Adaptive Fractional-order Sliding Mode Control Research Articles

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.

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.

Fault-tolerant adaptive fractional order sliding mode control for a quadrotor using disturbance observer

An adaptive fractional-order sliding mode control method using a disturbance observer is proposed for position tracking of a quadrotor. The mathematical model of the quadrotor considering disturbance is derived using the Euler–Lagrange equations. The model is divided into two fully actuated and underactuated subsystems. The proposed controller as the result of combining fractional calculus and the sliding mode method is designed for both subsystems separately. Furthermore, a disturbance observer is designed which deals with actuator fault, uncertainty, and wind disturbance. The stability of the closed-loop system is proved using Lyapunov theory and finite-time convergence of the variables to the desired values is guaranteed. In the numerical simulation, position tracking despite the actuator faults and effects of load and wind disturbance are investigated. Finally, the simulation results validate the superior performance and robustness of the proposed controller against actuator fault and wind disturbance and the results of controllers are compared.

A New Fractional-Order Adaptive Sliding-Mode Approach for Fast Finite-Time Control of Human Knee Joint Orthosis with Unknown Dynamic

This study delves into the implementation of Fast Finite Time Fractional-Order Adaptive Sliding Mode Control (FFOASMC) for knee joint orthosis (KJO) in the presence of undisclosed dynamics. To achieve this, a novel approach introduces a Fractional-Order Sliding Surface (FOSS). In the context of limited knowledge regarding the dynamics of knee joint arthrosis, Fractional-Order Fast Adaptive Sliding Mode Control (FOFASMC) is devised. Its purpose is to ensure both finite-time stability and prompt convergence of the KJO’s state to the desired trajectory. This controller employs adaptive rules to estimate the enigmatic dynamic parameters of KJO. Through the application of the Lyapunov theorem, the attained finite-time stability of the closed loop is demonstrated. Simulation results effectively showcase the viability of these approaches and offer a comparative analysis against conventional integer-order sliding mode controllers.

Adaptive Control Design for Euler–Lagrange Systems Using Fixed-Time Fractional Integral Sliding Mode Scheme

This paper presents an adaptive fixed-time fractional integral control for externally disturbed Euler–Lagrange systems. In the first step of the control design, the approach of fractional-order fixed-time integral nonsingular terminal sliding mode control (FoIFxTSM) is introduced. This scheme combines the benefits of fractional calculus with integral sliding mode control, resulting in fast convergence, smooth nonsingular control inputs, and fixed-time stability. By integrating an adaptive scheme, the proposed method is used to control the dynamical system in the presence of uncertainty and external perturbations. The findings of the fixed-time stability using Lyapunov analyses are provided for the closed-loop system. The simulation results are compared with the adaptive fractional-order sliding mode control scheme, and they show the better tracking and convergence performance of the proposed method.

Ship roll stabilization using an adaptive fractional-order sliding mode controller

The current study designs an adaptive fractional-order sliding mode controller (AFOSMC) to diminish the undesirable effects caused by the ship roll motions. The ship roll dynamics combined with the fin actuator are employed for the controller design. The design steps are given as follows. At first, a non-integer sliding surface is utilized to design a fractional-order sliding mode controller (FOSMC). Then, an appropriate Lyapunov-based adaptation mechanism is designed to construct the adaptive version of the FOSMC. A Lyapunov candidate function is adopted to attain the ship roll stabilization through this adaptive control approach. The designed controller is robust to uncertain parameters in the ship roll dynamics and the fin actuator. Moreover, the effect of sea waves is reduced, as well. The robust performance of the AFOSMC is shown through numerical simulations.

Fractional-order adaptive sliding mode control with disturbance observer for frequency regulation in isolated microgrid

Fractional-order adaptive sliding mode control with disturbance observer for frequency regulation in isolated microgrid

Embedded adaptive fractional-order sliding mode control based on TSK fuzzy system for nonlinear fractional-order systems

An adaptive fractional-order sliding mode control (AFOSMC) is proposed to control a nonlinear fractional-order system. This scheme combines the features of sliding mode control and fractional control for improving the response of nonlinear systems. The structure of AFOSMC includes two units: fractional-order sliding mode control (FOSMC) and the tuning unit that employs a certain Takagi–Sugeno–Kang fuzzy logic system for online adjusting the parameters of FOSMC. Tuning the parameters of the FOSMC improves its performance with various control problems. Moreover, stability analysis of the proposed controller is studied using Lyapunov theorem. Finally, the developed control scheme is introduced for controlling a fractional-order gyroscope system. The proposed AFOSMC is implemented practically using a microcontroller where the test is carried out using the hardware-in-the-loop simulation. The practical results indicate the improvements and enhancements introduced by the developed controller under external disturbance, uncertainties and random noise effects.

Adaptive fractional tracking control of robotic manipulator using fixed-time method

This paper proposes an adaptive fractional-order sliding mode controller to control and stabilize a nonlinear uncertain disturbed robotic manipulator in fixed-time. Fractional calculus is used to construct a fractional-order sliding mode controller (FtNTSM) that suppresses chattering to help the robotic manipulator converge to equilibrium in a fixed-settling time based on fixed-time stability theory. Then, adaptive control is introduced and combined with FtNTSM to overcome the unknown system dynamics. The convergence time of the proposed fixed-time fractional-order sliding mode controller (AFtNTSM) is independent of beginning circumstances and can be precisely assessed, unlike the finite-time control approach. Finally, numerical simulations show that the adaptive fractional-order sliding mode controller outperforms finite-time sliding mode controller.

High-speed train cooperative control based on fractional-order sliding mode adaptive algorithm

PurposeThis study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system, so as to improve the tracking efficiency and collision avoidance performance.Design/methodology/approachThe mathematical model of information interaction between trains is established based on algebraic graph theory, so that the train can obtain the state information of adjacent trains, and then realize the distributed cooperative control of each train. In the controller design, the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon, so as to suppress the chattering of sliding mode control, and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.FindingsThe simulation results show that compared with proportional integral derivative (PID) control and ordinary sliding mode control, the control accuracy of the proposed algorithm in terms of speed is, respectively, improved by 25% and 75%. The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control, the error value tends to 0, and the operation trend tends to be consistent. Therefore, the control method can improve the control accuracy of the system and prove that it has strong immunity.Originality/valueThe algorithm can reduce the influence of external interference in the actual operating environment, realize efficient and stable tracking of trains, and ensure the safety of train control.

Active management strategy for supply chain system using nonlinear control synthesis.

Nonlinear dynamical behaviours with chaotic phenomena are commonly observed in a typical logistics model and supply chain system. Bullwhip effect has been widely recognized as one of the main issues on affecting the supply chain management. In essence, this phenomenon will lead to unnecessary consumption and waste of natural and social resources by demand variability amplification as moving up in the supply chain networks. However, traditional modelling approaches may become complicated in dealing with uncertainty and chaotic behaviour that are prevalent in real supply chains. System dynamics theory has been employed as a potentially effective strategy to cope with chaotic supply chains which are unpredictable behaviours in time. Four-dimensional differential equations which exhibit chaotic behaviours are constructed to describe a multi-echelon supply chain with bullwhip effect. Furthermore, modern control theory is applied to deal with the multi-stage supply chain optimization problems against disruptions. Specifically, the novel fractional order adaptive sliding mode control (FO-ASMC) algorithm has been implemented for ensuring efficient supply chain management. In addition, the chaos synchronization scheme is implemented in an attempt to regulate the supply chain systems under the impact of extensive uncertainties caused by tumultuous real market. It is found that the chaos synchronization is effectively realised by new FO-ASMC theory to manage advanced supply chain networks. Finally, this advanced management optimization offers a new class of intelligent applications that connects demand to supply and planning to execution across the entire supply chains.

Data-driven model-free adaptive fractional-order sliding mode control for the SMA actuator with prescribed performance

In this paper, a novel data-driven model-free adaptive fractional-order sliding mode controller with prescribed performance is proposed for the shape memory alloy (SMA) actuator. Due to the strong asymmetric saturated hysteresis nonlinear characteristics of the SMA actuators, it is not easy to establish an accurate model and develop an effective controller. Therefore, we present a controller without using the model of the SMA actuators. In other words, the proposed controller depends merely on the input/output (I/O) data of the SMA actuators. To obtain the reasonable compensation for hysteresis, enhance the noise robustness of the controller, and reduce the chattering, a fractional-order sliding mode controller with memory characteristics is employed to improve the performance of the controller. In addition, the prescribed performance control (PPC) strategy is introduced in our work to guarantee the tracking errors converge to a sufficiently small boundary and the convergence rate is not less than a predetermined value which are significant and considerable in practical engineering applications of the SMA actuator. Finally, experiments are carried out, and results reveal the effectiveness and success of the proposed controller. Comparisons with the classical Proportional Integral Differential (PID), model-free adaptive control (MFAC), and model-free adaptive sliding mode control (MFAC-SMC) are also performed.

Adaptive Fractional-Order Non-Singular Fast Terminal Sliding Mode Control Based on Fixed Time Disturbance Observer for Manipulators

In this study, with the help of a disturbance observer, an adaptive fractional-order sliding mode control scheme is designed to achieve trajectory tracking control of indeterminate manipulators. Firstly, the fractional-order non-singular fast terminal sliding mode (FO-NFTSM) surface is presented to increase the convergence velocity of the controller. Secondly, the adaptive reaching law is designed on the strength of the super-twisting algorithm to ensure the control performance of the approaching stage. Meanwhile, aiming at the compound disturbance existing in the manipulator system, an adaptive fixed-time sliding mode disturbance observer (AFSMDO) is introduced to settle the problem, which can estimate the lumped disturbance in real-time. Moreover, compensate for the system and raise the precision of the controller. The Lyapunov method is applied to certify the stability of the control system. Simulation experiments verify the superior property of the controller designed in this article.

Container throughput analysis and seaport operations management using nonlinear control synthesis

This paper is to explore the dynamical analysis and active control synthesis for improving seaport operations through system optimization. First, the multi-dimensional system of the fractional Lotka-Volterra model is utilized to investigate its underlying dynamics of port competition and cooperation for container throughput. The nonlinear dynamical behaviors are intensely examined by using eigenvalue evaluation, bifurcation analysis and time series analysis to illustrate the stability of the competition and collaboration model. With the system theory based on fractional order calculus, various dynamic properties of ports system have been discovered. Based on the dynamical analysis, adaptive fractional-order sliding mode control with artificial neural network algorithm has been realized for port growth rate improvement against disruptions. Furthermore, the proposed approach is successfully validated by the case study of major Korean seaports for improving port operations through neural network prediction. The decision making policies implemented by control algorithms are guaranteed to improve the port growth rate against disruptions. Specifically, the novel management strategy is to provide managerial insights and innovative solutions for seaport authorities who can make more efficient strategic planning for handling risk management in maritime logistics.

Fractional order adaptive sliding mode control for nonlinear anti-roll of ship

Objectives In order to solve the problem of ship nonlinear rolling control, a fractional order adaptive sliding mode control (FOASMC) algorithm is proposed. Methods First, the spectral density of random waves, spectral density of wave inclination and spectrum of waves acting on ships are calculated using a random wave model with long peak waves. The rolling angle tracking error of the system is then verified on the basis of Lyapunov stability theory. Moreover, the switching function is designed to make the system robust to uncertainties and external disturbances. Finally, the effects of fractional order, control law gain and sliding surface mode gain are analyzed. Results The results show that the mean rolling angle and standard deviation of FOASMC are smaller than those of basic sliding mode control (SMC) for various speeds and wave directions. For example, when the ship's speed is 10 m/s and the encountering wave direction is five degrees, the average rolling angle is 25.89% of the basic SMC, and the mean square deviation is 14.32% of the basic SMC. Conclusions It is proven that the proposed control algorithm has good stabilization effectiveness at various navigation speeds and encountering wave directions, as well as such advantages as strong robustness, continuous control input and no high gain.

Adaptive Fractional-Order Sliding Mode Control for Admittance-Based Telerobotic System With Optimized Order and Force Estimation

This article proposes a variable structure control with neural network and optimized fractional-order selection policy for the sensorless telerobotic system with uncertain time delay, model uncertainty, fractional calculus numerical approximation bias, and external disturbance. Expanded from the integer-order calculus based on the definition of Caputo and the comparison principle, the Riemann–Liouville-based uniformly ultimately bounded stability is introduced to synthesize the sliding mode control with varying order, and the corresponding neural network based force estimation, which is optimized by the specified order based on the greed algorithm. Combined with the mixed-type error, the proposed hybrid integer-order and fractional-order analysis methodology is capable of guaranteeing the Riemann–Liouville-based uniformly ultimately bounded stability of tracking and synchronization errors under time delay. According to Euler difference, the proposed synthesis method can suppress the combined error in the boundedness of approximating double Euler difference errors. Numerical simulation and experiment of the telerobotic system under the control of the proposed method verify the stability analyses.

Control of Quadruple Tank Process Using an Adaptive Fractional-Order Sliding Mode Controller

In this paper, an adaptive fractional-order sliding mode controller is constructed to control a quadruple tank process. The pump voltages are considered as the inputs, while the water levels in two tanks are considered as the outputs. Now, a fractional-order sliding mode controller with a non-integer sliding surface is designed. To increase the robustness to the pump coefficients, an adaptive version of the mentioned controller is designed using an appropriate Lyapunov based adaptation mechanism. This adaptation mechanism is selected such that the water levels in the two tanks converge to their corresponding desired values. The simulation results are provided to demonstrate the robust performance of the proposed controller.

Adaptive fractional-order terminal sliding mode control of rubber-tired gantry cranes with uncertainties and unknown disturbances

Using three actuators for tracking five outputs, rubber-tired gantry (RTG) crane is found to be a highly under-actuated system subject to random wind due to working outdoors. Applying fractional calculus to sliding mode control (SMC), we construct an adaptive robust control system for RTG cranes under parametric variations and unknown wind. The adaptive feature is achieved by using an estimation mechanism for approximating five crane parameters and wind disturbances. The core of the sliding mode displays robust behavior against uncertainties. For comparison, another robust controller is proposed based on finite-time sliding mode. Simulation and experiment results show the superiority of adaptive fractional-order sliding mode control, in which the controller well tracks actuated states and stabilizes unactuated states despite parametric uncertainties and unknown disturbances.

Active control synthesis of nonlinear pitch-roll motions for marine vessels

This paper investigates the dynamical analysis and control synthesis for fractional-order pitch-roll system of marine vessels under regular waves. Suppression of the effects of roll and pitch motions is critical in improving maneuverability and stability of marine vessels with ensuring the safety of cargo and comfort to sailors. The pitch-roll mode shows complex behaviours such as period-2 motion, symmetry-breaking, torus attractor, and resonance depending on initial conditions, natural frequencies, wave frequencies, and wave amplitudes. Specifically, the nonlinear behaviours are characterized by phase portraits, bifurcation diagrams, and stability analysis. The nonlinear vibration patterns are observed even under regular waves because the pitch-roll motions are strongly coupled with two perpendicular directions. To secure the upright position of the vessels in heavy weather, adaptive fractional-order sliding mode control (AFOSMC) scheme has been employed to effectively regulate pitch-roll modes against extreme sea states. The closed stability of the ship pitch-roll system has been guaranteed by the Lyapunov theory. Numerical simulations have been extensively conducted to validate the effectiveness of the proposed control algorithms. To design more comfortable and safe vessels, this study presents pitch-roll resonance eliminations, stabilization and the challenges associated with robust vessel design.

Lag-synchronization of two different fractional-order time-delayed chaotic systems using fractional adaptive sliding mode controller

This paper investigates the lag-synchronization of two non-idantical fractional-order time-delayed chaotic systems in the presence of uncertainties and external disturbances. A fractional-order adaptive sliding mode control for lag-synchronizing two non-identical fractional-order time-delayed chaotic systems with unknown uncertainties, external disturbances and uncertain parameters is proposed. The suggested technique can be used for a large range of chaotic systems. Appropriate adaptive laws are established to overcome the uncertain parameters and bounds of parameters. Furthermore, to eliminate the undesirable phenomenon of chattering, instead of using the discontinuous sign function, the continuous tanh function with adaptive amplitude and slope is used. Using the Lyapunov theorem, the stability of the suggested strategy control is proved. Finally, the simulation results demonstrate the feasibility and robustness of our suggested scheme.