Adaptive Second-Order Sliding Mode Research Articles

Adaptive Second-order Sliding Mode Control of Electrical Throttles Based on Online Zero-crossing Checking

Adaptive Second-order Sliding Mode Control of Electrical Throttles Based on Online Zero-crossing Checking

Design of Adaptive SOSM Controller Subject to Disturbances With Unknown Magnitudes

The work is dedicated to handling the issue of a new adaptive second-order sliding mode (ASOSM) controller design for a class of nonlinear systems subject to disturbances and nonlinear control gains with unknown magnitudes. Significantly, the proposed controller involves two adaptive parameters, which are generated from a dual-layer adaptive mechanism. The mechanism directs at the reestablishment of the upper bounds of the unknown disturbances and the handling of the nonlinear control gains. Through a combination of the mechanism and the finely renovated adding a power integrator technique, a novel design procedure is introduced to skillfully design an ASOSM controller. A rigorous Lyapunov analysis is afforded to evince the finite-time stability of the whole system. Finally, two illustrative examples are given to exhibit the effectiveness of the developed approach.

Path tracking of unmanned agricultural tractors based on a novel adaptive second-order sliding mode control

Unmanned tractors are widely adopted in agricultural operations as autonomous driving technology progresses. The current path tracking control methods are limited by the unstructured farmland, the accuracy and anti-interference ability needed to be improved. This paper presents a novel adaptive second-order sliding mode (ASOSM) control method to tackle the aforementioned problems in practical implementation. First, we introduce a preview lateral offset model based on the preview kinematic and tractor dynamic model, which helps solve the under-actuated problem in path tracking. Then, the ASOSM controller is designed using the revamped adding a power integrator (API) and adaptive mechanism, which ensures that the sliding variable is converged to zero within the finite time. Meanwhile, the chattering problem in traditional sliding mode control is relieved. Finally, a high-fidelity and full-car model is established under Simulink/Carsim environment, and comparative simulations conrm the superiority of the designed control method.

A new adaptive second‐order sliding mode controller design for nonlinear systems with multiple uncertainties

SummaryThis study is dedicated to solving the problem of a new adaptive second‐order sliding mode (SOSM) controller design for a type of nonlinear systems with multiple uncertainties by using adding a power integrator (API) and the parameter separation techniques. Supported by the finite‐time Lyapunov theory, the finite‐time stability of the closed‐loop system under the proposed adaptive SOSM controller has been firmly guaranteed. The significant advantages here lie in that the prior knowledge about the bounds of uncertainties is not required in the designed adaptive SOSM control approach, and the switching gain can be tuned dynamically. Finally, a numerical example is presented to indicate the notable feature and effectiveness of the designed adaptive SOSM approach.

Adaptive Second-Order Sliding Mode Control: A Lyapunov Approach

This article proposes an adaptive second-order sliding mode (ASOSM) controller design by means of the Lyapunov method. The notable feature of the proposed algorithm is that it only needs boundedness of the uncertainties, whereas boundedness of the derivatives of uncertainties is not demanded. Under the proposed ASOSM control scheme, the gain can be dynamically tuned, which avoids gain overestimation. The finite-time stability of the closed-loop ASOSM dynamics is proved via the Lyapunov theory. Finally, the simulation results are shown to validate the theoretical analysis.

Research on the Trajectory Tracking of Adaptive Second-Order Sliding Mode Control Based on Super-Twisting

This article focuses on the trajectory tracking problem in the actuation control section of autonomous vehicles. Based on a two-degrees-of-freedom dynamics model, this paper combines adaptive preview control with a second-order sliding mode control method to develop a new control method. By designing an objective function based on lateral deviations, road boundaries, and the corresponding characteristics of the overall vehicle motion, the method adaptively adjusts the preview time to obtain the ideal yaw rate and then uses a second-order sliding mode control algorithm named Super-Twisting to calculate the steering wheel angle. Combining the low-pass filter with this controller can effectively suppress the chattering caused by the switching of the sliding mode plane while proposing a concept of smoothing based on gradient derivative, the smoothness after filtering is one-seventeenth of that before filtering, whereas the phase plane is used to prove its effectiveness and stability, it can be seen from the phase diagrams that all the state points are in the stable region. A joint simulation model of Matlab/Simulink and Carsim was built to verify the control effectiveness of the controller under the double-shift road, and the simulation results show that the designed controller has good control effect and high tracking accuracy. Meanwhile, the simulation model is also used for other simulations, firstly, simulation comparison tests were carried out with the Model Predictive Control algorithm at speeds of 36 and 54 km/h, compared to the MPC controller, the tacking accuracy of the ST controller has improved to 64.42% and 51.02% at 36 and 54 km/h; secondly, taking simulation of the designed controller against a conventional sliding mode controller based on isokinetic law of convergence, compared to the CSMC controller, the tracking accuracy of the ST controller has improved 41.78% at 54 km/h, and the smoothness of the ST controller is one-nineteenth of that of the CSMC controller; thirdly, carrying out simulations on parameter uncertainties, and replacing parameter uncertainty with Gaussian white noise, the maximum tracking error at 36 and 54 km/h did not exceed 0.3 m, and tracking remains good. Small fluctuations in the steering wheel angle do not affect the normal actuation of the actuator.

Adaptive Second-Order Sliding Mode Control of Buck Converters with Multi-Disturbances

In this paper, a novel adaptive second-order sliding mode (2-SM) control approach, based on online zero-crossing detection, was proposed to solve the problems of the chattering and fixed control gain for buck converters with multi-disturbances. In modeling, the possible parameter perturbations and external disturbances of the converter system were contained. Instead of the traditional first-order sliding mode (1-SM), the twisting algorithm with 2-SM was adopted for the controller design, which could overcome the chattering problem and realize control continuity. Meanwhile, a novel adaptive mechanism was introduced to replace the conventional fixed control gain by time-varying control gain, the idea of which is to calculate the number of the zero-crossing points of the sliding surface online. As a result, the control magnitude of the improved controller could be reduced to a minimal admissible level, and the steady error of the output voltage could converge to the expected value. Furthermore, the robust stability of the converter system with multi-disturbances wads investigated. Comparative simulations and experiments validated the advantages of this paper as offering better robustness and control performance.

Fuzzy Adaptive SOSM Based Control of a Type of Nonlinear Systems

This brief addresses the issue of devising a fuzzy adaptive second-order sliding mode (SOSM) controller for a type of nonlinear systems. First of all, the fuzzy logic systems are adopted to dynamically approximate the unknown functional bounds of uncertainties. Subsequently, a control strategy of fuzzy adaptive SOSM on the basis of the backstepping-like technique and the fuzzy adaptive control is developed. It is strictly proved via the Lyapunov theory that the resultant whole system is finite-time stable. Comparative simulation results confirm that under the proposed method, the states can be rapidly regulated to zero and meantime the chattering problem can be alleviated.

Adaptive Second-Order Sliding Mode Control for Grid-Connected NPC Converters With Enhanced Disturbance Rejection

In this article, a two-stage control scheme consisting of an adaptive-gain second-order sliding mode (SOSM) controller and a switched high-gain observer (HGO) is proposed for the three-level neutral-point-clamped (NPC) converter. The adaptive-gain SOSM control method is applied both in the voltage regulation loop and instantaneous power tracking loop, thus, the boundary of the disturbance derivative does not need to be known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> . Compared with the fixed-gain SOSM, it provides a faster dynamic and a better steady-state response for the NPC converter. On the other hand, the conventional disturbance compensation observer used in the power system suffers from the adverse effects of measurement noise, which limits the performance of the observer. A switched HGO is combined with the adaptive-gain SOSM controller in the voltage regulation loop to address this issue. By using a switched observer gain, the switched HGO greatly diminishes the performance degradation induced by the inevitable measurement noise. Finally, several experiments between the representative extended state observer-based SOSM control scheme and the proposed control method are carried out for a comparison. The results demonstrate the feasibility and effectiveness of the proposed approach.

Finite-Time Tracking Controller Design of Perturbed Robotic Manipulator Based on Adaptive Second-Order Sliding Mode Control Method

This article presents an adaptive finite time second-order sliding mode tracking control scheme for robotic manipulators. A new control law is suggested to force the trajectories of the robot manipulator to move from all initial conditions to proportional-integral-derivative switching surface in the finite time and stay on it. Moreover, the adaptation law rejects the requirement of knowledge about upper bound of the external perturbations. It is difficult to exactly determine the upper bound of the perturbations in the practical systems, such as robot manipulators. Unlike the existing methods, the new adaptive finite time second-order sliding mode tracker for $n$ -link robot manipulators enables accurate tracking control, robust performance and parameter tuning. The suggested approach presents the design of a robust controller such that the tracking errors of robot manipulator can reach the equilibrium in the finite time. Through the combination of the finite time tracker and disturbance observer, the position tracking purpose of manipulator joints is accurately performed not only in the nominal environment, but also in the existence of different types of perturbations. The robustness performance and effectiveness of the offered technique are studied in simulation and experimental results.

An Adaptive SOSM Controller Design by Using a Sliding-Mode-Based Filter and its Application to Buck Converter

In this paper, a novel adaptive second-order sliding mode (SOSM) control method is proposed by combining a new adaptive strategy with the backstepping-like technique. The new adaptive strategy is first constructed by means of the equivalent control for which a sliding-mode-based filter is employed rather than the widely-used low-pass filter such that the parameter restriction under the usage of low-pass filter can be relaxed. Then, by applying the proposed adaptive strategy and the idea of adding a power integrator, an adaptive SOSM method is established to finite-time stabilize the sliding variables. The feature of the proposed SOSM method lies in that the gain will vary with the size of the lumped uncertainty so as to avoid the overestimation of the gain. The stability analysis is given based on the finite-time Lyapunov theory. The theoretical results are finally applied to the voltage regulation problem of a Buck converter.

An Adaptive Backstepping Sliding Mode Controller to Improve Vehicle Maneuverability and Stability via Torque Vectoring Control

To improve the maneuverability and stability of a vehicle and fully leverage the advantages of torque vectoring technology in vehicle dynamics control, a finite-time yaw rate and sideslip angle tracking controller is proposed by combining a second-order sliding mode (SOSM) controller with the backstepping method in this paper. However, existing research indicates that first-order sliding mode (FOSM) control suffers from the chattering problem, while the traditional SOSM controller requires knowing the bound of the uncertain term in advance to obtain the switching gain, which is difficult in practice. To address these problems, this paper proposes an adaptive second-order sliding mode (ASOSM) controller based on the backstepping method by adding the high-frequency switching term to the first derivative of the sliding mode variable, which implies that the actual control can be acquired after an integration process. The switching gain in the ASOSM controller is obtained by an adaptive algorithm without knowing any information of the uncertainty. The proposed algorithm is compared with FOSM and SOSM in different scenarios to demonstrate its applicability and robustness. Simulation results show that the bandwidth of the vehicle transient response can be improved by 21%. In addition, ASOSM and SOSM controllers are insensitive to vehicle mass and tire type, implying their robustness to such disturbances. Furthermore, ASOSM requires less control action because of the adaptive law when it performs similarly with SOSM and FOSM.

Adaptive Second-Order Sliding Mode Control for a Tilting Quadcopter with Input Saturations

Abstract In this paper, we address the problem of tracking control for a novel tilting quadcopter in the presence of uncertainties and disturbance. To handle these effects, an adaptive second-order sliding mode control (ASOSMC) is proposed to obtain fast convergence rate and high precision with alleviating chattering effect. Considering the input saturations, a new scheme is designed toward the time derivative of the control inputs where an auxiliary system is adopted to the controller. Moreover, the overall uncertainties are expressed in a linearly parametric form without any prior knowledge. It can be proved that the sliding mode manifolds can fast converge to a small neighborhood around zero within finite-time, and then tracking errors exponentially. Finally, simulation results are carried out to demonstrate the effectiveness and robustness of the proposed controller.

Modified adaptive second order sliding mode control: Perturbed system response robustness

Sensitivity to parameters, which is negative for any system; for an aircraft is destructive. In this respect, an Adaptive Second-order Sliding Mode Control (AS-SMC) is proposed to manage the unknown time-varying aircraft parameter uncertainty and un-modeled coupling perturbations. The employed adaptivity relaxes the required knowledge of the perturbation bound, the suggested sliding surface improves the system stability and bypassing the SMC reaching phase enhances the performance robustness. The effectiveness of the scheme in providing low tolerance responses with respect to the basic controller is illustrated through extensive simulations. The response is more appreciated when the system operates in a high angle of attack/sideslip conditions.

Design and experimental validation of enhanced adaptive second-order SMC for PMSG-based wind energy conversion system

This paper presents Adaptive Second-Order Sliding Mode Control (SOSMC) for power control of Permanent Magnet Synchronous Generator (PMSG). The control objective is to force the PMSG to generate the desired power through regulating the winding current. Specifically, Super Twisting (ST) algorithm SOSMC is adopted in this paper to derive a robust and fast current control for PMSG-based Wind Energy Conversion System (WECS). ST algorithm is renowned for its robustness against parametric uncertainty and external disturbance, but it suffers from the chattering problem. The existing Adaptive Super Twisting (AST) algorithm can reduce the chattering effect, but often at the expense of degraded transient response. In this work, an alternative way is proposed to implement AST algorithm in order to achieve fast transient response, while at the same time attenuate the chattering problem. The controller performance is validated through an experimental setup consisting of a wind turbine emulator and a PMSG which is connected to the grid via back-to-back converter. The experimental results show better performance of the closed-loop system in terms of response time, steady-state error, and chattering despite the presence of parametric uncertainty.

Adaptive Second-Order Sliding Mode Fuzzy Control Based on Linear Feedback Strategy for Three-Phase Active Power Filter

The increasing use of nonlinear loads entails serious electrical energy quality problems in power grids. Active power filter could lead to significant improvement in harmonic compensation performance. In this paper, an adaptive second-order sliding mode fuzzy control based on linear feedback strategy for a three-phase active power filter is proposed to eliminate harmonics. This scheme is constituted by adaptive controller, second-order sliding mode controller, fuzzy controller, and linear feedback controller. The linear feedback controller can compensate the system’s nonlinearities and make the new system have a linear behavior between the input and output. Moreover, the second-order sliding mode controller could transfer the discontinuities in the controller and reduce system chattering. Simulation results illustrate the proposed controller has better performance compared with fuzzy control and adaptive sliding mode fuzzy control.

Quadcopter Robust Adaptive Second Order Sliding Mode Control Based on PID Sliding Surface

We present a robust adaptive second-order sliding mode controller that rejects external disturbances and uncertainties to improve the tracking performance of attitude and altitude in a quadcopter based on a Proportional–Integral–Derivative sliding surface. The algorithm provides a rapid adaptation and strict robustness of the flight control for the vehicle under the effect of perturbations. The proposed controller design is based on the theory of second order sliding mode technique that eliminates the chattering phenomenon present in first-order sliding mode controllers. In addition, we derive an adaptive law from the Lyapunov stability to ensure the robust control for the quadcopter even without knowing the upper bound for disturbances. Applying the same external disturbances, we use a numerical simulation to compare our algorithm to recent alternatives, such as normal adaptive sliding mode control, super-twisting sliding mode control, modified super-twisting sliding mode control, and nonsingular terminal sliding mode control. The results demonstrate the effectiveness of our proposed algorithm.

Fixed-Wing UAV Attitude and Altitude Control via Adaptive Second-Order Sliding Mode

This paper proposes an advanced control approach applied to a fixed-wing Unmanned Aerial Vehicle (UAV) to ensure the stabilization of its angular and vertical positions (attitude and altitude). Actually, the UAV is represented by a dynamic model and is controlled by a robust control law which is the adaptive super-twisting algorithm. This controller based on a second-order sliding mode (SOSM) control is justified by the fact that the fixed-wing UAV has a complex nonlinear, strongly coupled model and undergoes external disturbances. The proposed approach overcomes these problems and ensures finite time convergence. It should be noted that gain adaptation reduces chatter. The performance and effectiveness of the proposed controller are tested by simulations in trajectory tracking mode and compared to classical sliding and classical super-twisting controllers.

Robust control of internal states in a polymer electrolyte membrane fuel cell air-feed system by considering actuator properties

Air stoichiometry, pressure, and relative humidity in the air-feed system of a vehicular polymer electrolyte membrane fuel cell (PEMFC) influence efficiency, durability and reliability. It is critical to develop robust control algorithms for these internal states to improve system performance. There is limited extant research on designing robust control algorithms that consider the three internal states as well as the constraints of real actuators, such as an air compressor, a membrane humidifier, and a back-up pressure valve (BPV). This study examines robust control strategies for the three internal states based on adaptive second order sliding mode (ASOSM) and nonlinear proportional-integral (NPI) feedback control algorithms. In the study, control targets are established based on stable properties of the PEMFC system. The study involves proposing and comparing five control strategies that are a combination of NPI and ASOSM algorithms. The following results are obtained: (1) the stable control targets for the three internal states are followed adequately by using an NPI or an ASOSM algorithm and differences only exists in dynamic processes; (2) with respect to the control of air stoichiometry, an NPI algorithm performs better than an ASOSM algorithm as chattering in air stoichiometry can be avoided and the convergence time to the target value is acceptable; (3) with respect to the control of cathodic pressure, an ASOSM algorithm performs better than an NPI algorithm as the overshoots in cathodic pressures can be effectively reduced; (4) with respect to the control of relative humidity, both NPI and ASOSM algorithms lead to a practical bang–bang strategy. The strategy that performs the best among the five strategies is selected, and the robustness of the selected strategy with respect to parameter uncertainties is verified.

Adaptive second-order sliding mode control: A unified method

This paper develops a unified adaptive second order sliding mode (ASOSM) control method. By using the proposed control structure, the upper bounds of uncertainties are not required, the over-estimation of the control gains are avoided, and the chattering of the conventional sliding mode controllers can be attenuated. It should be noted that the adaptive gains are obtained based on the switching function and its derivative; as a result, the gains keep updating before and after the practical sliding mode is established. Meanwhile, the finite time convergence is proved based on a quadratic Lyapunov approach. Finally, to illustrate the performance of the presented method, an ASOSM controller is designed for a pendulum system and several simulations are performed.