Variable Gain Super-twisting Algorithm Research Articles

Multiple feedback recurrent neural network based super-twisting predefined-time nonsingular terminal sliding mode control for quad-rotor UAV

This research deals with the overall predefined-time stability (PTS) of Unmanned Aerial Vehicles (UAV) ensuring rapid convergence based on a novel sliding mode control (SMC). The strength of predefined-time sliding manifolds lies in the convergence rate can be adjusted by an explicit parameter. For the limitation of chattering encountered by predefined-time SMC (PTSMC), a variable gain super-twisting algorithm (STA) with additional linear items is designed as the switch controller. To conserve the restrained computational resources of quadrotors, the equivalent control input is approximated by a multiple feedback recurrent neural network (MFRNN) directly, which is challenging for general recurrent neural networks. The proposed MFRNN is characterized by the incorporation of double-loop feedback within the layers, augmenting its capacity for accurate approximation. To address the vanishing gradients commonly encountered with traditional activation functions, LeakyRelu is chosen. The Lyapunov theory is utilized to ensure the PTS of overall system and obtain the MFRNN weight update laws. An experiment is conducted to validate the proposed scheme.

Fixed-time stability super-twisting sliding mode control with mismatched disturbances

In practice, many systems are affected by mismatched disturbances, which do not satisfy the match condition. This study focuses on a variable gain super-twisting sliding mode controller that achieves global robust fixed-time stabilization of second-order systems with matched and mismatched disturbances without disturbances observers. The proposed controller and the sliding variables adopt a state-dependent variable exponent coefficient, which improves the robustness properties of a sliding surface and switching control law. At the same time, the control strategy alleviates the chattering phenomenon by using the variable-gain super-twisting algorithm. The settling time is calculated a priori by the Lyapunov method. Simulation results show that, compared with recently published controllers, our proposed control strategy can suppress the mismatched disturbance more rapidly, simply, and effectively.

Barrier Function-Based Adaptive Super-Twisting Controller

In this article, a variable gain super-twisting algorithm based on a barrier function is proposed for a class of first order disturbed systems with uncertain control coefficient and whose disturbances derivatives are bounded but the upper bounds of those derivatives are unknown. The specific feature of this algorithm is that it can ensure the convergence of the output variable and maintain it in a predefined neighborhood of zero independent from the upper bound of the disturbances derivatives. Moreover, thanks to the structure of the barrier function, it forces the gain to decrease together with the output variable and the control signal follows the absolute value of the disturbances.

Virtual-Vector-Based Model Predictive Current Control of Five-Phase PMSM With Stator Current and Concentrated Disturbance Observer

The finite control set model predictive current control(FCS-MPCC)can significantly improve the dynamic performance of the five-phase permanent magnet synchronous motor (5P-PMSM), but its control performance highly depends on the accuracy of the model parameters. The parameter error compensation based on the first-order sliding mode observer can improve the robustness of FCS-MPCC under Model parameter mismatch. The introduction of the sign function leads to chattering in the observation results. In order to eliminate this chattering, a first-order low-pass filter needs to be added for compensation. However, the introduction of filters will increase system design difficulty and bring system delays, which will affect the compensation effect. Therefore, a second-order sliding mode observer, based on the variable-gain Super-Twisting algorithm, is proposed to realize the parameter error estimation and one-beat delay compensation in this paper. By establishing the Lyapunov function, the stability proof of the proposed observer, and the calculation method of the observer parameters are given. Besides, the third harmonic current can be suppressed, and the computational burden of the control unit can be reduced by controlling the proportion of medium vector and large vector reasonably. According to the deadbeat control, the optimal virtual voltage vector action time in each cycle is obtained, which improves the tracking ability of the reference current. At last, Extensive experimental results validate that i) the proposed observer can significantly improve the robustness of model predictive current control even under parameters mismatch; ii) the proposed control method can effectively enhance the dynamic performance of the 5-phase PMSM.

Robust output‐feedback control for the cart–pole system: a coupled super‐twisting sliding‐mode approach

This study presents an output-feedback controller for a cart-pole system via coupled sliding-mode algorithms. Due to the fact that this system is underactuated, a special type of sliding surface is employed instead of using a transformation to the regular form. Then, a continuous sliding-mode controller is designed using the super-twisting algorithm so that robustness of the control scheme is guaranteed. Since the proposed controller requires the knowledge of the velocities, a homogeneous sliding-mode observer is introduced to estimate such velocities. Then, in order to improve the control effort, a variable gain super-twisting algorithm is also proposed. The closed-loop stability is also guaranteed by means of input-to-state stability properties and Lyapunov function approaches. All the results are validated by means of real-time experiments, providing also a comparison between the proposed controllers and a chattering attenuation approach.

Robust control design for air breathing proton exchange membrane fuel cell system via variable gain second‐order sliding mode

AbstractThe nonlinear and time‐dependent characteristic and unknown modeling uncertainty of proton exchange membrane fuel cell (PEMFC) such as complex electro‐chemical, thermal, and fluid mechanic phenomena make its controller design quite challenging. In this paper, a controller based on a super twisting algorithm (STA) with variable gains is proposed to control the air breathing system of PEMFC. The strategy includes regulating the oxygen excess ratio () for preventing the stack oxygen starvation and maintaining optimum net power output in spite of external disturbances and model uncertainties. The proposed algorithm has the main advantages of the fixed gain STA, such as robustness against the disturbance and parametric uncertainties with the unknown boundary, chattering reduction, and finite time convergence. The Lyapunov analysis was proposed to assess the stability of the Variable Gain Super Twisting Algorithm (VGSTA). The results verified the effectiveness of the proposed controller with attaining robust regulation against uncertainties, disturbances, and noisy circumstance compared to fixed gain SOSM controllers.

Implementation of the load frequency control by two approaches: variable gain super-twisting algorithm and super-twisting-like algorithm

In this paper we explore a variable gain super-twisting algorithm and super-twisting-like algorithm for the load frequency control of two-area interconnected power system with nonlinearities. The two-area system is based on two different kinds of turbine. The nonlinearities are contained in this model. The control objective is to adjust the area control error (ACE), frequency deviation and tie-line power deviation to zero. We also prove the convergence of the proposed two control methods. Additionally, the traditional super-twisting algorithm is designed and simulated. Finally, simulation results are discussed and in comparison with the traditional super-twisting algorithm, which shows the superiority of the proposed two methods.

Output-feedback variable gain super-twisting algorithm for arbitrary relative degree systems

ABSTRACTThis paper presents an output-feedback control strategy based on the variable gain super-twisting algorithm. The proposal achieves robust global/semi-global exact tracking results for plants with arbitrary relative degree. This is ensured in spite of parametric uncertainties and disturbances that may be state-dependent and time-varying. The construction of such controller is based on a (non)homogeneous higher order sliding-mode differentiator with dynamic gains. The gain adaptation schemes for the controller and differentiator are based on norm observers to overcome the lack of state measurement. The continuous nature of the obtained control signal alleviates the chattering phenomenon. The stability properties of the proposed controller are demonstrated by means of a Lyapunov function-based analysis. The theoretical results are verified through a simulation example, and experimentally tested on a seesaw module.

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

This study investigates integral sliding mode control problems for Markovian jump T–S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analysed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed.

Decentralized Control of Harmonic Drive Based Modular Robot Manipulator using only Position Measurements: Theory and Experimental Verification

This paper presents a decentralized control approach of harmonic drive (HD) based modular robot manipulator (MRM) using only position measurements. Unlike known methods that rely on joint torque and velocity sensing, this paper addresses the problem of controlling HD based MRM using only position measurements on the motor and link sides of each module. The dynamic model of HD based MRM is formulated by employing a high-fidelity HD model and the velocity of each robot joint is estimated based on a novel nonlinear velocity estimator. With only local information on each module, a decentralized integral sliding mode controller (ISMC) is designed based on variable gain super-twisting algorithm (VGSTA) to compensate the model uncertainty and to reduce the chattering effect of the controller. The asymptotic stability of the closed-loop system is proved using the Lyapunov theory. Finally, experiments are performed for a 3-DOF MRM to verify the advantage of the proposed method.

Decentralized Integral Nested Sliding Mode Control for Time Varying Constrained Modular and Reconfigurable Robot

This paper presents a novel decentralized integral nested sliding mode control approach for a time varying constrained modular and reconfigurable robot (MRR) and addresses the problem of joint trajectory tracking control of the MRR with strongly coupled model uncertainty. First, the dynamic model of the time varying constrained MRR is described as a synthesis of interconnected subsystems. Second, a decentralized control scheme is proposed based on only local dynamic information of each module. An integral nested sliding surface is implemented to reduce the chattering effect of the controller. Model uncertainties, including the unmodeled subsystem dynamics, the friction modeling error, and the interconnected dynamic coupling, are compensated by a variable gain supertwisting algorithm (VGSTA) based controller. The stability of the close-loop system is proved using the Lyapunov theory. Finally, simulations are performed for a time varying constrained 2-DOF MRR to study the effectiveness of the proposed method.

Variable Gain Super-Twisting Sliding Mode Control

In this note, a novel, Lyapunov-based, variable-gain super-twisting algorithm (STA) is proposed. It ensures for linear time invariant systems the global, finite-time convergence to the desired sliding surface, when the matched perturbations/uncertainties are Lipschitz-continuous functions of time, that are bounded, together with their derivatives, by known functions. The proposed algorithm has similar properties to the variable-gain first-order sliding mode control, but it provides alleviation to the chattering phenomenon. The results are verified experimentally.