Exponential Approach Law Research Articles

A Robust Controller Based on Extension Sliding Mode Theory for Brushless DC Motor Drives

This paper presents the design of a robust speed controller for brushless DC motors (BLDCMs) under field-oriented control (FOC). The proposed robust controller integrates extension theory (ET) and sliding mode theory (SMT) to achieve robustness. First, the speed difference between the speed command and the actual speed of the BLDCM, along with the rate of change of the speed difference, are divided into 20 interval categories. Then, the feedback speed difference and the rate of change of the speed difference are calculated for their extension correlation with each of the 20 interval categories. The interval category with the highest correlation is used to determine the appropriate control gain for the sliding mode speed controller. This gain adjustment tunes the parameters of the sliding surface in the SMT, thereby suppressing the overshoot of the motor’s speed. Because a sliding surface reaching law of the sliding mode controller (SMC) adopts the exponential approach law (EAL), the system’s speed response can quickly follow the speed command in any state and exhibit an excellent load regulation response. The simplicity of this robust control method, which requires minimal training data, facilitates its easy implementation. Finally, the speed control of the BLDCM is simulated using Matlab/Simulink software (2023b version), and the results are compared with those of the SMC using the constant-speed approach law (CSAL). The simulation and experimental results demonstrate that the proposed robust controller exhibits superior speed command tracking and load regulation responses compared to the traditional SMC.

Permanent magnet synchronous motor NFTSM control based on novel exponential convergence law and ESO

Abstract To solve the problems of slow convergence and serious system chatter in PMSM speed regulation of traditional exponential approach law sliding mode control (SMC), a PMSM fast terminal slip mode (NFTSM) beat free predictive current control (DPCC) strategy based on improved exponential control rate and extended sliding mode observer (ESO) is proposed. The non-singular fast terminal slip-mode controller based on improved exponential control rate and ESO is used in the speed loop. A new exponential approach law is proposed. The stability of the system is proved by using the Lyapunov function. The robustness of the speed controller is improved while reducing the vibration. DPCC control strategy based on ESO is adopted for the current loop to compensate comprehensive disturbance of the current loop. The experiment results show that the control strategy has good speed tracking performance and anti-jamming performance.

Adaptive Fuzzy Sliding Mode Control and Dynamic Modeling of Flap Wheel Polishing Force Control System

Polishing force is one of the key process parameters in the polishing process of blisk blades, and its control accuracy will affect the surface quality and processing accuracy of the workpiece. The contact mechanism between the polishing surface and flap wheel was analyzed, and the calculation model of the polishing force and nonlinear dynamic model of the polishing force control system was established. Considering the influence of friction characteristics, parameter perturbation, and nonlinear dead zone on the control accuracy of the polishing force system, an adaptive fuzzy sliding mode controller (AFSMC) was designed. AFSMC uses a fuzzy system to adaptively approximate the nonlinear function terms in the sliding mode control law, adopts an exponential approach law in the switching control part of the sliding mode control (SMC), and designs the adaptive law for adjustable parameters in the fuzzy system based on the Lyapunov Theorem. Simulation and experimental results show that the designed AFSMC has a fast dynamic response, strong anti-interference ability, and high control accuracy, and it can reduce SMC high-frequency chatter. Polishing experiments show that compared with traditional PID, AFSMC can improve the form and position accuracy of the blade by 42% and reduce the surface roughness by 50%.

An SMC-Based Accurate and Robust Load Speed Control Method for Elastic Servo System

In this paper, a modified sliding mode speed controller is designed in order to improve the load speed control performance of an elastic motor drive system with internal and external disturbances. Firstly, based on the load speed deviation and its first-order and second-order differentials, a two-dimensional sliding surface function is presented. The parameters of the sliding surface are determined by a novel particle swarm optimization (PSO) method. The method has improved inertia weights and evaluation functions, which can improve the accuracy and efficiency of the parameter search and enhance the immunity and robustness of the system. Secondly, on the basis of the integral of time-weighted absolute error (ITAE) criterion, the parameters of the exponential approach law are determined, which improves the tracking accuracy. Finally, the designed sliding mode control (SMC) with high tracking accuracy, fast dynamics, and strong robustness is verified by both simulations and experiments.

Research On Adaptive Sliding Mode Control of PMSM Based On Novel Reaching Law

Based on the jitter and slow convergence speed caused by the conventional approach law SMC, a new exponential approach rate is proposed to optimize dynamic characteristics of the PMSM control system. The approach law is based on the conventional exponential adience law, and the variable of state the system are added. It can ceaseless adapt to the changes of the controlled system, ensure the high tracking function of the system and reduce the jitter caused by the control input. Meanwhile, based on the new exponential approach law, an self-adaption SMC is designed to estimate the uncertain parameters of the control process, and the stability of the make better approach law and control algorithm is analyzed by the function. Finally, The designed controller is compared with traditional sliding mode control and PI control through simulation experiments. The results show that the new exponential approach law can effectively suppress chattering and improve the dynamic characteristics of the system.

Active adaptive continuous nonsingular terminal sliding mode controller for hypersonic vehicle

An active adaptive continuous nonsingular terminal sliding mode algorithm (ACNTSM) is designed for hypersonic boost glide vehicle to achieve higher control accuracy and faster response speed. Firstly, a continuous nonsingular terminal sliding mode controller is presented to make the tracking error and sliding variable converge to zero under the effect of time-varying disturbance in finite time. Compared with traditional terminal sliding mode control using exponential approach law, the ACNTSM algorithm can generate continuous control signal, which effectively reduces chattering. Secondly, a novel active adaptive law is proposed to reduce convergence error, to avoid excessive gain, and to attenuate chattering by adjusting the gain of ACNTSM. The adaptive scheme includes sliding variable and disturbance estimation. The disturbance estimation is obtained by using the integral term of generalized super twisting sliding mode algorithm. The method takes less computational resources and reduces complexity of algorithm. In addition, the gain can automatically increase to shorten convergent time until the sliding mode is reached and then decrease to reduce chattering until the sliding mode is lost. The novel adaptive law ensures the finite-time convergence to a neighborhood of origin for sliding variable without overestimation of gain. Finally, numerical simulations are carried out to demonstrate the effectiveness and superiority of ACNTSM.

New Sliding Mode Control Based on Tracking Differentiator and RBF Neural Network

In order to solve the problem that the control system of permanent magnet synchronous motor (PMSM) is difficult to meet the high control accuracy due to the influence of non-repeated disturbances such as external disturbance, system parameter variation, and friction force during operation, a novel sliding mode control (NSMC) method based on tracking differentiator (TD) and radial basis (RBF) neural network was proposed. Firstly, a new sliding mode reaching law is proposed by adding the state variables to the traditional exponential reaching law, which can effectively reduce the chattering of the system. Then, the speediest tracking differentiator is designed to estimate the given speed signal and its differential signal, to realize the novel sliding mode variable structure algorithm. Finally, the RBF neural network is used to compensate for the uncertainty and external interference of the system; the robustness of the system is further improved by adaptive weight updating. The simulation results show that, by comparing with the traditional exponential approach law, the overshoot of 22 r/min is reduced by the control method based on the new hybrid reaching law, the speed decrease amplitude is reduced by 77.1% under load disturbance, and the speed recovery time is shortened by 0.059 s. After the optimization of the new sliding mode control method based on tracking differentiator and RBF neural network, the overshoot of 86 r/min is further reduced, the speed decrease amplitude of load disturbance is reduced again by 48.5%, and the speed recovery time is shortened again by 0.073 s.

Optimal Slip Ratio Tracking Integral Sliding Mode Control for an EMB System Based on Convolutional Neural Network Online Road Surface Identification

As the main branch of the brake-by-wire system, the electro-mechanical brake (EMB) system is the future direction of vehicle brake systems. In order to enhance the vehicle braking effect and improve driver safety, a convolutional neural network (CNN) online road surface identification algorithm and an optimal slip ratio tracking integral sliding mode controller (ISMC) combined EMB braking control strategy is proposed in this paper. Firstly, according to the quarter-vehicle model and Burckhardt tire model, the vehicle braking control theory based on the optimal slip ratio is analyzed. Secondly, using the VGG-16 CNN method, an online road surface identification algorithm is proposed. Through a comparative study under the same dataset conditions, it is verified that the VGG-16 method has a higher identification accuracy rate than the SVM method. In order to further improve the generalization ability of VGG-16 CNN image identification, data enhancement is performed on the road surface image data training set, including image flipping, clipping, and adjusting sensitivity. Then, combined with the EMB system model, an exponential approach law method-based ISMC is designed to achieve the optimal slip ratio tracking control of the vehicle braking process. Finally, MATLAB/Simulink software is used to verify the correctness and effectiveness of the proposed strategy and shows that the strategy of real-time identifying road surface conditions through vision can make the optimal slip ratio of vehicle braking control reasonably adjusted, so as to ensure that the adhesion coefficient of wheel braking always reaches the peak value, and finally achieves the effect of rapid braking.

Study on improved droop control strategy of MMC-MTDC system based on novel sliding mode control

In view of the strong coupling, nonlinearity and uncertainty of HVDC system, and the poor consistency when the MMC control policy adopts the traditional PI double closed-loop control, an improved droop control policy with the novel sliding pattern controlling is given herein. The controller brings to the dual closed loop control structure, the internal loop takes current error in the dq axis as the sliding mode surface. A sliding mode controller with the novel exponential approach law is designed, which improves the convergence speed of the traditional exponential approach law and eliminates the chattering phenomena. Then the consistency of the system is identified by Lyapunov method. The outer-loop adopts a modified sag control policy. After comparing with the voltage reference value, the droop factor is proposed. Finally, an emulation model including MMC-MTDC with four terminal is constructed on the PSCAD/EMTDC, which is emulated and validated under stable and transient conditions. The consequences reveal that the given control policy not only has a good convergence effect, but also improves the kinematic respond speed. It can also reduce the direct current voltage deviation, and enhances the stability and reliability of the system.

Radial basis function neural network–based adaptive sliding mode suspension control for maglev yaw system of wind turbines

The maglev yaw system of wind turbines adopts maglev-driving technology instead of traditional gear-driving technology. It has many advantages, such as no lubrication, simple structure, and high reliability. However, the stable suspension control of maglev yaw system is difficult to achieve due to the unknown disturbance caused by crosswind in a practical environment. In this article, an adaptive sliding mode cascade controller based on radial basis function neural network is proposed for the stable suspension control of maglev yaw system. First, the dynamic mathematical model of maglev yaw system is established. Second, an adaptive sliding mode robust controller using radial basis function neural network is designed as the outer loop air gap tracking controller for precise position control, where radial basis function neural network is employed to estimate the unknown parameter containing disturbance. To eliminate the limitation of the traditional exponential approach law based on sign function in the sliding mode control, an exponential reaching law based on hyperbolic tangent function is introduced to guarantee the smooth suspension control of maglev yaw system. Third, an adaptive controller as the inner loop current tracking controller is designed. Finally, the corresponding simulations and analysis are carried out. The simulation results show that the proposed controller can guarantee the suspension stability of maglev yaw system and suppress the disturbance effectively. Compared with the cascade proportional–integral–derivative controller and improved double power reaching law integral sliding mode controller, the proposed controller has a faster dynamic response and stronger robustness in the presence of unknown external disturbance.

Particle Swarm Sliding Mode-Fuzzy PID Control Based on Maglev System

The magnetic levitation system is a typical open-loop unstable system. To weaken the chattering phenomenon of sliding mode control (SMC), a hybrid control strategy of particle swarm sliding mode-fuzzy PID control was designed. This strategy uses particle swarm optimization (PSO) to optimize the SMC using the method of exponential approach law, so as to obtain the best sliding mode surface parameters and exponential approach rate coefficients, thus shortening the time required to approach the stable region when the nonlinear system is far from the stable point; a state supervision controller was designed by analyzing the stable conditions of sliding mode. When the system approaches the stable region, it smoothly transitions to fuzzy PID control, thereby weakening the chattering phenomenon of SMC. To verify the dynamic performance of the designed algorithm, a magnetic levitation ball system was selected as the controlled object. Through simulation and experiment, it was verified that the controller had strong robustness and strong anti-interference performance. It effectively weakened the chattering and had good adaptability to external disturbance and state variable crossing.

Sliding-mode control for coal shearer drum height adjustment based on variable speed reaching law

Aiming at the shortcomings of the automatic height control of the existing coal shearer drum, the control strategy of the coal shearer drums height adjustment sliding mode based on the variable speed reach law is proposed. Firstly, the mathematical model of the coal shearer height-adjusting cylinder is established, and the sliding mode switching function and its derivative including the deviation variable are derived. The exponential approaching law sliding mode controller is designed. Secondly, the hydraulic simulation of the drum height is established. The model compares and analyzes the control effects of traditional PID control and exponential approach law sliding mode control. The results show that the exponential approach law sliding mode control is superior to PID control in signal tracking dynamic response and steady state error; when the coal shearer is under load, the height of the drum under control of the exponential approaching law is basically unaffected; finally, the method of shifting the approaching law of dynamically adjusting the arrival speed by the fuzzy parameter optimization strategy is used to adjust the drum height. The simulation results show that compared with the traditional control method, the coal shearer control mode of the coal shearer drum based on the variable speed reach law not only ensures faster response speed and higher control precision, but also effectively reduces system chattering. Improve the reliability of the coal shearer cutting drive system.

Sliding Mode Observer with Adaptive Parameter Estimation for Sensorless Control of IPMSM

To improve the observation accuracy and robustness of the sensorless control of an interior permanent magnet synchronous motor (IPMSM), a sliding mode observer based on the super twisting algorithm (STA-SMO) with adaptive parameters estimation control is proposed, as parameter mismatches are considered. First, the conventional sliding mode observer (CSMO) is analyzed. The conventional exponential approach law produces a large chattering phenomenon in the back EMF estimation, which causes a large observation error when filtering the chattering through the low-pass filter. Second, a high-order approach law of the super twisting algorithm is introduced to observe the rotor position and speed estimation, which uses the integral function to eliminate the chattering of the sliding mode. Third, an adaptive parameter estimation control (APEC) is presented to enhance the observation accuracy caused by parameter mismatches; the motor parameter adaptive law of the APEC is designed by Lyapunov’s stability law. Finally, the proposed method not only reduces both the chattering and the low-pass filter, but it also enhances accuracy and robustness against parameter mismatches, as discussed through simulations and experiments.

Sliding Mode Control of Bi-directional DC/DC Converter in DC Microgrid Based on Exact Feedback Linearization

The nonlinear property of bi-directional DC/DC converter in DC Microgrid will cause large voltage disturbance. To solve the above problems, a exact feedback linearization method based on nonlinear differential geometry theory is proposed to realize the linearization of the converter. Moreover, considering the approaching speed of the linearized Bruno standard model, a sliding mode controller is designed by using the exponential approach law. The simulation results show that the method has fast response speed, strong antiinterference ability and good steady-state characteristics.

Research on Radar Servo System Based On Disturbance Observer Sliding Mode Control

Radar turntable servo system has strong friction at low speed, and the traditional PID control method due to its fixed parameters, poor stability and low control accuracy, is difficult to meet the high requirements of modern radar servo system for control quality. In this paper, a sliding mode controller with disturbance observer is proposed for the radar servo system. The friction is estimated by the exponential convergence disturbance observer; meanwhile the exponential approach law sliding mode controller is also designed. The simulation results show that the radar servo system controlled by sliding mode disturbance observer is better than the traditional PID controlled system. It can overcome the friction at low speed and improve the response speed and control accuracy of the radar servo system.

Real-Time Implementation of Maximum Net Power Strategy Based on Sliding Mode Variable Structure Control for Proton-Exchange Membrane Fuel Cell System

Increasing in the net output power of proton-exchange membrane fuel cell (PEMFC) systems is an important aspect of improving the performance of PEMFC. In order to enhance the net output power of the PEMFC system, the maximum net power strategy of the PEMFC system is proposed. Since the PEMFC system is a nonlinear system with time delay and uncertainty, sliding mode variable structure control (SMVSC) based on the exponential approach law is applied to achieve real-time operation at the maximum net PowerPoint. This article has two main contributions. The first major contribution of this article is to obtain the maximum net power surface of the PEMFC by multivariate fitting and to design the maximum net power regulator. The second major contribution of this article is to design a sliding mode variable structure based on the exponential approach law. The Lyapunov function is used to converge the sliding mode surface to the defined neighborhood. The advantage of this structural design is that the approach speed is gradually reduced from a larger value, and the response time is shortened. The control effect of the maximum net power strategy based on SMVSC is verified by the PEMFC experimental platform.

Mitigation Strategy of Subsynchronous Oscillation Based on Fractional-Order Sliding Mode Control for VSC-MTDC Systems With DFIG-Based Wind Farm Access

To solve the subsynchronous oscillation (SSO) caused by doubly-fed induction generator (DFIG)-based wind farm access in voltage source converter based multi-terminal direct current (VSC-MTDC) systems, the fractional-order sliding mode control (FOSMC) strategy is proposed to suppress the SSO and improve the system robustness. First, the rotor side converter (RSC) of the DFIG and the converter connected with the wind farm are linearized by the feedback linearization method. The stability of the internal system is ensured by the application of zero-dynamic theory. Then, the appropriate switching manifold surface and the exponential approach law vs are selected for the design of FOSMC strategy. The control law of the system can be derived when the stability of the system is ensured. After that, the designed FOSMC strategy is applied to the RSC and the VSC connected with the wind farm. To verify the superior performance of the proposed control strategy, the FOSMC strategy is compared with the traditional subsynchronous damping controller (SSDC) by time-domain simulation under different operating conditions. The simulation results show that the FOSMC strategy can effectively suppress the SSO under different operating conditions, stabilize the system quickly, and enhance the robustness of the system against parameter disturbances.

Adaptive Variable Structure Control With Neuron for Path Tracking of Beaver AUV

In order to improve path tracking performance of Beaver AUV, a new method for path tracking controller design is proposed basing on variable structure control theory and nonlinear dynamics model of Beaver. Switching surface of variable structure controllers is founded with corresponding error and error derivative of surge displacement and yaw angle. Exponential approach law is adopted to derive control algorithm for surge and yaw in the process of path tracking. Chattering phenomenon is restrained due to adaptive neurons which are used for approaching speed adjusting online. Simulation results of sinusoidal path tracking, circular path tracking and planning path tracking show that tracking precision of Beaver AUV is improved more evidently through variable structure control with adaptive approaching speed compared with variable structure control using fixed approaching speed. The method proposed in this article is effective and feasible.

Double Closed-Loop General Type-2 Fuzzy Sliding Model Control for Trajectory Tracking of Wheeled Mobile Robots

In this paper, a double-loop control scheme, combining general type-2 fuzzy logic controller (GT2FLC) and non-singular terminal sliding mode control (NTSMC), is proposed to stabilize the non-holonomic wheeled mobile robot. In the double-loop tracking controller, the outer ring adopts the exponential approach law used to track the position state quickly and the inner ring adopts the double-power approaching law, which makes the attitude convergence faster than the position to ensure the stability of the closed-loop system and deal with the random disturbances. NTSMC is designed for both loops to achieve fast convergence of the system in a finite time. The GT2FLC is used to adjust the gain of the approaching law, so as to enhance the adaptability to random disturbances and weaken the chattering of sliding mode input. The simulation results show that the proposed method can achieve small error and fast tracking of position and attitude under random disturbance, and its performance is better than other controllers.

Novel Fuzzy Neural Nonsingular Terminal Sliding Mode Control of MEMS Gyroscope

This paper attempts to improve the robustness and rapidity of a microgyroscope sensor by presenting a double‐loop recurrent fuzzy neural network based on a nonsingular terminal sliding mode controller. Compared with the traditional control method, the proposed strategy can obtain faster dynamic response speed and lower steady‐state error with high robustness in the presence of system uncertainties and external disturbances. A nonlinear terminal sliding mode controller is designed to guarantee finite‐time high‐precision convergence of the sliding surface and meanwhile to eliminate the effect of singularity. Moreover, an exponential approach law is used to accelerate the convergence rate of the system to the sliding surface. For suppressing the chattering, the symbolic function in the ideal sliding mode is replaced by the saturation function. To suppress the effect of model uncertainties and external disturbances, a double‐loop recurrent fuzzy neural network is introduced to approximate and compensate system nonlinearities for the gyroscope sensor. At the same time, the double‐loop recurrent fuzzy neural network can effectively accelerate the speed of parameter learning by introducing the adaptive mechanism. Simulation results indicate that the control system with the proposed controller is easily implemented, and it has higher tracking precision and considerable robustness to model uncertainties compared with the existing controllers.