the establishment of a second-order sliding mode. Both the simulation and experimental results showed that the proposed control scheme, with a defined boundary layer width, can improve the steady-state positioning accuracy and significantly reduce system chattering.

A Novel Robust Smooth Control of Input Parallel Output Series Quasi-Z-Source DC–DC Converter for Fuel Cell Electrical Vehicle Applications

Input parallel output series Quasi-Z-source dc-dc converter is a promising option for fuel cell electrical vehicle applications for its features of low device stress and high voltage ratio. Besides, the interleaved structure can reduce the input current ripple which can extend the lifespan of fuel cell system. In order to achieve better dynamic and steady-state performance for the converter, a novel smooth super-twisting sliding mode control (STSMC) method is designed in this article. The proposed control strategy is realized by constructing a novel smooth switch function in the zero domain of STSMC which comprises the advantages of both smooth feedback control and nonsmooth feedback control. Compared with the conventional STSMC, it guarantees strong robustness while possesses better smoothness namely excellent steady-state performance. Finally, a 200-W prototype has been created and described in detail. Simulation and experimental results validate the effectiveness of the proposed control algorithm.

Artificial intelligence-based nonlinear control of renewable energies and storage system in a DC microgrid

To minimize the global warming and the impact of greenhouse effect, renewable energy sources-based microgrids are widely studied. In this paper, the control of PV, wind-based renewable energy system and battery, supercapacitor-based energy storage system in a DC microgrid have been presented. Maximum power points for PV and wind have been obtained using neural network and optimal torque control, respectively. Nonlinear supertwisting sliding mode controller has been presented for the power sources. Global asymptotic stability of the framework has been verified using Lyapunov stability analysis. For load-generation balance, energy management system based on fuzzy logic has been devised and the controllers have been simulated using MATLAB/Simulink® (2019a) along with a comparison of different controllers. For the experimental validation, controller hardware-in-the loop experiment has been carried out which validates the performance of the designed system.

Modeling and Evaluation of Adaptive Super Twisting Sliding Mode Control in Lower Extremity Exoskeleton

In this paper, an integrated human-in-the-loop simulation paradigm for the design and performance analysis of a 6 DOF lower extremity exoskeleton is presented. An adaptive Super Twisting Sliding Mode Controller (ASTSMC) is designed for the trajectory tracking control of the exoskeleton by considering the human motion as reference trajectory. The dynamic model, that include linear and rotational displacement of hip, knee and ankle joints of both the legs is developed using Lagrange energy formulation. The position and angular velocity error of the wearer and the exoskeleton are being considered to establish the control law. Super twisting SMC is a robust control scheme that works effectively in the presence of external disturbances and parameter variations. However, the STSMC introduces chattering in the closed loop because of its high gain, to overcome this drawback, an adaptive STSMC is proposed for the control of exoskeleton against unknown disturbances without chattering. An adaptation scheme using Lyapunov criterion is derived that ensures the stability of the system in closed loop. The performance of the proposed control strategy is verified by implementing on the integrated CAD model of the exoskeleton along with the wearer. The effectiveness of the controller is tested under wind disturbance of varying velocity and direction. The results demonstrate improved tracking performance of the proposed control scheme with least error and less control effort compared to constant gain STSMC in normal and uneven terrain.

Ride comfort analysis of driver seat using super twisting sliding mode controlled magnetorheological suspension system

In order to improve the ride comfort of the driver, a higher-order Sliding Mode Controller was proposed in this study for a semiactive magnetorheological (MR) suspension system. The work is mainly focused on improving the ride comfort of the driver with simultaneous improvement in road holding capability of the vehicle and to study the effects of using Super Twisting Sliding Mode Controller (STSMC) in a quarter car with driver seat model. The modified Bouc-Wen model was simulated using MATLAB/Simulink software and the STSMC was adopted to control the voltage variation in MR damper using Continuous State Control (CSC) algorithm. The controller and the suspension system parameters were analysed in time domain with random road inputs. Fast Fourier Transform (FFT) analysis was also carried out to show the effectiveness of the controller towards improving the driver seat comfort. The STSMC-controlled MR damper was used as a primary suspension and the effectiveness of its controllability was compared with passive suspension system. The uncontrolled MR suspension system was also analysed in order to verify the fail-proof advantage of the MR damper. From the results, it was found that the ride comfort was extremely improved when STSMC controller was used than when the uncontrolled MR and passive suspension systems were employed. The uncertainty of the STSMC was verified for different passenger masses and it achieved a robust control over load variation. The selected STSMC was validated with the first-order Sliding Mode Controller and the results were discussed in terms of time-domain analysis.

Adaptive Robust Trajectory Tracking Control of Multiple Quad-Rotor UAVs with Parametric Uncertainties and Disturbances.

Recently, formation flying of multiple unmanned aerial vehicles (UAVs) found numerous applications in various areas such as surveillance, industrial automation and disaster management. The accuracy and reliability for performing group tasks by multiple UAVs is highly dependent on the applied control strategy. The formation and trajectories of multiple UAVs are governed by two separate controllers, namely formation and trajectory tracking controllers respectively. In presence of environmental effects, disturbances due to wind and parametric uncertainties, the controller design process is a challenging task. This article proposes a robust adaptive formation and trajectory tacking control of multiple quad-rotor UAVs using super twisting sliding mode control method. In the proposed design, Lyapunov function-based adaptive disturbance estimators are used to compensate for the effects of external disturbances and parametric uncertainties. The stability of the proposed controllers is guaranteed using Lyapunov theorems. Two variants of the control schemes, namely fixed gain super twisting SMC (STSMC) and adaptive super twisting SMC (ASTSMC) are tested using numerical simulations performed in MATLAB/Simulink. From the results presented, it is verified that in presence of disturbances, the proposed ASTSMC controller exhibits enhanced robustness as compared to the fixed gain STSMC.

A nonlinear hybrid controller for swinging-up and stabilizing the rotary inverted pendulum

In this paper, we propose a new class nonlinear hybrid controller (NHC) for swinging-up and stabilizing the (under-actuated) rotary inverted pendulum system. First, the swing-up controller, which drives the pendulum up towards the desired upright position, is designed based on the feedback linearization and energy control methods. Then, the modified super-twisting sliding mode control is proposed based on the new sliding surface to stabilize both the fully-actuated (the rotary arm) and under-actuated (the pendulum) state variables. In the proposed NHC, around the upright position, the stabilization controller is applied, and in different circumstances aside from the upright position, the swing-up controller is used. We show that with the proposed NHC: (i) in the swing-up stage, the pendulum is able to reach the desired upright position; and (ii) in the stabilization stage, the closed-loop rotary inverted pendulum is asymptotically stable. We demonstrate the effectiveness of the proposed NHC through extensive experiments. In particular, (i) the faster swing-up under the similar control effort is obtained, compared with the existing fuzzy logic swing-up controller; (ii) the better stabilization control performance for the convergence of the angular positions of the rotary arm and pendulum is attained and the chattering is alleviated, compared with the existing sliding mode stabilization controllers; (iii) the better stabilization control accuracy with the faster convergence time and lower peak overshoot is accomplished, compared with the existing Fuzzy-LQR controller; and (iv) the good robustness against sudden external disturbances is achieved.

Super-Twisting Sliding Mode Control Law Design for Attitude Tracking Task of a Spacecraft via Reaction Wheels

The attitude control has been recognized as one of the most important research topics for spacecraft. If the desired attitude trajectory cannot be tracked precisely, it may cause mission failures. In the real space mission environment, the unknown external perturbations, for example, atmospheric drag and solar radiation, should be taken into consideration. Such external perturbations could deviate the precision of the spacecraft orientation and thereby lead to a mission failure. Therefore, in this paper, a quaternion-based super-twisting sliding mode robust control law for the spacecraft attitude tracking is developed. The finite time stability based on the formulation of the linear matrix inequality (LMI) is also provided. To avoid losing the control degree of freedom due to the certain actuator fault, a redundant reaction wheels configuration is adopted. The actuators distribution associated force distribution matrix (FDM) is analyzed in detail. Finally, the reference tangent-normal-binormal (TNB) command generation strategy is implemented for simulating the scenario of the space mission. Finally, the simulation results reveal that the spacecraft can achieve the desired attitude trajectory tracking demands in the presence of the time-varying external disturbances.

A Novel Adaptive Super-Twisting Sliding Mode Control Scheme with Time-Delay Estimation for a Single Ducted-Fan Unmanned Aerial Vehicle

This article proposes a novel adaptive super-twisting sliding mode control scheme with a time-delay estimation technique (ASTSMC-TDE) to control the yaw angle of a single ducted-fan unmanned aerial vehicle system. Such systems are highly nonlinear; hence, the proposed control scheme is a combination of several control schemes; super-twisting sliding mode, TDE technique to estimate the nonlinear factors of the system, and an adaptive sliding mode. The tracking error of the ASTSMC-TDE is guaranteed to be uniformly ultimately bounded using Lyapunov stability theory. Moreover, to enhance the versatility and the practical feasibility of the proposed control scheme, a comparison study between the proposed controller and a proportional-integral-derivative controller (PID) is conducted. The comparison is achieved through two different scenarios: a normal mode and an abnormal mode. Simulation and experimental tests are carried out to provide an in-depth investigation of the performance of the proposed ASTSMC-TDE control system.

Adaptive super-twisting non-singular terminal sliding mode control for tracking of quadrotor with bounded disturbances

In this research, a novel adaptive non-singular terminal sliding mode control (ANTSMC) is proposed for finite-time attitude and altitude tracking of aircraft system considering the bounded disturbances. By utilizing this structure, the desired reference is tracked in finite-time. Afterward, a new adaptive super-twisting sliding mode control (ASTSMC) is presented to decrease the control signals' chattering effect. This approach combines with the ANTSMC to compose this study's proposed approach as adaptive super-twisting non-singular terminal sliding mode control (ASTNTSMC). Additionally, an adaptive-regulation strategy is designed for estimating the unknown bounds of the disturbances. Finally, for evaluating the proposed strategies' ability, some simulations are performed based on quadrotor real parameters and confirmed the presented controllers' appropriate performances compared to other techniques.

Super-twisting-based sliding mode control of drum boiler energy conversion systems

ABSTRACT A drum boiler is the most critical part of power generation plants. The control of a highly nonlinear, multiple input and multiple output drum boiler system (DBS) is a challenging task. In this work super-twisting sliding mode controllers (STSMCs) are designed for the control-oriented model of the DBS, which maintain a desired water level and pressure of the drum. The unknown state of the DBS required for the control design is estimated using a gain-scheduled Utkin observer (GSUO). A rigorous mathematical analysis is also included to show that the closed-loop system is locally stable. The simulation results show that the closed-loop system yields the required performance even in the presence of parametric uncertainty, process and measurement noises, and external disturbance. To make a fair comparison, a quantitative analysis is also carried out for STSMC and PI controllers. Both controllers consume similar control energy, but STSMC shows better tracking performance.

Impedance control based on optimal adaptive high order super twisting sliding mode for a 7-DOF lower limb exoskeleton

In this paper, a novel hybrid optimal Adaptive High-Order Super Twisting Sliding Mode (AHOSTWSM) impedance control is proposed for a lower limb exoskeleton robot with 7 active joints, which takes the interaction forces between the robot and the user into account. First, the dynamic model of the robot is extracted using Lagrange approach. Then, an adaptive super twisting sliding mode controller is designed based on Lyapanov theory. Moreover, the interaction forces are obtained in every time-step and applied to the robot as a compensating torque to guard against disturbances. The desired trajectory of the upper limb joint has been extracted so that the stability of the robot is achieved based on Zero Moment Point (ZMP) criterion at any moment. Moreover, to achieve optimal performance (maximum stability, minimum tracking error, reduced interacting forces, and optimal energy consumption), parameters of the proposed controller, the upper limb desired trajectory, and the impedance system are optimized using Harmony Search Algorithm (HSA). Finally, in order to demonstrate the effectiveness of the proposed controller, optimal sliding mode controller (SMC) is designed and performance of the AHOSTWSM is compared with SMC. The simulation results reveal the superiority of the controller in comparison with SMC.

A Study on Gimbal Motion Control System Design based on Super-Twisting Control Method

Controlling an optical sensor’s line of sight (LOS) with an inertial stabilization system carried out on a dynamic platform is a challenging engineering task. The LOS needs to track a target object accurately despite intentional maneuvers, inadvertent motions, and additional disturbances. In this study, a super-twisting sliding mode controller (STSMC) is implemented to overcome this problem. The controller is designed based on the analysis of system dynamics. The stability is then proved to be satisfactory by the Lyapunov theory. Then, the control law is validated through experimental studies. In addition, a comparison to the performance of a linear controller is derived so that the effectiveness of the proposed controller is validated.

Validation of An Elbow Position Super-Twisting Sliding-Mode Controller for Upper-Limb Exosuit Using A Soft Position Sensor

Flexible exoskeletons, also known as exosuits, are robotic wearable devices intended to help healthy and unhealthy subjects in different tasks, such as daily life activities, load lifting or rehabilitation. A position control is required to assure stability and compliance in all assisted movements. In this paper, the authors propose the use of a flexible position sensor based on differential capacitance measurement as position feedback for the elbow joint in the flexible exoskeleton LUXBIT. This exosuit is controlled in position by a super-twisting sliding mode controller (SMC), which is robust against disturbances. Different movements involved in rehabilitation therapies are performed over three healthy subjects in order to evaluate the exosuit performance using this motion sensor. The measures given by the flexible sensor are compared to the ones obtained by OptiTrack motion capture system, which are used as ground truth.

Suppression of hydraulic transients for desalination plants based on active control synthesis

AbstractThis paper proposes a control strategy to stabilize a reverse osmosis desalination system against hydraulic shocks with enhancing productivity and sustainability. First, the effects of hydraulic transients on water quality have been reviewed. The transient waves are approximated by sinusoidal functions so that their effects are incorporated into the controlled system as external disturbances. Next, the active control is implemented based on the adaptive super-twisting (STW) sliding mode control (SMC) algorithms. Then, the robust performance is guaranteed whenever the sliding variables reach the sliding surfaces in finite time despite disturbances. The STW SMC scheme is to eliminate the chattering problems for protecting the valves and to improve the convergence precision for water production. The control gains are adaptable to enable formation of an effective controller for dealing with large disturbances such as water hammer during desalination process. The simulation results reveal the superior performances on controlling water product, while eliminating shock waves. Especially, the effect of hydraulic shocks has been dramatically attenuated, hence the plant components are protected to avoid fracture. Finally, the robust stability and performance of the desalination plants are guaranteed against large disturbances to ensure the population with quality water as well as system sustainability.