Fractional Order Sliding Mode Research Articles

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.

Fractional-order Sliding Mode Control of Manipulator Combined with Disturbance and State Observer

A fractional-order sliding mode control (FSMC) method for a manipulator based on disturbance and state observers is proposed. First, a state estimator is designed that can estimate the velocity and acceleration, and only joint position feedback and the mathematical model of the manipulator are needed. The state estimator converges in finite time. Then, the disturbance observer is designed. By designing the nominal system model of the manipulator, a disturbance observation error is introduced into the closed-loop control so that the performance of the manipulator can track the nominal system. Finally, a sliding mode controller (SMC) based on the fractional differential operator theory is also designed. The value of the sliding mode variable in the derivation of the controller is composed of the fractional derivative of the trajectory tracking error of the manipulator, whereas the fractional differentiation operation uses integration in its realization, and the integration is a low-pass filter, thus, high-frequency noise is suppressed. In the experimental section, the method designed is compared with the conventional sliding mode, which further reveals the rapidity and control accuracy of FSMC.

Fixed-Time Robust Fractional-Order Sliding Mode Control Strategy for Grid-Connected Inverters Based on Weighted Average Current

Fixed-Time Robust Fractional-Order Sliding Mode Control Strategy for Grid-Connected Inverters Based on Weighted Average Current

Enhanced Control Technique for Induction Motor Drives in Electric Vehicles: A Fractional-Order Sliding Mode Approach with DTC-SVM

The present paper proposes the use of fractional derivatives in the definition of sliding function, giving a new mode control applied to induction motor drives in electric vehicle (EV) applications. The proposed Fractional-Order Sliding Mode Direct Torque Control-Space Vector Modulation (FOSM-DTC-SVM) strategy aims to address the limitations of conventional control techniques and mitigate torque and flux ripples in induction motor systems. The paper first introduces the motivation for using fractional-order control methods to handle the nonlinear and fractional characteristics inherent in induction motor systems. The core describes the proposed FOSM-DTC-SVM control strategy, which leverages a fractional sliding function and the associated Lyapunov stability analysis. The efficiency of the proposed strategy is validated via three scenarios. (i) The first scenario, where the acceleration of the desired speed is defined by pulses, leading to Dirac impulses in its second derivative, demonstrates the advantage of the proposed control approach in tracking the desired speed while minimizing flux ripples and generating pulses in the rotor pulsation. (ii) The second scenario demonstrates the effectiveness of filtering the desired speed to eliminate Dirac impulses, resulting in smoother rotor pulsation variations and a slightly slower speed response while maintaining similar flux ripples and stator current characteristics. (iii) The third scenario consists of eliminating the fractional derivatives of the pulses existing in the expression of the control, leading to the elimination of Dirac impulses. These results demonstrate the potential of the FOSM-DTC-SVM to revolutionize the performance and efficiency of EVs. By incorporating fractional control in the control scheme for PV-powered EVs, the paper showcases a promising avenue for sustainable transportation.

Actor-Critic Neural-Network-Based Fractional-Order Sliding Mode Control for Attitude Tracking of Spacecraft with Uncertainties and Actuator Faults

This paper investigates the attitude control of rigid spacecraft in the presence of uncertainties, disturbances, and actuator faults. In order to effectively address these challenges and improve the performance of the system, a novel actor-critic neural-network-based fractional-order sliding mode control (ACNNFOSMC) has been developed for spacecraft. The integration of actor-critic neural network, fractional-order theory, and sliding mode control enables dual functionality: the actor-critic neural network serves to approximate the aggregate of uncertain parameters, disturbances, and actuator faults, thereby facilitating their compensation, while the fractional-order sliding mode control mechanism significantly improves the system’s tracking precision and overall robustness against uncertainties. Theoretical analyses are presented to analyze the stability of the proposed control framework. Thorough examination via simulation experiments affirms the effectiveness and control precision of attitude of our proposed control strategy, even in complex operational scenarios.

Distributed event-triggered formation control of UGV-UAV heterogeneous multi-agent systems for ground-air cooperation

Within the context of ground-air cooperation, the distributed formation trajectory tracking control problems for the Heterogeneous Multi-Agent Systems (HMASs) is studied. First, considering external disturbances and model uncertainties, a graph theory-based formation control protocol is designed for the HMASs consisting of Unmanned Aerial Vehicles (UAVs) and Unmanned Ground Vehicles (UGVs). Subsequently, a formation trajectory tracking control strategy employing adaptive Fractional-Order Sliding Mode Control (FOSMC) method is developed, and a Feedback Multilayer Fuzzy Neural Network (FMFNN) is introduced to estimate the lumped uncertainties. This approach empowers HMASs to adaptively follow the expected trajectory and adopt the designated formation configuration, even in the presence of various uncertainties. Additionally, an event-triggered mechanism is incorporated into the controller to reduce the update frequency of the controller and minimize the communication exchange among the agents, and the absence of Zeno behavior is rigorously demonstrated by an integral inequality analysis. Finally, to confirm the effectiveness of the proposed formation control protocol, some numerical simulations are presented.

Passivity-based Rieman Liouville fractional order sliding mode control of three phase inverter in a grid-connected photovoltaic system.

Photovoltaic (PV) system parameters are always non-linear due to variable environmental conditions. The Maximum power point tracking (MPPT) is difficult under multiple uncertainties, disruptions and the occurrence of time-varying stochastic conditions. Therefore, Passivity based Fractional order Sliding-Mode controller (PBSMC) is proposed to examine and develop a storage function in error tracking for PV power and direct voltage in this research work. A unique sliding surface for Fractional Order Sliding Mode Control (FOSMC) framework is proposed and its stability and finite time convergence is proved by implementing Lyapunov stability method. An additional input of sliding mode control (SMC) is also added to a passive system to boost the controller performance by removing the rapid uncertainties and disturbances. Therefore, PBSMC, along with globally consistent control efficiency under varying operating conditions is implemented with enhanced system damping and substantial robustness. The novelty of the proposed technique lies in a unique sliding surface for FOSMC framework based on Riemann Liouville (R-L) fractional calculus. Results have shown that the proposed control technique reduces the tracking error in PV output power, under variable irradiance conditions, by 81%, compared to fractional order proportional integral derivative (FOPID) controller. It is reduced by 39%, when compared to passivity based control (PBC) and 28%, when compared to passivity based FOPID (EPBFOPID). The proposed technique led to the least total harmonic distortion in the grid side voltage and current. The tracking time of PV output power is 0.025 seconds in PBSMC under varying solar irradiance, however FOPID, PBC, EPBFOPID, have failed to converge fully. Similarly the dc link voltage has tracked the reference voltage in 0.05 seconds however the rest of the methods either could not converge, or converged after significant amount of time. During solar irradiance and temperature change, the photovoltaic output power has converged in 0.018 seconds using PBSMC, however remaining methods failed to converge or track fully and the dc link voltage has minimum tracking error due to PBSMC as compared to the other methods. Furthermore, the photovoltaic output power converges to the reference power in 0.1 seconds in power grid voltage drop, whereas other methods failed to converge fully. In addition power is also injected from the PV inverter into the grid at unity power factor.

A Novel Hybrid Optimization-based Backstepping Fractional Order Sliding Mode Proportional-integral-derivative Controller for Nonlinear Biological System

Nowadays, the role of the control system in the bioengineering field plays a major part due to its significant improvement and demand. Usually, if there are any changes in the parameter of a biological system, then it tends to cause crucial diseases in humans. Previously, various control algorithms have been developed; however, the proper control process failed due to the high error rate, slow convergence, Computational Complexity, Tuning Complexity and inaccurate function. The proposed control strategy should ensure accurate tracking of the desired trajectory or reference signal, even in the presence of uncertainties and disturbances. The control system should be capable of adapting to changes in the system dynamics and maintaining stable operation. This complexity can lead to high computational requirements, making the controller computationally expensive and potentially unsuitable for real-time applications or systems with limited computing resources. To overcome these issues, in this work, the novel Hybrid Ant Lion Moth Flame Optimization (HALMFO) based Backstepping Fractional-Order Sliding mode Proportional-Integral-Derivative (BFO-SPID) controller is proposed for different nonlinear biological systems. The proposed method enhances the efficiency, improved performance, robustness, convergence speed, and solution quality of the optimization process. This paper addresses the challenge of controlling nonlinear biological systems by proposing a novel hybrid optimization-based backstepping approach combined with a fractional order sliding mode proportional-integral-derivative (PID) controller. This work’s essential contribution lies in addressing existing control strategies’ limitations by integrating multiple control techniques to achieve robust tracking performance and disturbance rejection. This system proposes predictive control with state estimation based on the backstepping sliding mode method. The gain parameters of the developed controller are optimized using the HALMFO method. The proposed control approach performance has been tested under biological systems such as Protein, Pancreas, and Genetic Regulatory Network (GRN). The execution of this proposed model is done in MATLAB/Simulink. Furthermore, the performance of the proposed control technique is compared with various state-of-the-art methods in terms of accuracy, Mean Average Error (MAE), Mean Square Error (MSE), settling time, overshoot, and rise time. The comparison illustrates that the projected controller has reached a steady condition with the least error rate in the control application. Thus the developed controller regulates the parameter variations in the biological system as per the desired level, providing significant effective outcomes to complex problems.

Robust fractional-order sliding mode tracker for quad-rotor UAVs: Event-triggered adaptive backstepping approach under disturbance and uncertainty

In this paper, tracking control of the quad-rotor UAVs in the presence of exterior perturbations and dynamical uncertainties is accomplished using an event-triggered adaptive backstepping fractional-order sliding mode control scheme. For this reason, tracking errors are considered as the difference between the actual and desired states of the quad-rotor system. Moreover, event-triggering errors are defined as the difference between tracking errors at time ti and tracking errors at time t. Afterward, a dynamical model of the quad-rotor system under external disturbance and model uncertainty is obtained based on the tracking errors’ states. Then, the fractional-order sliding mode surface based on the tracking errors and virtual control inputs is proposed to guarantee the convergence of desired tracking errors. Hence, to avoid the complexity in the control process, the virtual control inputs are presented as fractional-order integral-type laws to avoid high derivatives of virtual control inputs. In addition, the event-triggering condition is applied for backstepping fractional-order sliding mode control to prevent frequent periodic action of control inputs. Moreover, employing the backstepping control procedure and the Lyapunov stability concept, the convergence of fractional-order sliding surfaces is guaranteed. Later, the fractional-order adaptive laws are designed to estimate the unknown upper bounds of perturbations and uncertainties. Finally, to demonstrate the efficiency of the control algorithm recommended in this paper, the simulation results on MATLAB/Simulink environment are presented. A comparison between the control method in this paper and another existing technique is prepared to prove the productivity of performance of the offered control method on the quad-rotor system.

Anti-Disturbance Speed Control of Permanent Magnet Synchronous Motor Based on Fractional Order Sliding Mode Load Observer

Based on the fractional order sliding mode load observer, this paper presents an anti-disturbance speed control method of permanent magnet semi-direct drive transmission system for overhead manned equipment. According to the Lagrange equation, the dynamic model of semi-direct drive transmission system is established. Furthermore, the mathematical model of the permanent magnet synchronous motor (PMSM) is established based on the coordinate transformation theory. Subsequently, the fractional order sliding mode observer (FOSMO), which combines nonsingular terminal sliding mode control and fractional order theory is designed to observe the load disturbance changes in the permanent magnet semi-direct drive transmission system. Then, the concept of “active damping” is used to design the speed loop PI controller, and combined with the designed FOSMO to construct the composite speed controller. The designed composite speed controller is further improved by the anti-saturation design and parameter optimization. The results demonstrate that the designed FOSMO can precisely estimate the load disturbance on the PMSM output shaft. Additionally, the designed composite speed controller can realize stable speed control in the case of complex load disturbance, which meets the anti-disturbance speed control requirements of permanent magnet semi-direct drive transmission system, and the robustness of the control system is further improved by adding the anti-saturation link.

Fractional-Order Sliding Mode Load Frequency Control and Stability Analysis for Interconnected Power Systems With Time-Varying Delay

The universal use of open communication networks in interconnected power systems has changed the constant delay in the formerly dedicated channels into time-varying delay. The delay will deteriorate the dynamic performance of the load frequency control and lead to system frequency instability. This paper presents a fractional-order sliding mode controller for interconnected power systems with time-varying delay and performs stability analysis based on the Lyapunov direct method. Firstly, fractional-order integral sliding mode control is used to improve the stability of interconnected power systems containing time-varying delay. This expands the delay margin by taking advantage of the scalability of the fractional-order to the sliding mode surface. Then, the Riemann-Liouville fractional-order Lyapunov functional is introduced to stability analysis. This reduced the conservatism of the stability analysis by adjusting the upper limit of the functional integral. Lastly, combining Lyapunov's theory and integral inequality to obtain the stability conditions of the time-varying delay power system described by linear matrix inequality, and bring the stability margin of the system. The simulation results show that the designed controller can guarantee that the maximum delay time of the system is less than a predefined upper limit. The proposed control strategy obtains a larger stability margin than the other four scenarios. Additional simulation study was also conducted to verify its robustness to load variations and wind fluctuations.

ON THE ASYMPTOTIC STABILITY OF A NEW FRACTIONAL-ORDER SLIDING MODE CONTROL WITH APPLICATION TO ROBOTIC SYSTEMS

This paper presents an advanced control strategy based on Fractional-Order Sliding Mode Control (FO-SMC), which introduces a robust solution to significantly improve the reliability of robotic manipulator systems and increase its control performance. The proposed FO-SMC strategy includes a two-key term-based Fractional Sliding Function (FSF) that presents the main contribution of this work. Additionally, a fractional-order-based Lyapunov stability analysis is developed for a class of nonlinear systems to guarantee the asymptotic stability of the closed loop system. Four FSF-based versions of the designed FO-SMC are studied and discussed. Various scenarios of the proposed control strategy are tested on a 3-degree-of-freedom SCARA robotic arm and compared to recent FO-SMC works, demonstrating the effectiveness of the new proposed control strategy to (i) ensure the asymptotic stability, (ii) achieve a smooth start-up, (iii) cancel the static error, giving a good tracking trajectory, and (iv) reduce the control torques, yielding a consumed energy minimization.

Self-Constructing Fuzzy Neural Fractional-Order Sliding Mode Control of Active Power Filter.

In this article, a fractional-order sliding mode control (FOSMC) scheme is proposed for mitigating harmonic distortions in the power system, whereby a self-constructing recurrent fuzzy neural network (SCRFNN) is used to weaken the effect of compound nonlinearity caused by unknown uncertainties and environmental fluctuations. The fractional-order sliding mode controller (SMC) is constructed to maintain the control system to be asymptotically stable and a fractional-order calculus is introduced into an SMC to soften the sliding manifold design and realize chattering reduction. Considering parameter variations existing in the power system model, SCRFNN is adopted to approximate the unknown dynamics, which is able to dynamically update network structure by optimizing the fuzzy division, and a feedback connection is incorporated into the feedforward neural network, which is regarded as a storage unit to enhance the capability of coping with temporal problem. The control scheme combining the FOSMC with the SCRFNN can make the tracking error and its time derivative converge to zero. Experimental studies demonstrate the validity of the designed scheme, and comprehensive comparisons illustrate its superiority in harmonic suppression and high robustness.

A Novel Data-Driven Self-Tuning SVC Additional Fractional-Order Sliding Mode Controller for Transient Voltage Stability With Wind Generations

This paper proposes a novel data-driven self-tuning additional sliding mode controller for power system transient voltage stability enhancement considering wind integration. We first develop a new additional fractional-order sliding mode controller (FOSMC) for the static var compensator (SVC). The tuning of FOSMC parameter settings is then reformulated as a Markov decision process (MDP) and solved by the deep reinforcement learning (DRL) algorithm. In addition, a data-driven estimation method is proposed for the identification of an equivalent transfer function that is further used to calculate reward during the training process, yielding the model-free training. After that, the well-trained agent allows us to tune the controller parameters considering system uncertainties and achieve robustness against various operating conditions. Comparative results with other state-of-art methods demonstrate that the proposed method can effectively suppress the chattering issue of the sliding mode controller and ensure transient voltage stability under different operating conditions.

Fixed-Time Fractional-Order Sliding Mode Control for UAVs under External Disturbances

The present paper investigates a fixed-time tracking control with fractional-order dynamics for a quadrotor subjected to external disturbances. After giving the formulation problem of a quadrotor system with six subsystems like a second-order system, a fractional-order sliding manifold is then designed to achieve a fixed-time convergence of the state variables. In order to cope with the upper bound of the disturbances, a switching fixed-time controller is added to the equivalent control law. Based on the switching law, fixed-time stability is ensured. All analysis and stability are proved using the Lyapunov approach. Finally, the higher performance of the proposed controller fixed-time fractional-order sliding mode control (FTFOSMC) is successfully compared to the two existing techniques through numerical simulations.

Recurrent-Neural-Network-Based Fractional Order Sliding Mode Control for Harmonic Suppression of Power Grid

A continuous fractional order sliding mode controller (CFOSMC) based on a developed output feedback feature selection neural network (OFFSNN) for an active power filter (APF) is studied in this paper to effectively compensate grid harmonic current and improve power quality. A fractional order sliding mode manifold is introduced firstly. Then a continuous fractional order sliding mode controller is adopted to resolve the shortcoming of chattering phenomenon in the conventional one by designing a continuous control law. Furthermore, considering the unknown part of APF system, a new neural structure called OFFSNN is established to estimate the unknown dynamic characteristic with high precision and low computational burden. Compared with general neural network, the proposed OFFSNN is adept at adjusting neural structure and parameters by selecting beneficial nodes as well as deleting useless ones. To demonstrate the effectiveness and superiority of the presented scheme, experiments in various cases on the APF platform are given.

Operation Control Method for High-Speed Maglev Based on Fractional-Order Sliding Mode Adaptive and Diagonal Recurrent Neural Network

The speed profile tracking calculation of high-speed maglev trains is mainly affected by running resistance. In order to reduce the adverse effects and improve tracking accuracy, this paper presents a maglev train operation control method based on a fractional-order sliding mode adaptive and diagonal recurrent neural network (FSMA-DRNN). First, the kinematic resistance equation is established due to the three types of resistance that occur during the actual operation of a train: air resistance, guide eddy current resistance, and suspension frame generator coil resistance. Then, the FSMA-DRNN control law and parameter update law are designed, and a FSMA-DRNN operation controller is composed of three parts: speed feed forward, fractional-order sliding mode adaptive equivalent control, and diagonal recurrent neural network resistance compensation. Furthermore, by using the designed operation controller, it is proven effective by the Lyapunov theory for the stability of the closed-loop control system. Apart from the proposed theoretical analysis, the proposed approaches are verified by experiments on the high-speed maglev hardware-in-the-loop simulation platform Rt-Lab, in line with the 29.86 km test line and a five-car train from the Shanghai maglev, showing the effectiveness and superiority for operation optimization.

Optimal Tuning of Fractional Order Sliding Mode Controller for PMSM Speed Using Neural Network with Reinforcement Learning

An improved fractional-order sliding mode control (FOSMC) for PMSM is presented in this study to set the unavoidable parameters and to improve permanent magnet synchronous motors (PMSMs) drive performance, such as current and speed tracking accuracy. To determine the optimal parameters of the FOSMC for control speed in a PMSM drive, a neural network algorithm with reinforcement learning (RLNNA) is proposed. The FOSMC parameters are set by the ANN algorithm and then adapted through reinforcement learning to enhance the results. The proposed controller using RLNNA based on fractional-order sliding mode control (RLNNA-FOSMC) can drive the motor speed to achieve the referred value in a finite period of time, leading to faster convergence and improved tracking accuracy. For a fair comparison and evaluation, the proposed RLNNA-FOSMC is compared with conventional FOSMC by applying the integral of time multiplied absolute error as an objective function. The most commonly used objective functions in the literature were also compared, including the integral time multiplied square error, integral square error, and integral absolute error. To validate the performance of the RLNNA-FOSMC speed controller, different scenarios with different speeds steps were carried out. The computational results are promising and demonstrate the effectiveness of the proposed controller. Overall, the proposed RLNNA-FOSMC controller for the PMSM speed control system performed better than conventional FOSMC in numerical simulations.

Direct Torque Control of an Induction Motor Using Fractional-Order Sliding Mode Control Technique for Quick Response and Reduced Torque Ripple

The performance of electric drive propulsion systems is often degraded by the high torque and flux ripples of an electric drive. Traditional control methods, such as proportional plus integral (PI) controllers and classical sliding mode controllers (SMCs), have shown good response and reduced torque ripple, but even lower ripple content at low voltage levels is required for its effective use in electric vehicle (EV) applications. In this paper, a new direct torque control (DTC) technique with space vector pulse width modulation (SVPWM) using fractional-order sliding mode control (FOSMC) for a two-level inverter (2LI) at constant switching frequency is proposed. The effectiveness of this proposed controller is compared with a conventional proportional-integral controller and a conventional sliding mode controller (SMC). Simulink models are developed using MATLAB version R2018a to analyze the robustness of the proposed control strategy. Simulation results demonstrate the advantage of the proposed controller in reducing the torque ripples at steady state with less settling time during sudden load change conditions. The proposed control technique also demonstrates better utilization of the stator flux through flux trajectory waveforms.

Fractional Order Sliding Mode Controller Based on Supervised Machine Learning Techniques for Speed Control of PMSM

Tracking the speed and current in permanent magnet synchronous motors (PMSMs) for industrial applications is challenging due to various external and internal disturbances such as parameter variations, unmodelled dynamics, and external load disturbances. Inaccurate tracking of speed and current results in severe system deterioration and overheating. Therefore, the design of the controller for a PMSM is essential to ensure the system can operate efficiently under conditions of parametric uncertainties and significant variations. The present work proposes a PMSM speed controller using machine learning (ML) techniques for quick response and insensitivity to parameter changes and disturbances. The proposed ML controller is designed by learning fractional-order sliding mode control (FOSMC) controller behavior. The primary purpose of using ML in FOSMC is to avoid the self-tuning of the parameters and ensure the speed reaches the reference value in finite time with faster convergence and better tracking precision. Furthermore, the ML model does not require the mathematical model of the speed controller. In this work, several ML models are empirically evaluated on their estimation accuracy for speed tracking, namely ordinary least squares, passive-aggressive regression, random forest, and support vector machine. Finally, the proposed controller is implemented on a real-time hardware-in-the-loop (HIL) simulation platform from PLECS Inc. Comparative simulation and experimental results are presented and discussed. It is shown from the comparative study that the proposed FOSMC based on ML outperformed the traditional sliding mode control (SMC), which is more commonly used in industry in terms of tracking speed and accuracy.