Traditional Sliding Mode Control Research Articles

Dynamic Sliding Mode Control of Spherical Bubble for Cavitation Suppression

Cavitation is a disadvantageous phenomenon that occurs when fluid pressure drops below its vapor pressure. Under these conditions, bubbles form in the fluid. When these bubbles flow into a high-pressure area or tube, they erupt, causing harm to mechanical parts such as centrifugal pumps. The difference in pressure in a fluid is the result of varying temperatures. One way to eliminate cavitation is to reduce the radius of the bubbles to zero before they reach high-pressure areas, using a robust approach. In this paper, sliding mode control is used for this purpose due to its invariance property. To force the radius of the bubbles toward zero and prevent chattering, a new dynamic sliding mode control approach is used. In dynamic sliding mode control, chattering is removed by passing the input control through a low-pass filter, such as an integrator. A general model of the spherical bubble is used, transferred to the state space, and then a state proportional-integral feedback is applied to obtain a linear system with a new input control signal. A comparison is also made with traditional sliding mode control using state feedback, providing a trusted comparison.

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.

H ∞ prescribed tracking performance-based fractional-order sliding mode control for disturbed discrete-time systems: an LMI approach

This paper presents a novel approach to the design of a discrete-time Fractional-Order Sliding Mode Control (FSMC) system for Single Input Single Output (SISO) applications, utilising the Autoregressive with exogenous input (ARX) method for system modelling. The proposed methodology emphasises the Prescribed Performance Control (PPC) to ensure minimal tracking errors through a transformation of tracking errors based on a specified performance function. A Fractional-Order Quasi-Sliding Mode Control (FQSMC) is subsequently developed to maintain the tracking error within predetermined bounds, effectively addressing the chattering phenomenon commonly associated with the traditional sliding mode control. The integration of fractional calculus enhances the smoothness of the output while ensuring accurate tracking, making it ideal for real-world applications. Additionally, a novel Linear Matrix Inequality (LMI) observer is introduced to bolster the system's resilience against uncertainties and disturbances without complicating the computational process. The effectiveness of the proposed Prescribed Performance Fractional-Order Quasi-Sliding Mode Control (PP-FQSMC) is validated through extensive MATLAB simulations and experimental studies conducted on a Tank system. Results demonstrate that the PP-FQSMC significantly outperforms traditional methods, with maximum tracking errors of 1.6 × 10−4 compared to 0.2 for the PP-QSMC and a Root Mean Square Tracking Error (RMSTE) of 1.3 × 10−3 compared to 1.2 × 10−4 for the PP-QSMC, ensuring strong tracking performance and stability. The findings indicate that the proposed controller effectively mitigates chattering in control signals while maintaining a smooth output. It showcases its potential for practical applications in environments characterised by model inaccuracies, time delays, and external disturbances.

Barrier function–based adaptive STSMC for steering feel feedback of SBW vehicle with uncertainty

As an essential component of human–computer interaction in steer-by-wire (SBW) vehicles, the steering feel feedback system provides drivers with accurate steering feel by precisely controlling the output torque of the steering feel motor. Meanwhile, the existence of uncertainties makes the accurate control of steering feel feedback torque become an acknowledged challenging issue. This article proposes an adaptive super-torque sliding mode control strategy based on barrier functions for the steering feel feedback system of SBW vehicles with highly complex dynamics in the presence of uncertainties. First, to achieve intelligent modeling under the influence of uncertainty factors, a dynamic system with unknown uncertainty based on adaptive fuzzy logic system (FLS) is proposed. In the framework of this model, the uncertainty factors introduced by unknown external disturbance, parameter uncertainty, and model couplings are considered as a lumped uncertainty function. Furthermore, the membership functions of the FLS are dynamically adjusted based on nearest neighbor clustering, aiming to enhance the modeling accuracy beyond traditional fuzzy modeling. To further offset the system uncertainty and FLS approximation error, an adaptive super-twisting sliding mode control (STSMC) method based on barrier function is proposed. This algorithm retains the advantages of traditional sliding mode control (SMC) methods in dealing with systems with uncertainty and eliminates the need for a priori knowledge of the upper bound of uncertainties by introducing the adaptive law based on barrier function, avoiding the use of complex identification algorithms. Moreover, it eliminates the gain of overestimation and significantly reduces chattering phenomenon in traditional sliding mode control. Finally, based on Lyapunov stability theory, this article proves the proposed system can achieve convergence within a finite time. Compared with STSMC, traditional SMC and proportional–integral–derivative (PID) control, the results verify the effectiveness of the proposed control method. The proposed strategy provides a new solution to reduce the steering feel feedback torque error under the influence of uncertain factors.

Robust position regulation of a 2-DOF experimental helicopter using higher order super twisting sliding mode control

This study presents a third-order super twisting sliding mode control algorithm for robust position regulation of a two-degree-of-freedom (2-DOF) experimental helicopter. The proposed approach explores high-order sliding mode control, offering advantages such as finite-time convergence and continuous control signals. The controller is implemented and validated on the Quanser Aero 2 platform, an inherently unstable and nonlinear system that presents significant challenges for control design including cross-coupling effects, model uncertainties, and external disturbances. Extensive simulations and experimental results are presented to validate the efficacy and robustness of the proposed control strategy. They highlight the controller's ability to achieve precise position control while significantly mitigating the chattering phenomenon, a common drawback associated with traditional sliding mode control. This study contributes to the field of nonlinear control systems by demonstrating the potential of high-order sliding mode control in managing nonlinear, coupled dynamic systems. The successful implementation on a real-world platform underscores the practical applicability of the proposed method in aerospace and robotics applications.

A novel combined control of flexible single-link manipulator based on singularly perturbed theory

PurposeThis study aims to improve the control accuracy and antidisturbance performance of the manipulator with the flexible link, a combined controller, which combines the novel backstepping sliding mode controller based on the extended state observer (ESO) and super-twisting sliding mode controller.Design/methodology/approachFirst, the dynamic of the system is constructed by Lagrange method and assumed mode method, and then the dynamic is decoupled by the singular perturbation theory to obtain the slow-varying subsystem and fast-varying subsystem. For the slow-varying subsystem, the novel backstepping sliding mode controller based on ESO is used to achieve joint tracking. For the fast-varying subsystem, the super-twisting sliding mode controller is used for vibration suppression. At the same time, to suppress chattering, the tanh function is used to replace the sign function in the reaching law.FindingsThe simulation results show that the combined control has better trajectory tracking performance, antiinterference performance and vibration suppression performance than traditional sliding mode control (SMC).Originality/valueA novel backstepping sliding mode controller based on ESO is designed to guarantee the performance of the tracking trajectory. The new controller improves the converge rate. A super-twisting sliding mode controller, which can stabilize the fast-varying subsystem, is used to suppress the vibration of flexible link.

Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems.

For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper's method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

Fast Terminal Sliding-Mode Predictive Speed Controller for Permanent-Magnet Synchronous Motor Drive Systems

This paper proposes a kind of discrete-time sliding-mode predictive control (SMPC) based on a nonlinear sliding function for permanent-magnet synchronous motors’ (PMSMs’) speed control to improve the convergence performance. Compared with traditional sliding-mode predictive control based on a linear sliding function, the proposed SMPC has a faster convergence rate thanks to the design of a nonlinear fast terminal sliding function. Moreover, one-step prediction is employed, which greatly simplifies the algorithm and improves the real-time performance of its operation. The sliding state will follow the expected trajectory of a predefined sliding-mode reaching law. The stability and convergence performance of the proposed method is analyzed. The results of the theoretical analysis, simulations, and experiments indicate that the proposed method has excellent convergence performance and robustness.

An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System

The rotary inverted pendulum system (RIP), which is highly favored in control applications, is examined in this work. By determining the coordinates of the Rip elements' centers of gravity, the system's total kinetic and potential energies were determined. The kinetic and potential energy expressions were used to generate the Lagrangian function. Expressions providing the system's equations of motion were discovered by taking the Lagrangian approach into consideration. The motor's equations, which will initiate the system, have also been considered. Through the use of state variables and a Matlab program, the system's pendulum angle was managed by using a moving sliding surface and the traditional sliding mode control technique. Based on the dynamics, the slip surface's slope was computed. The sliding surface's slope was computed based on the system's dynamics. The genetic algorithm was utilized to determine the ideal values for the coefficients employed in the control structure. The findings showed that the inaccuracy was roughly zero and that the pendulum angle took around 1.5 seconds to reach the intended reference value. Furthermore, it noted that the motor torque and current values are 12 Nm and 2.5 amps, respectively. The findings show that the motor values are reasonably similar to the values seen in real-world applications. Control in real-time applications won't be an issue if the motor is chosen based on these values

An advanced integral sliding mode controller design for residual current compensation inverters in compensated power networks to mitigate powerline bushfire hazards

AbstractThis work deals with designing an advanced integral sliding mode controller (AISMC) for residual current compensation (RCC) inverters connected with arc suppression coils to compensate for power distribution networks where the main idea is to alleviate hazardous circumstances caused by electric faults on powerlines. The key advancement in the proposed AISMC over traditional sliding mode controllers is the utilization of an improved exponential reaching law which ensures the faster convergence of the desired control objective that is the fault current compensation in this particular application. An improved exponential reaching law (IERL) used in this work is a combination of the exponential and constant‐proportional reaching laws (while existing approaches use constant reaching laws) which assists to minimize the current injection error through the RCC inverter in the steady‐state. The integral action in conjunction with the exponential function in the sliding surface, based on which the proposed controller is designed, helps to eliminate the chattering effects in a quickest way that can be evidenced from the settling time and percentage overshoot. The feasibility of the proposed AISMC is theoretically assessed by analyzing the stability using the Lyapunov stability theory. Simulation and processor‐in‐loop results further justify the theoretical foundation by confirming the desired current injection and compensating voltage and current due to the fault. Finally, results are compared with a TIMSC for demonstrating the superiority of the AISMC.

Robust Speed Control of Permanent Magnet Synchronous Motor Drive System Using Sliding-Mode Disturbance Observer-Based Variable-Gain Fractional-Order Super-Twisting Sliding-Mode Control

This paper proposes a novel nonlinear speed control method for permanent magnet synchronous motors that enhances their robustness and tracking performance. This technique integrates a sliding-mode disturbance observer and variable-gain fractional-order super-twisting sliding-mode control within a vector-control framework. The proposed control scheme employs a sliding-mode control method to mitigate chattering and improve dynamics by implementing fractional-order theory with a variable-gain super-twisting sliding manifold design while regulating the speed of the considered motor system. The aforementioned observer is suggested to enhance the control accuracy by estimating and compensating for the lumped disturbances. The proposed methodology demonstrates its superiority over other control schemes such as traditional sliding-mode control, super-twisting sliding-mode control, and the proposed technique. MATLAB/Simulink simulations and real-time implementation validate its performance, showing its potential as a reliable and efficient control approach for the system under study in practical applications.

Fuzzy sliding mode control with adaptive exponential reaching law for inverters in the photovoltaic microgrid

Photovoltaic inverters are widely utilized in microgrid systems working as the key equipment for converting solar energy into usable electricity. This paper presents a fuzzy sliding mode control (FSMC) method for the photovoltaic inverter in a microgrid. The inverter module uses voltage control to achieve stable AC output voltage. Moreover, to deal with system uncertainty and non-linearity in the photovoltaic inverter, a fuzzy controller was designed to realize real-time adaptation of the gains of the constant term and the reaching term in the sliding mode control law, which serves as a compensating controller for traditional sliding mode control. The gains of the exponential reaching law can be adjusted according to the system state instead of fixed gains, which can effectively reduce the chattering phenomenon and improve the robustness of the photovoltaic microgrid. Finally, the Lyapunov stability theory was used to ensure the stability of the entire control system, achieving a high-performance independent power supply for loads in a microgrid. Simulation results show that the designed control system is more robust to load disturbances and has superior dynamic performance.

RBF neural network dynamic sliding mode control based on lambert W function for piezoelectric stick-slip actuator.

This paper presents a novel approach for increasing the precision of high-precision positioning control experiments for a piezoelectric stick-slip actuator system. This is achieved through dynamic sliding mode control with a radial basis function neural network (RBFNN) based on the Lambert W function. The proposed control strategy is divided into two parts: scanning mode control and stepping mode control. For scanning control, a dynamic sliding mode controller was designed to solve the jitter problem in traditional sliding mode control. The introduction of the RBFNN avoids the effects of uncertainty terms and unknown disturbances in the model; reduces the controller gain, which must be adjusted; and improves the robustness of the system to disturbances. The stability of the dynamic sliding mode controller based on the RBFNN was verified through a Lyapunov analysis, and the Lambert W function was introduced to optimize the controller parameters responsible for the time lag in the closed-loop control system. This optimization improved the system's robustness against time delays, which can adversely affect its performance. Simulation and experimental results indicated that the proposed control strategy achieved a positioning control accuracy of <40nm during the scanning phase and was robust in the presence of a load. In long-distance positioning control experiments, the control strategy achieved a control target of 40 μm while maintaining the positioning control accuracy and reducing the impact of time lag on the system.

An adaptive integral sliding mode control strategy for medical linear accelerator vacuum system

Medical linear accelerators (MLAs) are critical components for radiation therapy, providing a state-of-the-art treatment platform for cancer therapy. The vacuum system is one of the most important MLA subsystems and its stable operation is necessary to generate high-quality beams. For vacuum system pressure control, traditional proportional-integral-derivative (PID) strategies have disadvantages such as inaccurate and imprecise control response due to its simple calculation. This paper presents an innovative adaptive integral sliding mode control (AISMC) strategy aimed at enhancing the response time, precision of control, and capability to reduce disturbances within the MLA vacuum system. In addition, a nonlinear MLA vacuum system mathematical model is established based on mechanism method. Stability of the developed vacuum control system is validated using Lyapunov stability theory. Simulation results illustrate that the proposed AISMC strategy has better response speed and accuracy than traditional PID-based systems, achieving better pressure tracking performance than traditional sliding mode control strategy with PID control. Most important for the proposed controller, system chattering is effectively mitigated.

Adaptive Neural Network Finite-Time Prescribed Performance Consensus Control for a Class of Second-Order Multi-Agent Systems

This research investigates the semi-global practical finite-time prescribed performance consensus control issue for a class of second-order multi-agent systems with unknown nonlinear functions. Unlike the previous finite-time control set by a finite-time performance function, we give finite-time control by constraining the terminal sliding manifold in a performance function. In addition, an adaptive neural network control scheme is designed, which simplifies the controller and avoids the chattering issue existing in traditional sliding mode control. Eventually, a novel adaptive finite-time prescribed performance consensus control strategy is designed, which ensures that all system variables are semi-globally practical finite-time stable and consensus errors of the multi-agent systems converge within the prescribed region in finite time. The effectiveness and practicality of the presented control strategy are evaluated by conducting simulation cases.

Trajectory tracking control of the pushing ore truck manipulator based on adaptive sliding mode control with interference observer

An improved sliding mode controller was designed to solve the problem of low tracking accuracy caused by various disturbances and errors existing in the hydraulic-driven manipulator for pushing ore truck. The state space equation of the hydraulic system of the pushing ore truck manipulator was modeled and derived, and a sliding mode function was designed. For interference signals, use interference observers for observation. For the unobserved parts, adaptive laws are used for compensation to reduce system chattering, and system’s stability is verified using Lyapunov functions. The simulation results show that, compared with the traditional Sliding mode control and adaptive sliding mode control, the adaptive sliding mode control strategy based on interference observer proposed in this paper can effectively weaken the system chattering, reduce the uncertainty caused by external interference and modeling error, and improve the trajectory tracking accuracy of the pushing ore truck manipulator.

Performance improvement of predictive voltage control for interlinking converters of integrated microgrid

Voltage quality in Renewable Energy System may be harmed by varying power demand and fluctuating energy source outputs. The model predictive voltage (MPV) control approach is suggested in this study. The proposed control strategy enables appropriate power interactions between the AC and DC subgrids while sharing power fluctuations in a coordinated way. Both the AC and DC subgrids support each other in accordance with their normalized relative changes in AC frequency and DC voltage, respectively. A typical photovoltaic (PV) wind-battery-based hybrid AC/DC microgrid is modelled and investigated, and the usefulness of the proposed scheme is validated under the renewable energy variations and load perturbations. MATLAB/Simulink has validated the efficacy of the suggested strategy. A set of comparative tests was conducted between conventional Proportional-Integral (PI) control, Sliding Mode Control (SMC) strategies, and a novel Model Predictive Voltage Control (MPV) approach under diverse conditions. The aim was to comprehensively assess the advantages of the proposed MPV method. Results demonstrate that, in contrast to traditional PI and SMC control strategies, the MPV technique exhibits distinct benefits in terms of superior control performance and achieves exceptionally low Total Harmonic Distortion (THD) values. Ultimately, the proposed solution not only raises the performance standard but also ensures the stable operation of the Renewable Energy System (RES).

Model Prediction and Optimization of Belt Drive System Vibration Suppression Based on Industrial Robot Joints

Addressing the vibration issues caused by torsional angle changes in the belt transmission systems of industrial robots during practical applications, this paper introduces a control strategy that integrates a Model Predictive Control (MPC) compensation mechanism. By applying the Lagrangian method, a dynamic mathematical model correlating torsional angle and torque was established, and an algorithm design combining MPC with its compensatory controller was developed. This strategy was validated in a MATLAB simulation environment. Simulation results demonstrate that, compared to traditional sliding mode control, the newly proposed controller significantly improved response speed in tracking the torsional angle's position and angular velocity, achieving enhancements of approximately 2 seconds and 1 second, respectively. This led to higher tracking accuracy and faster convergence speed, effectively enhancing the vibration suppression performance of industrial robot joint belt transmission systems.

Multi-motor average deviation coupling control strategy based on hyperbolic convergence law high-order sliding mode control using extended state sliding mode observer

This paper aims to develop a multi-motor synchronous drive control system for the direction of the width of the lifting arm of a catamaran. Firstly, we establish a mathematical model of permanent magnet synchronous motor and introduce the composition of AC servo control systems. We then analyze the sources of control interference in multi-motor drive systems. Based on the mean deviation coupling control strategy of multi-motor synchronous control, we design a speed tracking controller and a speed synchronization controller using hyperbolic convergence law high-order sliding mode control. Then, we design an extended state sliding mode observer to estimate the unmodeled dynamics of the system in real time. We prove the global stability of the controller using Lyapunov stability theory. Finally, the control model is simulated, and the results confirm the effectiveness of the multi-motor synchronization control method based on the hyperbolic convergence law of higher-order sliding mode control. The control method effectively mitigates the jitter associated with traditional sliding mode control and demonstrates improved synchronization and tracking performance.

Evaluation of Interval Type-2 Fuzzy Neural Super-Twisting Control Applied to Single-Phase Active Power Filters

This research introduces an improved control strategy for an active power filter (APF) system. It utilizes an adaptive super-twisting sliding mode control (STSMC) scheme. The proposed approach integrates an interval type-2 fuzzy neural network with a self-feedback recursive structure (IT2FNN-SFR) to enhance the overall performance of the APF system. The IT2FNN with STSMC proposed here consists of two components, with one being IT2FNN-SFR, which demonstrates robustness for uncertain systems and the ability to utilize historical information. The IT2FNN-SFR estimator is used to approximate the unknown nonlinear function within the APF. Simultaneously, the STSMC component is integrated to reduce system chattering, improving control precision and overall system performance. STSMC combines the robustness and simplicity of traditional sliding mode control, effectively addressing the chattering problem. To mitigate inaccuracies and complexities associated with manual parameter setting, an adaptive law of sliding mode gain is formulated to achieve optimal gain solutions. This adaptive law is designed within the STSMC framework, facilitating parameter optimization. Experimental validation is conducted to verify the harmonic suppression capability of the control strategy. The THD corresponding to the designed control algorithm is 4.16%, which is improved by 1.24% and 0.55% compared to ASMC and STSMC, respectively, which is below the international standard requirement of 5%. Similarly, the designed controller also demonstrates advantages in dynamic performance: when the load decreases, it is 4.72%, outperforming ASMC and STSMC by 1.15% and 0.38%, respectively; when the load increases, it is 3.87%, surpassing ASMC and STSMC by 1.07% and 0.36%, respectively.