Adaptive Super-twisting Algorithm Research Articles

Ultralocal Model-Free Adaptive Supertwisting Nonsingular Terminal Sliding Mode Control for Magnetic Levitation System

The magnetic levitation technology has attracted blooming attention from all walks of life thanks to its superiorities such as non-contact and active control. While the intrinsic features of open-loop instability and strong nonlinearity, along with the uncertain external disturbance make the levitation control particularly significant and difficult. For speeding up the convergence and obtaining a better stability and disturbance robustness, this paper proposes an ultra-local model-free adaptive super-twisting nonsingular terminal sliding mode control (ULMF-ASTNTSMC) strategy for the magnetic levitation system. Different from the conventional model-based control, ultra-local model-free control breaks the constraint of a precise system model. Therefore, an improved second-order ultra-local model is established for the magnetic levitation system. For the benefit of finite time convergence and non-singularity, the nonsingular terminal sliding mode surface is chosen. As a second-order algorithm, super-twisting (ST) algorithm can fundamentally suppress the chattering effect of the sliding mode control (SMC). An adaptive super-twisting algorithm is designed for the further improvement of the system dynamic response. The stability of the proposed scheme is strictly verified based on the Lyapunov stability theory. Simulation and experimental comparisons with the existing control methods validate the exceeding performance of the proposed strategy under various operating conditions.

Exponential super-twisting control for nonlinear systems with unknown polynomial perturbations

The study focuses on the control of nonlinear dynamic systems in the presence of parameter uncertainties, unmodeled dynamics, and external disturbances. The lumped perturbation is assumed to be bounded within a polynomial in the system state with the polynomial parameters and degrees unknown a priori such that it accommodates a quite wider range dynamic systems. Based on the studies in recent super-twisting algorithm designs and the idea from adaptive sliding mode control for nonlinear systems with uncertainties, we propose a novel adaptive super-twisting algorithm with exponential reaching law, or exponential super-twisting algorithm (ESTA), for the high-stability and acceptable accuracy control of the aimed nonlinear dynamics. The stability analysis and practical finite-time (PFT) convergence are proven using Lyapunov theory and an intuitive analysis of the control behaviour. Simulations are performed to compare the proposed ESTA with the existing super-twisting method and the traditional proportional integral differential control. The simulation results demonstrate the effectiveness of the proposed ESTA in terms of the fastest settling time and the smallest overshoot.

One new composite control based smooth nonlinear fractional order sliding mode algorithm and disturbance compensation for PMSM with parameter uncertainties

To achieve high-quality control of PMSM with parameter uncertainties, a nonlinear smooth fractional order sliding mode composite control (NSFOSMCC) strategy is designed in this paper. This approach incorporates a novel nonlinear smooth fractional order sliding mode controller, a novel adaptive super-twisting (AST) algorithm, and a modified nonlinear extended state observer (ESO) to achieve enhanced motor performance. To effectively overcome the disadvantages of simplicity and toughness associated with the conventional fractional order sliding mode controller, a novel nonlinear smooth fractional order sliding mode controller is designed. A novel AST technique is introduced to effectively weaken chattering issues. The modified nonlinear ESO is used to estimate the uncertainty parameters of the PMSM. By combining the modified nonlinear ESO with the latest sliding mode controller, a new composite controller called NSFOSMCC strategy is developed for PMSM. The proposed NSFOSMCC strategy, utilizing a combination of “feedforward plus feedback,” is implemented for PMSM with parameter uncertainties. The reliability and stability of the controller are thoroughly established through the utilization of the Lyapunov stability theorem. Furthermore, comparative results show strong evidence supporting the effectiveness of the novel composite control strategy.

Finite-time adaptive super-twisting sliding mode control for autonomous robotic manipulators with actuator faults

This paper proposes a new adaptive super-twisting global integral terminal sliding mode control algorithm for the trajectory tracking of autonomous robotic manipulators with uncertain parameters, unknown disturbances, and actuator faults. Firstly, a novel global integral terminal sliding mode surface is designed to ensure that the tracking errors of autonomous robotic manipulators converge to zero in finite time and the global robustness of the system is also enhanced. Then a new adaptive method is devised to deal with the adverse effect of nonlinear uncertainty. To suppress the chattering phenomenon, the adaptive super-twisting algorithm is used in this paper, which can ensure that the control torque is a continuous input signal. Based on the adaptive mechanism, the adaptive super-twisting global integral terminal sliding mode controller is developed to provide superior control performance. The stability analysis of the system is demonstrated by using the Lyapunov method. Ultimately, the effectiveness of the control scheme is confirmed by a simulation study.

Adaptive Super-Twisting Sliding Mode Control of Underwater Mechanical Leg with Extended State Observer

Underwater manipulation is one of the most significant functions of the deep-sea crawling and swimming robot (DCSR), which relies on the high-accuracy control of the body posture. As the actuator of body posture control, the position control performance of the underwater mechanical leg (UWML) thus determines the performance of the underwater manipulation. An adaptive super-twisting sliding mode control method based on the extended state observer (ASTSMC-ESO) is proposed to enhance the position control performance of the UWML by taking into account the system’s inherent nonlinear dynamics, uncertainties, and the external disturbances from hydrodynamics, dynamic seal resistance, and compensation oil viscous resistance. This newly designed controller incorporates sliding mode (SMC) feedback control with feedforward compensation of the system uncertainties estimated by the ESO, and the external disturbances of the hydrodynamics by fitting the parameters, the dynamic seal resistance, and the compensation oil viscous resistance to the tested results. Additionally, an adaptive super-twisting algorithm (AST) with integral action is introduced to eliminate the SMC’s chattering phenomenon and reduce the system’s steady-state error. The stability of the proposed controller is proved via the Lyapunov method, and the effectiveness is verified via simulation and comparative experimental studies with SMC and the adaptive fuzzy sliding mode control method (AFSMC).

Modified Super-Twisting Algorithm-Based Model Reference Adaptive Observer for Sensorless Control of the Interior Permanent-Magnet Synchronous Motor in Electric Vehicles

In this paper, the model reference adaptive system (MRAS) method has been employed to observe speed in sensorless field-oriented control (FOC) with flux weakening (FW) and maximum torque per ampere (MTPA) operations for the interior permanent-magnet synchronous motor (IPMSM). This paper focuses on the modified MRAS observer, which is based on the sigmoid function as a switching function and also the adaptive sliding mode coefficient. The sliding mode strategies are employed for the adaptation mechanism instead of the PI controller. The conventional PI-MRAS causes oscillations in rotor speed. To solve this problem, the modified adaptive super-twisting algorithm (STA)-based MRAS method is proposed by utilizing the sigmoid function. The proposed modified MRAS is compared to conventional methods. Additionally, it is examined for performance against the fast terminal sliding mode (FTSM), which is applied to the MRAS as an adaptation mechanism in terms of sliding mode strategies. The modified STA-MRAS is explored under the ECE and EUDC (Extra Urban Driving Cycle) drive cycles for electric vehicle applications. Finally, the obtained results show the validity and capability of the proposed adaptive STA-MRAS in terms of speed tracking.

Adaptive Super-Twisting Sliding Mode Forward Tracking Guidance Law Considering Missile Body Characteristics

Aiming at the problem of forward tracking guidance munitions with missile body characteristics intercepting maneuvering targets, and to improve the hit accuracy of forward tracking guidance system, this paper proposes an adaptive super-twisting sliding mode forward tracking guidance algorithm considering the impact of first-order overload characteristics of missile body and input saturation limitation. Firstly, the nonlinear model of the guidance system is made by the kinematic relation for projectile-target, the principle for the forward tracking interception, the overload characteristic of the missile body, and the input saturation limitation. Secondly, a finite time interference observer (FTIO) is adopted to accurately estimate the nonlinear interference in the guidance system, furthermore, an adaptive super-twisting algorithm for slide mode control is used to design the forward tracking guidance algorithm considering the characteristics of the projectile body. Finally, the results by simulation indicate the adaptive super-twisting slide mode for forward tracking guidance algorithm considering characteristics of the projectile body designed in this paper has better-hit accuracy.

Anti-unwinding adaptive super-twisting attitude control for spacecraft

This article addresses the attitude maneuver control without unwinding based on variable gain(i.e. adaptive) super-twisting algorithm and the modified Rodrigues parameters(MRPs). First, a selection logic for the MRP set and its shadow set is designed in order to construct an attitude control system model for rigid spacecraft. Second, a nonlinear sliding function is presented, and on the sliding phase, finite-time convergence and anti-unwinding performance are guaranteed. As a result, a first order sliding mode controller is created to ensure finite-time convergence and anti-unwinding performance on the reaching phase. To alleviate the chattering and improve convergence speed, an adaptive super-twisting algorithm is presented, and the finite-time convergence and anti-unwinding performance are guaranteed on the reaching phase. Furthermore, the adaptive gains are designed based on dual-layer adaptive law, which allows the gains to be increased and decreased as appropriate. It is further demonstrated that when the controller gains are time-varying according to adaptive law, the convergence property and anti-unwinding performance are guaranteed. Numerical simulations are carried out to illustrate the closed-loop system's performance under the proposed control scheme.

Fuel Cell Module Control Based on Switched/Time-Based Adaptive Super-Twisting Algorithm: Design and Experimental Validation

Fuel cells (FCs) have emerged as a sound promising technology for their application in emissions-free generation systems. Their high efficiency, reliability, and clean energy make these electrochemical devices especially suitable for manifold applications such as transportation, stationary generation, and portable devices. In view of the inherent complexity of this technology, the FC control plays a fundamental role to guarantee stability and high performance against system uncertainties and disturbances. Regarding this, sliding mode control has proved to be a powerful technique for the design of robust controllers for generation systems involving FCs. However, its discontinuous control action gives rise to some undesired effects when applied to real nonideal systems, being control chattering is usually the main drawback. In this framework, the brief presents the design and experimental implementation of an FC module control via a switched/time-based adaptive super-twisting algorithm (STA). The designed algorithm is evaluated in an experimental platform of a hybrid generation system based on a commercial 1.2-kW FC. The proposed controller exhibits a low value of chattering and similar robustness features compared to traditional STA.

Composite Terminal Guidance Law for Supercavitating Torpedoes with Impact Angle Constraints

A novel composite terminal guidance law with impact angle constraints is proposed for supercavitating torpedoes to intercept maneuvering warships. Based on an adaptive super-twisting algorithm and nonsingular terminal sliding mode (NTSM), the proposed guidance law can guarantee the finite-time convergence of line-of-sight (LOS) angle error and the LOS angular rate error. The new guidance law is a combination of finite-time stability theory, sliding mode control (SMC), tracking differentiator (TD), disturbance observer (DO), and dynamic surface control. A high-order sliding mode TD is used for denoising, tracking, and differentiating the measured target heading angle. A novel DO, with its finite-time stability proved, is designed to estimate the target lateral acceleration for feedforward compensation to attenuate chattering in control input. In the case of a first-order-lag autopilot, a new kind of tracking differentiator is adopted to compute the first-order time derivative of the virtual control command, which can improve the accuracy of dynamic surface control and avoid the “explosion of items” problem encountered with the backstepping control. Finally, numerical simulation results are presented to validate the effectiveness and superiority of the proposed TD, DO, and the composite guidance law.

Adaptive Super-Twisting Cooperative Guidance Law with Fixed-Time Convergence

For the guidance problem of multiple missiles cooperatively intercepting a maneuvering target, fixed-time cooperative guidance law is proposed with impact angle constraints. First, fixed-time consensus, integral sliding mode technique, and adaptive super-twisting algorithm are implemented to construct cooperative guidance law along the line-of-sight (LOS) direction. Second, based on fixed-time convergence observer and terminal sliding mode control, one fixed-time guidance law along the normal direction of LOS is designed to ensure that the missiles attack the target with expected angles. Finally, simulation results are carried out to demonstrate the effectiveness of the proposed fixed-time cooperative guidance law.

Safe operation for teleoperated robotic manipulators with restricted synchronization error via non-singular terminal sliding-mode control

This study presents the design of a robust controller based on the sliding mode theory to ensure the safe operative synchronization of a teleoperated robotic system (TRS). The TRS is integrated by two fully actuated robotic manipulators (RMs) with n degrees of freedom (DoF). The proposed controller implements a decentralized adaptive super-twisting algorithm to obtain the force applied by the human operator and the environment over the TRS. Then, a decentralized non-singular terminal sliding mode (NTSM) controller solves the synchronization problem for the proposed RMs. The novel control approach ensures synchronization, considering that both manipulators have restricted working spaces. The suggested controller enforces the convergence to the origin for the tracking error in a finite time, at least theoretically. The stability analysis of the proposed controller is developed using the second stability method of Lyapunov, considering a class of barrier Lyapunov controlled function. Finally, simulation results are presented to evidence the effectiveness of both proposed algorithms, the adaptive force estimator and the NTSM.

Current Distortion Rejection in PMSM Drives Using an Adaptive Super-Twisting Algorithm

Unavoidably, the controlsystem of any permanent magnet synchronous motor (PMSM) is subjected to perturbations, e.g., motor nonidealities and inverter nonlinearities. To reject these perturbations, a new super-twisting (ST) control variant, called speed adaptive super-twisting (S-AST) control, is proposed in this paper. In the S-AST control, a proportional-integral (PI) and a ST controllers are merged using an adaptive law that is based on the motor speed measurement. This is done to reduce the chattering problems that the standard ST control presents. In addition, a mathematical design for the S-AST control is proposed, where the relationship between the chattering amplitude, the switching frequency and the system perturbations is shown. The main contribution in this paper is the application of the S-AST controller to reduce the total harmonic distortion (THDi) of the PMSM currents. By comparing the S-AST control against PI control, the THDi is reduced from 9.9% to 1.27%, in simulation, and the THDi is reduced from 22.79% to 1.56%, experimentally. These results demonstrate how the S-AST control is an excellent alternative to improve the waveform of the PMSM currents.

Back-Stepping Formation Control of Unmanned Surface Vehicles With Input Saturation Based on Adaptive Super-Twisting Algorithm

Aiming at the formation control problem for unmanned surface vehicles under input overload and external disturbance, a leader-follower formation control law based on input saturation and the adaptive super-twisting algorithm was designed in this paper. Firstly, the mathematical model of underactuated unmanned surface vehicle formation based on the leader-follower method is established, and the virtual expected velocity is designed by the back-stepping method to improve the control accuracy of formation. Secondly, the parametric uncertainties and unknown external disturbances in the USV’s dynamical model are compensated by the proposed adaptive super-twisting control laws. In addition, the input saturation function is added to the controller to avoid machine necrosis caused by input overload. Finally, Simulation results show that the controller can roughly keep the trajectory of the USV consistent with the expected trajectory and ensure that the input values are within the safe range, which proves the effectiveness of the method in this paper.

A Generalized Multivariable Adaptive Super-Twisting Control and Observation for Amphibious Robot

This paper aims at the problem of fast stability control of amphibious robot after state switch. A novel method named as generalized multivariable adaptive super-twisting algorithm (GMASTA) is proposed for the finite time attitude control of amphibious robot. In the proposed method, the standard multivariate super-twisting algorithm is improved by introducing a linear term and a higher power term, in order to reduce convergence time and chattering. In addition, the adaptive gain is employed based on a disturbance observer which can avoid a conservative overestimation of the disturbance. For the designed attitude controller, the finite time stability is proved by Lyapunov method. Two numerical examples were carried out. The results from the first example show that GMSTA is better than MSTA in convergence and robustness. The other example is used to illustrate that the disturbance observer based on the GMASTA can realize the accurate observation of the integrated interference. Compared with PID, the proposed method based on GMASTA can converge faster and has better robustness.

Nonsingular fast terminal control for the DFIG-based variable-speed hydro-unit

Pumped storage power plants (PSPPs) with variable-speed hydro-units are credible when tackling the impact caused by the introduction of renewable energy into grids. However, the units suffer from instability when the grid transients occur because the adopted doubly-fed induction generators (DFIG) have a strong coupling and nonlinearity. Conventional controllers failed to handle this situation. Although the sliding mode controller (SMC) is robust enough, it has problems of infinite convergence time and chattering issues. Nonsingular fast terminal sliding mode controller (NFTSMC) - an advanced SMC - is a promising method to solve these problems. This paper took the DFIG-based variable-speed hydro-unit as the studied object and adopted a newly-designed NFTSMC in the rotor side converter to secure the stable operation of the unit. Especially, a feedback control law and a modified coefficient of the sliding mode surface were combined with the adaptive super-twisting algorithm to handle the additional information of the derivatives of the sliding mode surface and guarantee the theoretical stability. Simulations under load rejection, parameter variation, voltage dips were imposed on the unit. Results showed the proposed controller has lower settling times, oscillations, and less over-shooting. The efficiency of the proposed controller is thus proved.

An adaptive super-twisting algorithm based on conditioning technique

This paper presents an adaptive conditioning-technique-based super-twisting algorithm aiming at improving the convergence speed and reducing the overshoot at the same time. Compared with a recently proposed method called new modified super-twisting algorithm, in which a linear acceleration factor and a damping factor are added to achieve this goal, the proposed method has several advantages. First, the proposed method enhances the convergence performance of the system by resorting to the characteristics of the conditioned super-twisting algorithm and the adaptive gains, without changing the basic structure of the classical super-twisting controller. Thus, stability proof of this method is much simpler and more concise. Furthermore, unlike the new modified super-twisting algorithm, in which an unnatural assumption on the Lipschitz disturbance is made for the stability proof, this method can counteract not only typical bounded Lipschitz disturbances but also square-root growth disturbances. Also, a set of less conservative control gains can be obtained with the proposed algorithm than with the compared algorithm. Apart from these benefits, several simulation results illustrate that the performance of the proposed method is even better in convergence and recovering from disturbance.

Design of an Adaptive Super-Twisting Control for the Cart-Pole Inverted Pendulum System

A cart-pole inverted pendulum system is one of the underactuated systems that has been used in many applications. This research aims to study the design and the effectiveness of the Adaptive Super-Twisting controller to stabilize the system by comparing it with other previous control methods. A stabilization control of the pendulum upright using the Adaptive Super-Twisting algorithm (ASTA), was investigated. The proposed controller was designed based on the decoupling algorithm method to solve the coupled control input in the system model. We then compared the proposed stabilizing controller with first-order sliding mode control (FOSMC) and Super-Twisting algorithm (STA) in Matlab/Simulink simulation and realistic computer simulation. We developed the computer simulation using anyKode Marilou software, which adopted Open-Dynamic Engine (ODE) as a physics engine. In Matlab/Simulink simulation, we considered three different scenarios: a nominal system, a system with uncertainty, and a disturbed system. Meanwhile, in a computer simulation, we only presented the comparison of different controllers' performances for the realized system. Both results showed that the three controllers could stabilize the pendulum upright with a 0.1 rad initial angular position around the vertical axis. Under the same conditions, the ASTA and STA controllers had similar performances; they both have less chattering and faster convergence than the FOSMC approach. However, the FOSMC approach had the least energy delivered and smallest errors than the other two approaches.

Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function

This study introduces a design of robust finite-time controllers that aims to solve the trajectory tracking of robot manipulators with full-state constraints. The control design is based on the construction of a distributed state constraint non-singular terminal sliding mode (CNTSM). The CNTSM design includes the gain self-adapting tuning method, which can ensure finite-time convergence to the sliding surface aside from the states to its corresponding reference trajectories. The implementation of the time-varying gain ensures the fulfillment of the accurate tracking for the references while the position and velocity constraints are satisfied permanently. A barrier Lyapunov function is proposed to develop the finite-time stability analysis of the designed controllers. The CNTSM realization uses the tracking error as well as its estimated derivative, which is calculated using a variant of adaptive super-twisting algorithm operating as robust differentiator. The proposed CNTSM is numerically evaluated on a two-link RM with uncertain inertia and Coriolis matrices. Simulation and experimental results evidence the efficiency of the CNTSM controller demonstrating a better tracking performance while the full-state constraints are satisfied in counterpart with the classical non-singular terminal sliding mode which is not able to keep such restrictions.

A Novel Continuous Nonsingular Finite–Time Control for Underwater Robot Manipulators

In this paper, the tracking control problem of underwater robot manipulators is investigated under the influence of the lumped disturbances, including unknown ocean current disturbances and parameter uncertainties. The proposed novel continuous nonsingular finite–time (CNFT) control method is twofold. Firstly, the modified adaptive super–twisting algorithm (ASTA) is proposed with a nonsingular fast terminal sliding mode (NFTSM) manifold to guarantee the finite–time convergence both in the sliding mode phase and the reaching phase. Secondly, a higher–order super–twisting disturbance observer (HOSTDO) is exploited to attenuate the effects of the lumped disturbances. Considering the time–varying gain matrix of the closed–loop control system, the bounded stability is strictly proved via the Lyapunov theory. Hence, the superiority of the proposed controller is singularity–free, fast convergence, chattering–free, high steady–state tracking performance, and good robustness by resorting to the methods of CNFT control and ASTA in combination with a disturbance observer. Finally, numerical simulations are conducted on a two degree–of–freedom (DOF) underwater robot manipulator to demonstrate the effectiveness and high tracking performance of the designed controller.