Chattering Of Sliding Mode Control Research Articles

Quadrotor Cascade Control System Design Based on Linear Active Disturbance Rejection Control

In this paper, we propose a cascade control system design based on linear active disturbance rejection control (SMC&A-LADRC) to address the following quadrotor UAV problems: that the path is easily yawed when disturbed, the control parameters are difficult to optimize, and the tracking accuracy is low. The strategy can effectively eliminate external disturbances and adjust the controller parameters online so that the quadrotor UAV always flies on the optimal path to achieve energy optimization and long-endurance flight. The proposed cascade control system combines the advantages of sliding mode control (SMC) and linear active-disturbance rejection control (LADRC), using the linear extended state observer (LESO) to estimate the uncertain external disturbances and unmodeled internal dynamics of the quadrotor system, compensate for the uncertain signals under SMC chattering, optimize the PD controller parameters online using adaptive control to eliminate the effects of parameter deviations, and simplify the parameter adjustment process. Finally, a stability analysis of the quadrotor cascade control system is carried out by using the Lyapunov theorem of stability, and a simulation analysis is carried out using MATLAB to compare the results with those obtained with classical LADRC. The test results indicate that the control strategy of this paper is reasonable for utilization with a quadrotor attitude and displacement control system, allowing the quadrotor to fly on the optimal path with good anti-interference ability and a fast response speed.

Adaptive fuzzy fractional-order sliding-mode control of LCL-interfaced grid-connected converter with reduced-order

This paper proposes a discrete-time fuzzy fractional-order sliding-mode control (Fuzzy-FOSMC) dual loop current controller for a three-phase LCL-type grid-connected converter (GCC) with reduced order. Conventional sliding-mode control (SMC) has been widely used in GCC due to its robustness to disturbances. However, the chattering in SMC may reduce the tracking performance of the controller, and even lead to system instability. To solve this problem, a Fuzzy-FOSMC controller is proposed in this paper. The introduced fractional-order term can suppress the chattering, and the fractional-order of FOSMC is further adjusted by the fuzzy controller to improve the overall system performance. In addition, the inner loop is implemented by a Fuzzy-FOSMC controller to ensure the tracking of the converter-side current, making the LCL-GCC converter behave like a controllable current source converter with a capacitive-inductive filter, the grid current control problem falls from a third-order to a reduced order system, which solves some difficulties on the design of most controller types. The stability of the two-stage PV system is analyzed. Finally, the effectiveness of the proposed controller is verified by experiments.

Robust Fuzzy-Fractional-Order Nonsingular Terminal Sliding-Mode Control of LCL-Type Grid-Connected Converters

Sliding-mode control (SMC) has been widely used in grid-connected converter system (GCC) systems because of its robustness to parameter variations and external disturbances. However, chattering in SMC may deteriorate the tracking accuracy and can easily excite high-frequency unmodeled dynamics. To solve this problem, this article presents a fuzzy-fractional-order nonsingular terminal sliding-mode controller (Fuzzy-FONTSMC) for the grid current control of LCL–GCCs. First, the system modeling, design of the integer-order NTSMC controller, and state estimation based on the Kalman filter to minimize the sampling sensors are described. Second, the Fuzzy-FONTSMC controller is introduced for optimal fraction-order selection and chattering mitigation, this controller exhibits fast convergence with high tracking accuracy and strong robustness. Finally, the Lyapunov theorem is used to analyze the system stability. Experimental comparisons on a 10-kVA laboratory prototype validate the superior performance and effectiveness of the proposed method under many scenarios.

Based on robust sliding mode and linear active disturbance rejection control for attitude of quadrotor load UAV

In this paper, a mass adaptive control method combining with robust sliding mode control (SMC) and linear active disturbance rejection control (LADRC) is designed for the quadrotor load unmanned aerial vehicle (UAV) with mass variation. In detail, firstly, the mass variation in the quadrotor affects the position of its centroid, taking into account the changes of centroid position, which makes the established model more accurate. Moreover, a mass adaptive law is designed to eliminate the influence of mass variation. Secondly, SMC can enhance the robustness of the controller, improve the anti-disturbance performance and overcome the problem of low control precision caused by bandwidth limitation of LADRC. The linear extended state observer estimates the external disturbances of the system and the internal unmodeled dynamics caused by the SMC chattering in real time, and then, the total disturbance is compensated by the proportional–derivative controller. The proposed scheme combines the advantages of SMC and LADRC and complements each other. Thirdly, in order to simplify the parameter setting, the adaptive control is introduced in LADRC to adjust the controller parameters in real time, which is beneficial to the stability analysis of the control system. Then Lyapunov stability theory is used to prove the stability of the whole system. Finally, the simulation is compared with LADRC and dynamic surface active disturbance rejection control. The results show that the designed scheme has smaller overshoot and faster response speed, which proves its superiority. Moreover, the designed adaptive law is also effective, it can eliminate the influence of parameter deviation, so that the proposed scheme can track the reference signal stably even in the presence of disturbances.

Convergence Enhancement of Super-Twisting Sliding Mode Control Using Artificial Neural Network for DFIG-Based Wind Energy Conversion Systems

The technological development of wind energy conversion systems (WECS) is emphasized on the injection of wind power into the utility grid more smoothly and robustly. Sliding mode control (SMC) has proven to be a popular solution for the grid-connected WECS due to its robust nature. The super twisting sliding mode control (STSMC), a variant of SMC, is an effective approach to suppress the inherent chattering in SMC and provide error-free control. The anti-disturbance capabilities of STSMC deteriorate due to the non-linear part that is based on variable approaching law and time delay created by the disturbance and uncertainties. This paper enhances the anti-disturbance capabilities of STSMC by combining the attributes of artificial intelligence with STSMC. Initially, the STSMC is designed for both the inner and outer loop of a doubly fed induction generator (DFIG) based WECS is proposed. Then, an artificial neural network (ANN)-based compensation term is added to improve the convergence and anti-disturbance capability of STSMC. The proposed ANN based STSMC paradigm is validated using a processor in the loop (PIL) based experimental setup carried out in Matlab/Simulink.

Invariant Manifold Based Output-Feedback Sliding Mode Control for Systems With Mismatched Disturbances

This brief proposes an invariant manifold based output-feedback sliding mode control (SMC) strategy for systems with mismatched disturbances to achieve asymptotic tracking and disturbance rejection. Different from the existing output-feedback SMC methods, the invariant manifold is employed to transform the multiple mismatched disturbances into matched ones, which can provide full system dynamics for controller design to improve accuracy. An observer is developed to estimate unmeasurable states, then an output-feedback sliding mode controller is proposed. Moreover, the switching gain of the controller adaptively changes with the estimation error, which reduces chattering in SMC. Experiments on a converter-driven DC motor system verify the superiority of the proposed method.

Interval Type-2 Fuzzy Sliding-Mode Control of Three-Axis Stabilization Gimbal

Aiming at the attitude control problem of three-axis stabilization gimbal, an algorithm combining interval type-2 fuzzy control and sliding-mode control was designed. Firstly, the mathematical model of the three-axis stabilization gimbal actuator was established after analyzing the mechanical structure of the three-axis stabilization gimbal. Then, a sliding-mode controller was designed based on the position ring of the actuator of three-axis stabilization gimbal. An interval type-2 control was used to reduce chattering in sliding-mode control. The switching function and its derivative are taken as the input of fuzzy control, and the rate of change of the approach law is taken as the output of fuzzy control. Fuzzy control can adjust the gain of sliding-mode surface dynamically, enhance the adaptability on external random disturbance, improve the speed of convergence and weaken chattering. The simulation results show that the output of the controller designed in this paper is more stable, and the tracking of the three-axis stabilization gimbal is more rapid and accurate.

Particle Swarm Algorithm Sliding Mode Control on Spacecraft’s Attitude with Switching Function Method Thorough Error Feedback

Small spacecraft requires capable processors with energy efficiency, low cost and low computational burden while maintaining the output tracking accuracy. This paper presents the extension of work in [1], to enhance the transient performance using particle swarm optimization (PSO) on decaying boundary layer and switching function thorough error feedback (DBLSF) in Sliding Mode Control (SMC). Generally, SMC is known for having chattering as the main drawback which can introduce wear and tear to moving mechanical parts. As a solution, a DBLSF proposed in [1] and capable of eliminating the chattering in SMC while considering the essential requirements for small spacecraft operation. Then, the extension implemented on spacecraft’s attitude, which is one-of-six subsystems in spacecraft, used to orient the spacecraft referred to reference objects and control the dynamics of a spacecraft time-to-time according to the needs. However, the SMC’s transient response can be tuned using some coefficients in the SMC algorithm. The parameters in [1] were tuned using outputs observation technique. In this paper, then, an improvement is introduced to optimize the outputs by adding a PSO in the SMC-DBLSF in term of transient performances and accuracy while reducing the chattering permanently.

Adaptive-Gain Second-Order Sliding Mode Direct Power Control for Wind-Turbine-Driven DFIG under Balanced and Unbalanced Grid Voltage

In a wind turbine system, a doubly-fed induction generator (DFIG), with nonlinear and high-dimensional dynamics, is generally subjected to unbalanced grid voltage and unknown uncertainty. This paper proposes a novel adaptive-gain second-order sliding mode direct power control (AGSOSM-DPC) strategy for a wind-turbine-driven DFIG, valid for both balanced and unbalanced grid voltage. The AGSOSM-DPC control scheme is presented in detail to restrain rotor voltage chattering and deal with the scenario of unknown uncertainty upper bound. Stator current harmonics and electromagnetic torque ripples can be simultaneously restrained without phase-locked loop (PLL) and phase sequence decomposition using new active power expression. Adaptive control gains are deduced based on the Lyapunov stability method. Comparative simulations under three DPC schemes are executed on a 2-MW DFIG under both balanced and unbalanced grid voltage. The proposed strategy achieved active and reactive power regulation under a two-phase stationary reference frame for both balanced and unbalanced grid voltage. An uncertainty upper bound is not needed in advance, and the sliding mode control chattering is greatly restrained. The simulation results verify the effectiveness, robustness, and superiority of the AGSOSM-DPC strategy.

Adaptive fractional fuzzy sliding mode control of microgyroscope based on backstepping design.

In this paper, a robust sliding mode control (SMC) based on backstepping technique is studied for a microgyroscope in the presence of unknown model uncertainties and external disturbances using adaptive fuzzy compensator and fractional calculus. At first, the dynamic of microgyroscope is transformed into analogically cascade system to guarantee the application of backstepping design. Then a novel fractional differential sliding surface is proposed which integrates the capacities of the fractional calculus and SMC. In order to reduce the chattering in SMC, a fuzzy logical system is utilized to approximate the external disturbances. In addition, fractional order adaptive laws are derived to estimate the damping and stiffness coefficients and angular velocity online based on Lyapunov stability theory which also guarantees the stability of the closed loop system. Finally, simulation results signify the robustness and effectiveness of the proposed control schemes and the comparison of root mean square error under different fractional orders and integer order are given to demonstrate the better performance of proposed controller.

Fuzzy sliding-mode control with low pass filter to reduce chattering effect: an experimental validation on Quanser SRIP

Stabilization of a single rotary inverted pendulum (SRIP) system is a benchmark nonlinear control problem. Inherent instability of SRIP in upright position and the presence of modelling uncertainty pose a challenge for control engineers. Sliding-mode control (SMC) is the most widely accepted robust control technique. Various versions of SMCs to stabilize SRIP have been reported in literature. Advantages of SMC come at the cost of chattering of input, which inhibits its usage in many practical applications. Several works have been done to reduce the chattering in SMC. Application of fuzzy logic in SMC to reduce chattering has been analysed extensively in the literature. Even though implementation of fuzzy SMC (FSMC) in theory/simulations completely eliminates chattering, practical implementation of FSMC does not reduce chattering to zero. In this paper, a filtered FSMC is proposed, which filters the high frequency component in the system input. Experimental results of SMC, FSMC and a fuzzy sliding-mode controller with filter (FSMCF) are given in this paper. Results indicate that filtering the output of FSMCF reduces the chattering effect in the system without affecting the closed loop dynamics.

Design of Spacecraft Controller Based on Adaptive Fuzzy Sliding Mode Variable Structure

Using of feedback linearization technique to solve the problem of traditional sliding mode control chattering. The fuzzy adaptive control and sliding mode variable structure was designed by combining a novel adaptive fuzzy sliding mode variable structure controller. Through fuzzy inference and the stability analysis based on Lyapunov function to obtain fuzzy control rules adaptive law and effective solution to the traditional sliding mode control of the need to determine the parameter perturbation and external interference supremum uncertainty. Simulation results show that this method has better stability and robustness.

Cooperative Control of Regenerative Braking and Antilock Braking for a Hybrid Electric Vehicle

A new cooperative braking control strategy (CBCS) is proposed for a parallel hybrid electric vehicle (HEV) with both a regenerative braking system and an antilock braking system (ABS) to achieve improved braking performance and energy regeneration. The braking system of the vehicle is based on a new method of HEV braking torque distribution that makes the antilock braking system work together with the regenerative braking system harmoniously. In the cooperative braking control strategy, a sliding mode controller (SMC) for ABS is designed to maintain the wheel slip within an optimal range by adjusting the hydraulic braking torque continuously; to reduce the chattering in SMC, a boundary-layer method with moderate tuning of a saturation function is also investigated; based on the wheel slip ratio, battery state of charge (SOC), and the motor speed, a fuzzy logic control strategy (FLC) is applied to adjust the regenerative braking torque dynamically. In order to evaluate the performance of the cooperative braking control strategy, the braking system model of a hybrid electric vehicle is built in MATLAB/SIMULINK. It is found from the simulation that the cooperative braking control strategy suggested in this paper provides satisfactory braking performance, passenger comfort, and high regenerative efficiency.

Algorithms for chattering reduction in system control

Sliding mode control (SMC) is among the popular approaches for control of systems, especially for unknown nonlinear systems. However, the chattering in SMC is generally a problem that needs to be resolved for better control. A time-varying method is proposed for determining the sliding gain function in the SMC. Two alternative tuning algorithms are proposed for reducing the sliding gain function for systems. The first algorithm is for systems with no noise and disturbance but with or without unmodeled dynamics. The second algorithm is for systems with noise, disturbance, unmodeled dynamics, or any combination of them. Compared with the state-dependent, equivalent-control-dependent, and hysteresis loop methods, the proposed algorithms are more straightforward and easy to implement. The performance of the algorithms is evaluated for five different cases. A 90% to 95% reduction of chattering is achieved for the first algorithm used for systems with sensor dynamics only. By using the second algorithm, the chattering is reduced by 70% to 90% for systems with noise and/or disturbance, and by 25% to 50% for systems with a combination of disturbance, noise, and unmodeled dynamics.

Application of Sliding Mode Control for Electric Vehicle Antilock Braking Systems

An antilock braking method based on sliding mode control (SMC) for electric vehicles (EVs) is proposed on the basis of antilock braking dynamics model, and hence an SMC controller of antilock braking system is designed. Aiming at the chattering of SMC, a method of parameter fuzzy optimization for exponential approach law is proposed, which can meet the requirements for small chattering, strong disturbance attenuation and fast convergence. In order to take full advantage of regenerative braking force, a method of braking force distribution between mechanical and electrical braking systems is elaborated. The simulations on the road with different friction coefficients show that the vehicle speed is in good agreement with the wheel speed during braking, and the slip ratio is kept within an optimal range. Adopting SMC based on fuzzy optimization, optimal slip ratio can be tracked fast and accurately. Furthermore, since the regenerative braking force is made full use of during braking, the energy recovery efficiency is high.

State feedback sliding mode control without chattering by constructing Hurwitz matrix for AUV movement

This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.

A neuro-fuzzy-sliding mode controller using nonlinear sliding surface applied to the coupled tanks system

The aim of this paper is to develop a neuro-fuzzy-sliding mode controller (NFSMC) with a nonlinear sliding surface for a coupled tank system. The main purpose is to eliminate the chattering phenomenon and to overcome the problem of the equivalent control computation. A first-order nonlinear sliding surface is presented, on which the developed sliding mode controller (SMC) is based. Mathematical proof for the stability and convergence of the system is presented. In order to reduce the chattering in SMC, a fixed boundary layer around the switch surface is used. Within the boundary layer, where the fuzzy logic control is applied, the chattering phenomenon, which is inherent in a sliding mode control, is avoided by smoothing the switch signal. Outside the boundary, the sliding mode control is applied to drive the system states into the boundary layer. Moreover, to compute the equivalent controller, a feed-forward neural network (NN) is used. The weights of the net are updated such that the corrective control term of the NFSMC goes to zero. Then, this NN also alleviates the chattering phenomenon because a big gain in the corrective control term produces a more serious chattering than a small gain. Experimental studies carried out on a coupled tank system indicate that the proposed approach is good for control applications.

Chattering Free Sliding Mode Control in Magnetic Levitation System

It is well known that sliding mode control (SMC) is capable of tackling systems with uncertainties. However, the discontinuous control signal causes a significant problem of chattering. In this paper, a new and simple approach to chattering free SMC methodology is proposed. The main purpose is to eliminate the chattering phenomenon. As a result, the chattering is eliminated and error performance of sliding mode control is improved. The reduction of the chattering of sliding mode control is achieved by using a distance function which measure the distance between the trajectory of state errors and the sliding surface as the corrective control term instead of discontinuous sign function. Experimental study carried out on a magnetic levitation system is presented. Experiments verified that the proposed control has the advantage of less chattering in SMC.

Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems

To reduce chattering in sliding-mode control, a boundary layer around the switching surface is used, and a continuous control is applied within the boundary. The effects of various control laws within the boundary layer on chattering and error convergence in different systems are studied. New functions for chattering reduction and error convergence inside the boundary layer are proposed which are discontinuous in magnitude but not in sign. The internal model principle has been used to generalize the design for the class of nonlinear systems being considered.