Fractional-order Terminal Sliding Mode Control Research Articles

An anti-swing control method combining deep learning prediction models with a multistate fractional-order terminal sliding mode controller for wave motion compensation devices

Shipborne multidimensional wave motion compensation devices eliminate the relative motion of cargo between supply and supplied ships. However, the random sway of ships and complicated disturbances still cause various cargo swings. Therefore, an anti-swing control method is proposed that combines deep learning prediction models with a multistate fractional-order terminal sliding mode controller for wave motion compensation devices. First, the constrained workspaces and anti-swing trajectories of cargo based on deep learning prediction models are constructed to decrease the swings of cargo originating from ship sway and inaccurate control parameters. Second, a multistate fractional-order terminal sliding mode controller is presented to eliminate the disturbance-caused cargo swings. Third, the stability of the multistate sliding mode controller is proven. Finally, the effectiveness of the anti-swing control method is verified through simulations and experiments, and the experimental results demonstrate that the maximum amplitude of cargo swings is only a few millimetres and that the maximum mean absolute error of the payload swings is less than four millimetres.

Magnetically Suspended Control Sensitive Gyroscope Rotor High-Precision Deflection Decoupling Method using Quantum Neural Network and Fractional-Order Terminal Sliding Mode Control

To achieve high-precision deflection control of a Magnetically Suspended Control and Sensitive Gyroscope rotor under high dynamic conditions, a deflection decoupling method using Quantum Radial Basis Function Neural Network and fractional-order terminal sliding mode control is proposed. The convergence speed and time complexity of the neural network controller limit the control accuracy and stability of rotor deflection under high-bandwidth conditions. To solve the problem, a quantum-computing-based structure optimization method for the Radial Basis Function Neural Network is proposed for the first time, where the input and the center of hidden layer basis function of the neural network are quantum-coded, and quantum rotation gates are designed to replace the Gaussian function. The parallel characteristic of quantum computing is utilized to reduce the time complexity and improve the convergence speed of the neural network. On top of that, in order to further address the issue of input jitter, a fractional-order terminal sliding mode controller based on the Quantum Radial Basis Function Neural Network is designed, the fractional-order differential sliding mode surface and the fractional-order convergence law are proposed to reduce the input jitter and achieve finite-time convergence of the controller, and the Quantum Radial Basis Function Neural Network is used to approximate the residual coupling and external disturbances of the system, resulting in improving the rotor deflection control accuracy. The semi-physical simulation experiments demonstrate the effectiveness and superiority of the proposed method.

Variable structure based control strategy for treatment of HCV infection

Hepatitis C is such a harmful disease which can lead to serious health problems and it is caused by the Hepatitis C Virus (HCV) which causes liver inflammation and sometimes liver cancer. In this work, the control treatment strategy for HCV infection has been proposed. The advanced nonlinear dynamical mathematical model of HCV that has two control inputs and three state variables such as virions, infected hepatocytes and uninfected hepatocytes are considered for controller design in this research work. Moreover, four nonlinear controllers such as the Fractional Order Terminal Sliding Mode Controller (FOTSMC), Integral Terminal Sliding Mode Controller (ITSMC), Double Integral Sliding Mode Controller (DISMC) and Integral Sliding Mode Controller (ISMC) have been proposed in this work for HCV infection control inside the human body. In order to control the amount of uninfected hepatocytes to its required maximum safe limit, controllers are designed for antiviral therapy in which the amount of virions and infected hepatocytes are tracked to zero. One control input is ribavirin which blocks virions production and the other is pegylated interferon (peg-IFN-α) that acts as reducing infected hepatocytes. By doing so, uninfected hepatocytes increase and achieve the required maximum safe limit. To prove the stability of the whole system, Lyapunov stability analysis is used in this work. Simulation results and comparative analysis are carried out by using MATLAB/Simulink. It can be depicted from the given results that the virions and infected hepatocytes are reduced to their required levels completely using FOTSMC and the Sustained Virologic Response (SVR) rate is also enhanced in it. It reduces the treatment period as compared to previous strategies introduced in the literature and also system behaves very nicely even in the presence of un-modeled disturbances.

Performing trajectory tracking control of an unmanned ground vehicle using fractional order terminal sliding mode controller

In this paper, fractional order terminal sliding mode control (FOTSMC) method is used for trajectory tracking control performance of an unmanned ground vehicle (UGV). Firstly, a kinematic controller is designed to estimate the linear and angular velocities of the vehicle. Then, a FOTSMC design is carried out to track the vehicle reference velocities. Terminal sliding mode control (TSMC) and sliding mode control (SMC) methods are also used to demonstrate the performance of the proposed controller. The simulation results show that the proposed controller improves the tracking error by about 13% over SMC and 6.146% compared to TSMC.

Fractional-Order Terminal Sliding-Mode Control Using Self-Evolving Recurrent Chebyshev Fuzzy Neural Network for MEMS Gyroscope

To maintain the vibrations of the gyroscope proof mass, a trajectory tracking control system using a neural network estimator is proposed. The proposed control system incorporates a fractional controller based on the terminal sliding-mode and a recurrent Chebyshev fuzzy neural network using a self-evolving mechanism. The fractional-order terminal sliding-mode control can guarantee the tracking error exponential stable, and a self-evolving recurrent Chebyshev fuzzy neural network (SERCFNN) is introduced to relax the requirement of nonlinear functional certainty. In addition, the SERCFNN develops the advantages of the self-evolving fuzzy neural network (SEFNN), recurrent fuzzy neural network (RFNN), and Chebyshev function network (CFN). The SEFNN can adaptively update the dynamic structure through generating and adjusting fuzzy logic rules. The RFNN improves the performance for coping with a temporal problem with the capability to store prior information. The CFN is capable to enlarge the dimensionality of the input variables. Moreover, the asymptotic stability of the proposed control system can be proved by the Lyapunov stability theory. The effectiveness and superiority of the performance are exhibited with simulation studies and comprehensive comparisons.

Neural network–based adaptive fractional-order terminal sliding mode control

This paper proposes an adaptive fractional-order (FO) terminal sliding mode control (TSMC) scheme to the robust current control of active power filter (APF) using a recurrent meta-cognitive fuzzy neural network (RMCFNN). An FO TSMC is developed by considering that the parametric perturbations and the external disturbances of APF are bounded. Compared with conventional TSMC approach, the proposed scheme, with an FO sliding surface, can obtain enhanced finite-time high-precision tracking performance due to another degree of freedom. Then, a novel observer-based FO TSMC is derived to achieve an absorbing model-free feature arising from RMCFNN. To improve the capabilities in managing the uncertainties, the specific online updating schemes for the structure and parameters of RMCFNN are designed. Meanwhile, closed-loop stability and finite-time convergence characteristic can be achieved using Lyapunov theory. Finally, simulation and experimental results indicate that the proposed observer-based FO TSMC can be easily implemented by microcontroller and has superior control performance compared with other existing schemes.

TDE Based Model-free Control for Rigid Robotic Manipulators under Nonlinear Friction

This paper establishes a model-free finite-time tracking control of nonlinear robotic manipulator systems. The proposed controller incorporates both time delay estimation (TDE) and an enhanced terminal sliding mode control (TSMC). The improved TSMC scheme is devised using fractional-order TSMC (FOTSMC) and proportional-integral-derivative (PID) control to obtain robust tracking and high control performance. The TDE is designed to estimate the unknown nonlinear dynamics of robotic manipulators including the Stribeck friction and the external disturbances. Due to Stribeck friction, the effect of TDE error may fail to obtain the desired error performance; thus, another TDE loop is devised to compensate for TDE error generated by non-smooth frictions. The Lyapunov criterion is used to investigate the finite-time stability to analyze the behavior of the designed approach. Finally, computer simulations of the proposed method on PUMA 560 robotic manipulators are performed in contrast with FOTSMC and adaptive fractional-order nonsingular terminal sliding mode control (AFONTSM).

Dynamic Analysis and Fractional-Order Terminal Sliding Mode Control of a Fractional-Order Buck Converter Operating in Discontinuous Conduction Mode

Fractional calculus provides a new tool for designing the control scheme of a PWM converter. However, in most studies of fractional-order converters, one has used the fractional orders of the converters to construct the controllers. Essentially, this controller does not add any additional fractional-order parameters, which will affect its flexibility. Taking the fractional-order Buck converter operating under discontinuous conduction mode (DCM) as well as the chaotic state as an example, this study proposes a novel fractional-order terminal sliding mode control strategy utilizing additional fractional orders. In order to analyze the nonlinear behaviors attributed to load changes, the discrete iterated mapping model of the voltage-controlled fractional-order Buck converter is proposed and built. According to the discrete iterated map, the bifurcation diagrams and Lyapunov exponent spectrums following different fractional orders are generated, indicating a process attributable to chaos. To suppress the undesirable nonlinear behaviors, a novel fractional-order terminal sliding surface is formed, and the corresponding controller is established. Moreover, the hyperbolic tangent function is introduced to solve the chattering problem. The proposed controller provides greater flexibilities to further improve the control capability. Furthermore, to verify the robustness of the proposed control method, the Mittag–Leffler stability condition of fractional-order systems is adopted. The effects of fractional orders on control performance are also discussed. Finally, circuit simulations with the approximate fractal structures of fractional-order components are implemented and compared so as to further verify the feasibility of the proposed controller.

Hybrid super‐twisting fractional‐order terminal sliding mode control for rolling spherical robot

AbstractThe unmodeled parameters, uncertainties, chattering, and disturbances can be serious problems for a controller. These issues decrease the performance of the controller and make it difficult to have a satisfactory movement path as well. This paper presents a novel hybrid super‐twisting fractional‐order terminal sliding mode controller (HSTFOTSMC) for a rolling spherical robot (RSR) considering bounded model uncertainties for robot dynamics in presence of external disturbances and noise. The controller is based on a new adaptive fractional‐order terminal sliding surface. The stability of the proposed controller is proved by the Lyapunov theory, and then, it is tuned by a novel extended grey wolf optimizing (EGWO) algorithm to adjust the controller parameters, and assure to achieve the precise robot performance. The results of the optimized controller (EGWO‐HSTFOTSMC) are compared with the typical sliding mode controller (SMC), fractional‐order terminal sliding mode controller (FOTSMC), and super‐twisting fractional‐order terminal sliding mode controller (STFOTSMC), which demonstrate the effectiveness of the controller scheme. The controller implementation can potently eliminate the impacts of disturbances, noise, and uncertainties; meanwhile, it decreases the tracking error and increases the convergence speed of robot responses.

Adaptive fractional order control of doubly fed induction generator based wind energy conversion system under uncertainty

Conventional fossil fuel sources are being reduced and simultaneously became more and more sources of considerable undesirable influences on the environment. In an attempt to expand renewable energy sources, wind energy is playing a significant role. A doubly fed induction generator as an alternative concept of different prevalent generators in wind power industry has a conspicuous efficiency improvement impact. There are nonlinear dynamics and many uncertainties in wind power plants, such as matched and mismatched disturbances and uncertainties of parameters. Designing a convenient controller to address these nonlinearities and uncertainties is a problematic task and has been the topic of much great research. Sliding mode control is a powerful nonlinear high-frequency switching controller, which has been widely applied. In a more specialized scope, combining fractional order calculus with controllers provides more degrees of freedom for responding to the demands of existing fractional dynamics of systems. To this regard, this paper presents an adaptive fractional-order terminal sliding mode controller to extract maximum energy from a wind turbine based doubly fed induction generator, which as the name of the controller implies is adaptive and robust against uncertainties, improves control accuracy, reduces chattering and mechanical stresses, and speeds up response time. A novel and unique sliding surface has been selected for this controller. Lumped uncertainties and switching control signal parameters have been estimated by adaptation laws. Maximized aerodynamic wind energy has been harvested by utilizing the proposed controller for the rotor side converter. The Lyapunov theorem is applied to guarantee the closed-loop system stability. Under normal conditions and in the presence of uncertainty and disturbance, the proposed method has been compared with SMC and a feedback linearization proportional integral controller.

Adaptive High-Order Terminal Sliding Mode Control Based on Time Delay Estimation for the Robotic Manipulators With Backlash Hysteresis

This paper presents the results for model-independent control of uncertain n -degree of freedom robotic manipulators in the presence of external disturbances and backlash hysteresis. In order to improve the response characteristics of the system and attenuate the uncertainties, the developed robust model-free controller incorporates time delay control (TDC) as well as adaptive terminal sliding mode control (ATSMC) methods. Particularly, the time delay estimation is designed to estimate the unknown dynamics of the robotic manipulators by adopting the theory of TDC. Further, the ATSMC is utilized to obtain the robustness, finite-time convergence, and an adaptive tuning is exploited to deal with bounded derivative of unknown dynamics. The overall system stability is investigated by the Lyapunov theorem application and computed the finite convergence rate thereafter. Finally, a simulation comparison with an existing adaptive fractional-order terminal sliding mode control under backlash hysteresis is provided to illustrate the effectiveness and the superiority of the proposed method.

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.

Fast Fractional-Order Terminal Sliding Mode Control With RBFNN Based Sliding Perturbation Observer for 7-DOF Robot Manipulator

A new perturbation estimator, using radial basis function (RBF) neural networks (RBFNN) to modify the sliding perturbation observer (SPO), is proposed with the fast fractional-order terminal sliding mode control (FFOTSMC). It aims to control a seven-degree-of-freedom (7-DOF) robot manipulator. The new perturbation estimator applies the data-driven method RBFNN to compensate for the estimation error in the conventional SPO for the first time. The modified SPO estimates the perturbation, which contains the disturbance, dynamic uncertainties, and modeling errors. The estimated perturbation is used to design with the FFOTSMC, which improves the tracking accuracy and reduces the chattering. The FFOTSMC was designed using the fractional-order derivative to design the sliding surface and the reaching/law for reaching the sliding surface. In experiments on the robot, the proposed estimation method has been evaluated by comparing with the conventional SPO or only RBFNN with the same controller, FFOTSMC. The asymptotic stability of the controller with the new estimator is proved using Lyapunov functions for fractional-order systems.

Sensorless fractional order composite sliding mode control design for wind generation system

A high-performance control system is essential to transfer maximum power from wind power generation system (WPGS) to the utility grid. In this paper, a fuzzy fractional-order terminal sliding mode control (Fuzzy-FOSMC) is presented based on the boundary layer approach. This boundary layer approach leads to the trade-off between chattering elimination and control performances. Initially a fractional order terminal sliding mode control (FOTSMC) is designed in this paper. Then, the reaching control part of the FOTSMC is replaced by a fuzzy system that eliminates the chattering even in the presence of lumped parametric uncertainties. The fuzzy control part is designed such that:(a) it maintains the stability of the system by introducing a non-linear slope inside the thin boundary layer near the sliding surface, and (b) it eliminates the chattering by acting like a saturation function. A novel wind speed estimation technique is also proposed in this paper based on Gaussian process regression (GPR). The inputs to the GPR framework are selected as the wind turbine power and its rotational speed. The superior performance of the proposed wind speed estimation technique is verified using error comparison with pre-existing techniques. The stability of the proposed GPR-based Fuzzy-FOSMC control paradigm is ensured by using the Lyapunov stability theorem. The proposed paradigm is compared with benchmark sliding mode control (SMC) and FOTSMC strategies. The proposed Fuzzy-FOSMC performance in terms of chattering elimination and stability is validated under normal conditions and lumped parametric uncertainties using extensive simulations in Matlab/SIMULINK and processor in the loop based experimental workbench.

Fast Fractional-Order Terminal Sliding Mode Control for Seven-Axis Robot Manipulator

This paper proposes a novel controller, fast fractional-order terminal sliding mode control (FFOTSMC), for a seven-degree-of-freedom (7-DOF) robot manipulator with tracking control. The new controller applies the fractional-order derivative on both the sliding surface design and the sliding control/reaching law. Compared to previous research, which only applies the fractional-order derivative on the sliding surface design, the proposed controller has a faster convergence for reaching the sliding surface and maintaining stay on it because of the new fractional-order control law, which helps the tracking accuracy. To implement the controller on the robot with less chattering, a sliding perturbation observer (SPO) is used to estimate the disturbance and uncertainties. Stability analysis is analyzed using Lyapunov functions for fractional-order systems. The controller performance is evaluated by a simulation of a single-input and single-output (SISO) system in MATLAB Simulink and experiments on the robot manipulator.

A Novel Conformable Fractional-Order Terminal Sliding Mode Controller for a Class of Uncertain Nonlinear Systems

This paper proposes a conformable fractional-order terminal sliding mode controller for a class of nonlinear systems subject to uncertainties. First, a novel conformable fractional terminal sliding surface is proposed and its finite-time stability to the equilibrium point is proven. Subsequently, a switching function with a time-varying gain is presented. The system’s stability is guaranteed by the fractional-order Lyapunov stability theorem. The reaching and convergence time are analytically calculated. The designed controller has simple calculations. The control scheme improves the convergence speed, chattering phenomena, and control effort in the presence of disturbance and uncertainty. The simulation results show the efficiency of the proposed controller.

Trajectory Tracking Control Using Fractional-Order Terminal Sliding Mode Control With Sliding Perturbation Observer for a 7-DOF Robot Manipulator

A novel control scheme utilizing fractional-order terminal sliding mode control with sliding perturbation observer (FOTSMCSPO) is proposed herein. It was used to solve the trajectory tracking problem on a seven-degree-of-freedom robot manipulator. The fractional-order terminal sliding mode in FOTSMCSPO provides a finite convergence time for reaching the sliding surface. In this article, a sliding perturbation observer (SPO) is used to estimate the disturbance from the environment and modeling uncertainties. The new control scheme exhibits high precision, fast convergence, and robust performance against the lumped uncertainties. These advantages are ensured through the newly designed fractional-order terminal sliding surface and the SPO. The stability is analyzed based on the Lyapunov functions for general and fractional-order systems. An implementation on a real robot manipulator demonstrated the effects and performance of the new control method.

Design, Analysis and Experimental Validation of a Fractional Order Terminal Sliding Mode Controller on Active Suspension System

ABSTRACT The vibrations in the vehicles are one of the discomforts to the passengers. The reduction of vibrations is a challenging task in the suspension system of the vehicle. The researchers are proposing different types of control strategies in the active suspension system to reduce the vibration and increase the ride comfort of the passengers. In this paper, Fractional Order Terminal Sliding Mode Controller (FOTSMC) is proposed to reduce the vibration and it is implemented with the Quanser experimental active suspension system (EASS). To validate the performance of the proposed controllers, its performances are compared with FOTSMC, terminal sliding mode controller and sliding mode controller. The designed controllers are tested with four types of road inputs with the Quanser EASS. Furthermore, the ride comfort is analyzed as per the ISO 2631–1 standard and the stability of the Quanser EASS with the designed controllers is tested. The power spectrum density is plotted to test the performance of the deigned controllers in the human-sensitive frequencies. The proposed FOTSMC outperforms other controllers in all aspects of the analysis considered in this paper.

A Super Twisting Fractional Order Terminal Sliding Mode Control for DFIG-Based Wind Energy Conversion System

The doubly fed induction generator (DFIG)-based wind energy conversion systems (WECSs) are prone to certain uncertainties, nonlinearities, and external disturbances. The maximum power transfer from WECS to the utility grid system requires a high-performance control system in the presence of such nonlinearities and disturbances. This paper presents a nonlinear robust chattering free super twisting fractional order terminal sliding mode control (ST-FOTSMC) strategy for both the grid side and rotor side converters of 2 MW DFIG-WECS. The Lyapunov stability theory was used to ensure the stability of the proposed closed-loop control system. The performance of the proposed control paradigm is validated using extensive numerical simulations carried out in MATLAB/Simulink environment. A detailed comparative analysis of the proposed strategy is presented with the benchmark sliding mode control (SMC) and fractional order terminal sliding mode control (FOTSMC) strategies. The proposed control scheme was found to exhibit superior performance to both the stated strategies under normal mode of operation as well as under lumped parametric uncertainties.

Fractional‐order fault‐tolerant pitch control design for a 2.5 MW wind turbine subject to actuator faults

This paper proposes an active fault-tolerant pitch control design for a 2.5 MW wind turbine. The proposed scheme combines the robustness properties of fractional-order terminal sliding mode control with the accurate estimation of virtual actuators. Its main objective is to enable the wind turbine to retain its nominal pitching performance under faulty conditions whereas simultaneously attenuating chattering. The fault detection scheme implements a bank of modified unscented Kalman filters. The proposed approach was implemented to a 2.5-MW wind turbine subject to pitch actuator faults and sensor noise. Its performance was compared with that of an integer-order terminal sliding mode approach. Guaranteeing the finite time stability of the pitching system under faulty conditions whereas alleviating the chattering phenomena are among the positive features of the proposed fractional-order fault-tolerant pitch control design.