Super-twisting Differentiator Research Articles

Active disturbance rejection control for systems with uncertainties and noise using super twisting differentiator-based event-triggered ESO

This paper focuses on the noise suppression issue of high-gain extended state observer (ESO) for systems with uncertainty and unknown measurement noise in the active disturbance rejection control (ADRC) paradigm. A special combination of super twisting differentiator (STD) and event-triggered ESO is devised with a designed event-triggered mechanism. Specially, the proposed STD-ETESO incorporates a finite-time switching strategy, which improves the poor transient performance of the STD acting as a pre-filter to prepare relatively smooth signals for the ESO. The locally asymptotic boundedness of the estimation error can be guaranteed by the Input-state-stability (ISS) and existing research for the STD. The effectiveness of the proposed method is validated by a general example and a practical motion control system. Different integral criteria is introduced to evaluate the overall tracking accuracy and energy usage for comparison with existing different ESOs, which reveals the superiority of the proposed STD-ETESO in noise attenuation and disturbance rejection.

Identification of Hamiltonian systems using neural networks and first integrals approaches

This research introduces a class of non-parametric identifiers based on differential neural networks represented by Hamiltonian dynamics. The structure of the identifier corresponds to the form of a canonical Hamiltonian system that uses the evolution of generalized coordinates and momentums. The learning laws of the identifier come from applying the first integrals approach, which justifies the design of an exact identifier considering the time invariance of the Hamiltonian, with a finite number of activation functions in the identifier structure. The first integrals approach derives several learning laws for the proposed class of identifiers. The learning laws design uses the estimated derivative of the generalized momentum assessed via a super-twisting differentiator with multiple inputs and outputs. All proposed laws require the solution of differential continuous-time Riccati equations and nonlinear differential equations for the learning laws, which depend on the identification error and state constraints. The developed identifier was evaluated compared to an identifier that did not consider the Hamiltonian constraint using first integrals. This comparison included a numerical evaluation of the identifier considering its application to a classical Hamiltonian system associated with the Kepler dynamics representing satellite orbital evolution. This evaluation confirmed that the identification results were improved with the proposed learning laws regarding the class of Hamiltonian structures, and the quality indicators based on the mean square error were several times lower.

Fuzzy-tolerant-strategy for constrained nonlinear system via adaptive observer

This article considers the tracking control of nonlinear system with state constraints and faults. A fuzzy tolerant control approach on adaptive sliding-mode observer is proposed to accomplish good tracking performance. Firstly, for the purpose of getting the unknown state, a state estimator based on the fuzzy logic systems (FLSs) is designed. Secondly, a fuzzy observer by variable structure method is posed to approximate the faults, and the finite time convergence of observation error is proven. Furthermore, a two-layer nested adaptive law is constructed to improve the observer. Thirdly, a fuzzy backstepping tolerant controller based on super-twisting differentiator is proposed. In which, the barrier Lyapunov function is designed to counter the state constraints, and the super-twisting estimator is employed to estimate the derivative of virtual control input. Finally, two simulation results are analyzed to demonstrate the potential of the developed schemes.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

Worst-case error bounds for the super-twisting differentiator in presence of measurement noise

The super-twisting differentiator, also known as the first-order robust exact differentiator, is a well known sliding mode differentiator. In the absence of measurement noise, it achieves exact reconstruction of the time derivative of a function with bounded second derivative. This note proposes an upper bound for its worst-case differentiation error in the presence of bounded measurement noise, based on a novel Lipschitz continuous Lyapunov function. It is shown that the bound can be made arbitrarily tight and never exceeds the true worst-case differentiation error by more than a factor of two. A numerical simulation illustrates the results and also demonstrates the non-conservativeness of the proposed bound.

Transient stability increase of multi-machine power system by using SSSC and DFIG control with TEF technique and super twisting differentiator

This paper suggests a nonlinear controller of a Static Synchronous Series Compensator (SSSC) and a doubly-fed induction generator (DFIG) for transient stability enhancement by transient energy function (TEF) technique and super-twisting differentiator in the multi-machine power system. Initially, the TEF approach is employed to damping control and stability enhancement in a multi-machine power system including an SSSC, DFIG, and synchronous generator (SG). Then, the signals of time-derivative in the controller with a super-twisting differentiator are estimated. The significance and novelty of this work are the employs of the TEF method obtained for the multi-machine power system containing DFIG and SG. Another novelty is the use of the DFIG and SSSC simultaneous control whose uncertain parameters are estimated with a super-twisting differentiator. The feature of the nonlinear control approach is robust versus modifications in the topology of the system. Simulation is performed on the IEEE 9-bus system to appraise the operation of the nonlinear controller approach compared to back-stepping and sliding mode control. The simulation results demonstrate that the nonlinear controller approach satisfactorily reduces the first swing of oscillations.

Robust dynamic backstepping averaged sub-gradient integral sliding mode control for navigation of mobile robots

The main goal of the current investigation is to present an output feedback robust control that regulates the motion of mobile robotic autonomous devices based on the application of the dual averaged sub-gradient descendant method. Sub-gradient realization aims to solve the design of a proposed extremum seeking control to stabilize the trajectory tracking error between the three-dimensional position of mobile robotic autonomous devices and some attainable reference trajectories in the same spatial domain. The controller belongs to a class of sliding mode controller with variable gain based on a sliding surface depending on the tracking error and its time derivative. This derivative is estimated with the application of a distributed time-dependent super-twisting robust differentiator. The proposed mobile robotic autonomous device dynamics considers the dynamics of actuators (direct current motors) which drives the mobilization of mobile robotic autonomous devices. The dynamic nature of the mobile robotic autonomous devices regulated by motor actuators induces a backstepping-like controller design based on a two-stage sequential application of the sub-gradient strategy, one for the mobile robotic autonomous devices and the second for the motor dynamics. The mixed strategy appears as a novel formulation to solve the path track for reference trajectories of mobile robotic systems. The proposed control considers the optimization of the tracking error dependent functional without the full knowledge of the mobile robotic autonomous device dynamics. With the aim of proving the effectiveness of the suggested design, two numerical examples are developed. In these examples, the tracking performance, minimization of the proposed functional as well as control evolution are evaluated. The controlled tracking outcomes of the proposed integral sliding mode control are contrasted with the outcomes produced by a set of proportional–derivative and selected sliding mode (first-order type) controllers. The suggested controller shows a superior tracking of the reference trajectory than the other two comparative controllers, using quality measures such as least mean square error and its integral.

Observer-Based Sliding-Mode Control for Grid-Connected Power Converters Under Unbalanced Grid Conditions

This article proposes a novel robust control strategy for three-phase power converters operated under unbalanced grid conditions. A consolidated control objective is obtained in the stationary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha \beta$</tex-math></inline-formula> frame, which can be flexibly adjusted according to the degree of oscillation in the active and reactive powers and the balance of the three-phase current. Based on the dynamics of the converter and control objective, a control scheme in a cascaded framework is presented, in which an adaptive observer is applied to estimate the positive and negative sequences of the grid voltage. In the current tracking loop, a super-twisting algorithm current controller coupled with a super-twisting differentiator is implemented to track the current references, featuring rapid dynamics, and improved robustness. Additionally, in the voltage regulation loop, an effective composite controller is developed to regulate the dc-link voltage, where a super-twisting observer is used to estimate the load disturbance, thereby improving the performance of the converter. The experimental results are provided to confirm the effectiveness and superiority of the proposed control strategy.

Hybrid position/force output feedback second-order sliding mode control for a prototype of an active orthosis used in back-assisted mobilization.

This article shows the design of a robust second-order sliding mode controller to solve the trajectory tracking problem of an active orthosis for assisting back physiotherapies. The orthosis was designed in agreement with morphological dimensions and its articulations distribution followed the same designing rules. The orthosis has six articulated arms attached to an articulated column. The orthosis was fully instrumented with actuators and position sensors at each articulation. The controller implemented a class of hybrid/position controller depending on the relative force exerted by the patient and the orthosis movement. The position information provided by each articulation was supplied to a distributed super-twisting differentiator to recover the corresponding angular velocity. A set of twisting controllers was implemented to regulate the position of the robot in agreement to predefined reference trajectories. Reference trajectories were obtained from a biomechanical-based analysis. The hybrid tracking control problem solved the automation of the assisted therapy to the patient, including the force feedback. The performance of the orthosis was tested with different dummy bodies with different resistance. The robust output feedback controller successfully tracked the reference trajectories despite the material of the dummy used during the testing. The orthosis was evaluated with two volunteers using a simple reference trajectory. Graphical Abstract General structure of the active back assisted orthosis.

Super-Twisting Differentiator-Based High Order Sliding Mode Voltage Control Design for DC-DC Buck Converters

This paper aims to focus on the smooth output of DC-DC buck converters in wireless power transfer systems under input perturbations and load disturbances using the high-order sliding mode controller (HOSM) and HOSM with super-twisting differentiator (HOSM + STD). The proposed control approach needs only measurement of converter output voltage. Theoretical analysis and design procedures, as well as the super-twisting differentiator of the proposed controller are presented in detail with the prescribed convergence law of high-order sliding modes. Comparisons of both simulation and experimental results among conventional proportional-integral (PI) control, traditional sliding mode control (SMC), HOSM and HOSM + STD under various test conditions such as steady state, input voltage perturbations and output load disturbances, are presented and discussed. The results demonstrate and validate the effectiveness and robustness of the proposed control method.

An adaptive sliding mode differentiator for actuator oscillatory failure case reconstruction

This paper proposes an adaptive sliding mode super-twisting differentiator which allows the gains to adapt based on the ‘quality’ of the sliding motion. A Lyapunov based analysis for the adaptive super-twisting scheme is presented to demonstrate its properties. As an example, the adaptive differentiator proposed in this paper has been used as part of a nonlinear FDI scheme for an Oscillatory Failure Case (OFC) in an actuator. The FDI scheme requires an estimate of the rod speed which is provided by the adaptive super-twisting differentiator. Due to the conditions in which the actuator operates, normally the differentiator gains are initialised at low values to ensure good rod speed estimation in fault free conditions. However for large amplitude/frequency OFCs, the gains must adapt in order to maintain sliding and provide a good estimation. Simulations on a high fidelity nonlinear aircraft benchmark model have been carried out for both liquid and solid OFCs.

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers' family achieves convergence to time-varying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.

A Lyapunov approach to output feedback control using second-order sliding modes

The objective of this paper is to provide for the second-order sliding modes (SOSM) output feedback (OF) a Lyapunov-based approach, in the same spirit as it is done for the observer-based output feedback control in conventional non-linear control. To reach this objective, we consider first the Lyapunov design of a state feedback (SF) control based on the twisting algorithm. We propose a (new) Lipschitz continuous strict Lyapunov function for the twisting controller, which assures its finite-time convergence and its robustness under bounded perturbations. In a second step, a Lyapunov design of a finite-time convergent and robust observer estimating the state of the plant is considered. It generalizes the super-twisting differentiator. In a final step, the properties of the interconnection of the observer and the controller in the OF controller are established by Lyapunov arguments, much in the same form as in the conventional non-linear control literature. It is shown that the SOSM-based OF controller (almost) satisfies a separation principle, a result similar to the linear case. Here, however, in order to guarantee the robustness of the OF, the observer has to be designed taking into account the SF controller.

A Hybrid Robust Non-Homogeneous Finite-Time Differentiator

A variant of super-twisting differentiator is proposed. Lyapunov function is designed and an estimate on finite time of derivatives estimation is given. The differentiator is equipped with hybrid adaptation algorithm that ensures global differentiation ability independently on amplitude of the differentiated signal and measurement noise.