Fractional-order Sliding Mode Control Research Articles

Piecewise Time Polynomials-Based Control Methods for Obstacle Avoidance and Precision Positioning of Tower Crane Systems with Varying Cable Lengths

During the hoisting and lowering operations of a tower crane, dynamic variations in cable lengths significantly influence the oscillation frequency and amplitude of the load. These variations complicate the oscillation characteristics, heightening the challenge of balancing obstacle avoidance with precise positioning. To tackle this issue, we propose a trajectory planning and tracking control method that integrates hoisting control to reduce the impact of varying cable lengths on load swinging and achieve accurate positioning during obstacle navigation. A novel definition of swing angle is introduced to model the crane’s rigid and swinging components separately, enhancing model accuracy while simplifying complexity. A piecewise polynomial constructs the load trajectory in a low-dimensional flat space, which is then mapped to a high-dimensional generalized state space through a homeomorphic transformation, ensuring trajectory smoothness and traceability. A fractional-order sliding mode controller is employed to facilitate rapid and precise tracking of the actuated degrees of freedom, suppressing load oscillation while maintaining positioning accuracy. Experimental validation on a tower crane platform shows that the proposed strategy enables smooth obstacle avoidance and precise target point reaching, even with varying cable lengths.

Observer based finite-time adaptive fractional-order sliding mode control of DFIG wind turbines with unknown dynamic parameters

In this study, we investigate adaptive finite-time fractional-order sliding mode control (AFFSMC) of DFIG wind turbines (DWTs) under model uncertainty in finite time. A fractional-order sliding surface is first constructed to develop the concept. A robust terminal adaptive sliding mode controller is then designed for pitch angle control of wind turbine to achieve finite-time stability at high wind speeds to regulate the produced electric power in Zone III of the turbine’s working range. This is all with this assumption that there is no any information about the dynamics of the turbine due to the significant uncertainties. Through the use of a stable adaptive law, the vector of the wind turbine’s unknown dynamic parameters is approximated in this method. An observer is also proposed to estimate both turbine speed and external disturbances term. The closed-loop system’s finite-time stability study and the finite-time convergence of the turbine output were both carried out using the dynamic model of the system and the proposed Lyapunov theory. Some numerical examples are also presented together with a comparison to the standard integer sliding mode control to demonstrate the correctness of the control law.

Adaptive Fault-Tolerant Control of Mobile Robots with Fractional-Order Exponential Super-Twisting Sliding Mode

Industrial mobile robots easily experience actuator loss of some effectiveness and additive bias faults due to the working scenarios, resulting in unexpected performance degradation. This article proposes a novel adaptive fault-tolerant control (FTC) strategy for nonholonomic mobile robot systems subject to simultaneous actuator lock-in-place (LIP) and partial loss-of-effectiveness (LOE) faults. First, a nominal fractional-order sliding mode controller based on the designed exponential super-twisting reaching law is investigated to reduce the reaching phase time and eliminate the chattering. To address the time-varying LIP faults and uncertainties, a novel barrier function (BF)-based gain is explored to assist the super-twisting law. An estimator is designed to estimate the lower bound of the time-varying partial LOE fault coefficients, thus without requiring the boundary information of faults that is commonly requested in traditional FTC schemes. Combined with the nominal controller clubbed with BF and estimator-based LOE fault compensation term, the fault-tolerant controller is finally constructed. The proposed FTC scheme achieves fast convergence and the sliding variables can be confined in a predetermined neighborhood of the sliding manifold under actuator faults. The results show that the proposed controller has superior tracking performance under faulty conditions compared with other state-of-the-art adaptive FTC approaches.

Fractional order slide mode droop control for simultaneous voltage and frequency regulation of AC microgrid

AbstractThis research proposes the application of fractional‐order sliding mode control (FOSMC) at the primary controller level to improve the stability of an islanded microgrid by adjusting its voltage and frequency. The control strategies used in the microgrid are performed in two levels (primary and secondary) in the islanded mode. Practically, most previous studies have worked to improve the primary controller. Droop control is one of the most commonly used methods at the primary level and is adopted in this study as well. The sliding mode control (SMC) strategy is normally used to control linear equations. Thus, the non‐linear microgrid equations were transformed into some linear ones using the input‐output feedback linearization technique. Further, a fractional sliding surface was acquainted. The sliding surface and FOSMC were designed to reject system uncertainties and organize the voltage and frequency. Design parameters were chosen using the Lyapunov stability theorem. The validation of the proposed method using Simulink‐MATLAB confirms its effectiveness in enhancing level power sharing, regulating frequency, and maintaining voltage stability across the system.

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.

Adaptive backstepping and sliding mode control of a quadrotor

This article proposes a simple robust adaptive control architecture with minimum parameter estimation laws for trajectory tracking of a quadrotor subjected to parametric variations and environmental disturbances. This simple control architecture aims to achieve highly accurate, robust, and fast trajectory tracking of the quadrotor in a short time with low computational cost. Firstly, the quadrotor model is divided into altitude, attitude, and position subsystems for which appropriate control methods are designed without prior knowledge of the upper bound of external disturbances. A simple adaptive fractional-order sliding mode control (AFSMC) is designed to enhance the tracking of the altitude subsystem and estimate the upper bound of the disturbances. Then, a simple adaptive backstepping control (ABC) is developed for the horizontal position to generate the required roll and pitch orientations. The adaptation laws not only estimate the upper bound of the disturbances but also adjust the controller gains thereby enhancing the robustness of the ABC. A nonsingular fast terminal sliding mode control (NFTSMC) is incorporated with a finite-time disturbance observer (FDO) to accurately suppress the disturbances, and follow the target rotation angles within a short finite-time. Simulation results showed that the compounded control structure ensures accurate, fast, and robust tracking. The AFSMC can achieve the desired altitude with a settling time of 0.31 s and root mean square error (RMSE) of 0.0454 m. The ABC can attain the target horizontal position coordinates with a settling time of (0.47 s, 0.47 s) and RMSE of (0.0370 m, 0.0518 s). The NFTSMC-FDO can achieve the desired attitude angles with a settling time of (0.11 s, 0.13 s, 0.52 s) and RMSE of (0.0098 rad, 0.0092 rad, 0.0935 rad). Performance comparisons with existing control methods in terms of settling time and RMSE demonstrated that the proposed control architecture is superior.

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.

Sliding mode control design using a generalized reduced-order fractional model for chemical processes

This article presents a comprehensive study that evaluates the potential advantages of adopting a unified, systematic, and organized general fractional model within the Sliding Mode Control (SMC) design framework. The exploration extends to the model's applicability in a variety of disciplines. Although prior research has utilized SMC and fractional-order systems independently, no previous work has established a mathematical framework that integrates a generic fractional-order SMC model. The study addresses this gap and highlights potential implications for control design and applications in a variety of fields, particularly for chemical processes.

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

Robust observer-based-α-variable model-free supertwisting fractional order sliding mode control for nonlinear PEMFC system with uncertainties and disturbance

The service life and efficiency of proton exchange membrane fuel cells (PEMFCs) are significantly related to the control performance of the air supply system. Therefore, this research develops a novel robust observer-based- [Formula: see text]-variable model-free supertwisting fractional-order sliding mode control ([Formula: see text]-MF-STFOSMC) for complex nonlinear PEMFC air supply system with unmeasurable state variables, model uncertainties, and external disturbance. First, the fifth-order nonlinear PEMFC air supply system model is presented, and the unmeasured state variables are estimated using a nonlinear disturbance observer (NDOB1). Second, the ultra-local model (ULM) algorithm is employed to reconstruct the complex nonlinear PEMFC air supply system, avoiding the need for precise modeling and reducing the controller design difficulty. To estimate and compensate for the uncertain dynamics in the ULM algorithm, another NDOB2 is proposed to realize zero estimation error and finite-time observation. Besides, to achieve optimal control performance with less input chattering, finite-time convergence, and fast response speed, the [Formula: see text]-MF-STFOSMC is designed using super-twisting fractional-order sliding mode control (STFOSMC) algorithm. Furthermore, the stability of [Formula: see text]-MF-STFOSMC via a closed-loop system is verified using the Lyapunov theorem. Finally, the nonlinear PEMFC air supply system model with the proposed controller is realized in MATLAB/Simulink environment, and the simulation results are given to show the superiority and effectiveness of the proposed technique.

Fixed-time fractional-order sliding mode controller with disturbance observer for U-tube steam generator

Water level control of a U-tube steam generator plays a critical and challenging role in ensuring safe and reliable operation for a pressurized-water reactor-type nuclear power plant, as both excessively high and low water level in the U-tube steam generator would affect the normal operation of the nuclear power plant and even lead to unplanned shutdown events. This work presents a fixed-time fractional-order sliding mode water level controller coupled with a fixed-time disturbance observer, aiming to further improve the water level control performance under full operating conditions, considering uncertainties and actuator saturation. The proposed scheme is formulatedbased on the popular Irving water level model with uncertainties and the pre-existing actual water level control framework, while at the same time incorporating the benefits of the state-of-the-art anti-windup techniques, disturbance observer-based feedforward compensation techniques, fractional-order calculus, sliding mode control techniques, and fixed-time stability theorem, such that the transient water level response and steady-state control accuracy can be further enhanced even in the presence of uncertainties and actuator saturation phenomenon. It is theoretically proved that under the proposed scheme, both the estimation error of the uncertainties and the water level control error can be driven to zero within a fixed time regardless of their initial values by Lyapunov’s theorem. Meanwhile, simulation studies, involving the comparisons with a real-world adopted water level controller and a pre-existing integer-order sliding mode water level controller coupled with an uncertainty estimator, reveal the feasibility and superiority of the proposed approach.

A hierarchical energy management strategy for DC microgrid hybrid energy storage systems based on fractional-order sliding mode controller

A hierarchical energy management strategy (EMS) for a fuel cell (FC)-supercapacitor (SC)‑lithium battery hybrid energy storage system (HESS), based on a fractional-order sliding mode controller (FOSMC), is proposed to address the nonlinear behavior of low-voltage direct current (DC) microgrid HESS. To fully exploit the energy of the SC, the system management layer divides the EMS into maximum power operation mode and state machine control algorithm operation mode. For the first time in equipment control layer, a FOSMC, more suitable for handling nonlinear characteristics, is employed, and its stability is evaluated using the Lyapunov method. Finally, a 48 V HESS experimental platform is constructed for validation, demonstrating that the proposed EMS enhances the stability, response speed, and robustness of the HESS. Compared to conventional sliding mode controller (SMC) and integral sliding mode controller (ISMC), the adoption of a FOSMC reduces the steady-state error of the bus voltage by at least 9.1 % and increases the response speed by at least 11.1 %, while exhibiting good robustness to external disturbances and uncertainties in controller parameters. This fills the current research gap in parameter robustness validation.

Performance Comparison of NN based PI and Fractional Order SMC for Sensorless Speed Control of IPMSM Drive

Performance Comparison of NN based PI and Fractional Order SMC for Sensorless Speed Control of IPMSM Drive

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.

Reinforcement learning based fractional fuzzy controller for photovoltaic systems

This article presents an innovative artificial nonlinear control technique for photovoltaic (PV) systems. A boost converter extracts maximum power from the PV system under different weather conditions. A fuzzy logic maximum power point (MPP) finding algorithm is used to determine the reference voltage of the PV system under various atmospheric conditions. It is assumed that the nonlinear dynamic model, parameters, and uncertainties of the converter are unknown. To estimate a precise model that contains nonlinearities, model uncertainties, and disturbances of the converter, proximal policy optimization (PPO) with a special reward function is applied. PPO is optimal in policy learning and sampling, fast to implement, and is a simple reinforcement learning (RL) algorithm. Then, estimations of dynamics and uncertainties are used to enhance the robustness of the suggested fractional order sliding mode controller. Furthermore, the controller coefficients are optimally adjusted by the PPO algorithm. The Lyapunov theorem is used for proving the control system's closed-loop stability. Also, the proposed methods can be generalized and used for other control systems. The simulation is conducted by MATLAB to evaluate the suggested controller's performance effectiveness. Robustness against the presence of parameter uncertainty is investigated. Moreover, the suggested technique is also compared with sliding mode controller.

Fractional order sliding mode control for power quality improvement in the distribution system

This paper presents fractional order sliding mode control (FOSMC) based distribution system compensator (DSTATCOM) for power quality improvement in the distribution system. The three-phase two-level inverter-based voltage source converter (VSI) with DC-link capacitor is used as DSTACOM. In this paper, the FOSMC-based DSTATCOM improves supply current harmonics, load balancing, and reactive power and reduces THD. The sinusoidal pulse width modulation (SPWM) is generating gating pulses for VSI. The performance of the presented system is verified in MATLAB/Simulink software. The simulations are verified source voltage, current and load current as well as compensating current. The FOSMC has maintained a constant supply current when connecting non-linear load. The hardware results are also presented in the manuscript. The hardware results are supply current, voltage, compensating current, and load current.

Parameter optimization of type II fuzzy sliding mode control for bridge crane systems based on improved grey wolf algorithm

AbstractBridge cranes are complex nonlinear dynamic systems with underactuated characteristics, making it challenging for controllers to man age the spatial swing of the load effectively. Additionally, uncertainties both within and outside the system adversely impact control performance. To address these issues, a Type‐II fuzzy sliding mode controller has proven effective in enhancing the anti‐swing control performance of the payload. However, due to the intricate parameter adjustment optimization problem and potential challenges in dealing with nonlinearity and uncertainty, especially in complex dynamic systems, this paper proposes a grey wolf algorithm based on a dynamic spiral hunting mechanism. This enhancement endows the algorithm with improved convergence speed and higher robustness, enabling more effective parameter tuning for the second‐order fractional‐order sliding mode controller (FSMC). The proposed algorithm demonstrates superior convergence speed and solution accuracy performance through testing and comparison. Finally, simulation verification under two conditions of the bridge crane system validates the effectiveness of the proposed approach.

Fractional order adaptive sliding mode control method of manipulator

A new controller (NAFOFTSMC) is designed and successfully applied to the manipulator system. Compared with traditional integer-order sliding mode control methods (IOSMC), the fractional order sliding mode control method (FOSMC) adopted additional degrees of freedom and, to some extent, weakens the drawback of sliding mode control chattering problem. Fractional-order adaptive rate compensation is utilized to compensate for the total disturbance set of the system. The new sliding surface reduces the derivative signals that are difficult to obtain due to external interference and other factors in the robotic arm system. It also reduces the unknown parameters for adjustment, increases the proportion term, and thus enables the system to have higher control accuracy and shorter adjustment time. While designing the controller, the stability is proved at the end of the fourth section. At the same time, this control method was compared and analyzed with IOSMC, simple FOSMC, and a Pre-improved controller (AFOFTSMC).

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.

Intelligent fractional-order sliding mode control based maneuvering of an autonomous vehicle

Intelligent fractional-order sliding mode control based maneuvering of an autonomous vehicle