Fractional-order Control Research Articles

Comparative performance analysis of robust and adaptive controller for three-link robotic manipulator system

Abstract Three-link robotic manipulator systems (TLRMS) often used in automation industries offer many capabilities, but become very complex in terms of their control and operations. In order to enhance trajectory tracking in the X and Y axes, this study investigates the application of a fractional-order nonlinear proportional, integral, and derivative (FONPID) controller for a three-link robotic manipulator system (TLRMS). Using a cost function that combines the integral of square error (ISE) and the integral of absolute change in controller output (IACCO), the cuckoo search algorithm (CSA) maximises the performance of the controller. The fractional-order term enhances the robustness and the nonlinear term supports the adaptiveness of the FONPID controller. The fractional-order proportional, integral, and derivative (FOPID) and classic PID controllers are contrasted with the FONPID controller's efficacy. The findings show that the CSA-tuned FONPID performs better than the other controllers, providing more robust and accurate tracking. By demonstrating fractional-order control's promise for intricate robotic systems, this study advances the discipline.

Deep neural data-driven Koopman fractional control of a worm robot

This paper proposes an innovative approach for enhancing the locomotion control of a worm robot by integrating deep neural networks with Koopman operator theory and fractional order control techniques. Traditional control methods often struggle with the nonlinear dynamics and uncertainties inherent in such systems. The Koopman operator framework facilitates the representation of these dynamics in a linear and infinite-dimensional space, thereby enabling advanced control strategies. By leveraging deep neural networks, we approximate the Koopman operator efficiently, enhancing the system’s adaptability and performance. Additionally, fractional order control is introduced to provide robustness against uncertainties and disturbances, offering greater flexibility in capturing the complex dynamics of the worm robot. Extensive simulations validations demonstrate the effectiveness and efficiency of the proposed approach across various environmental conditions. Results show superior performance compared to traditional methods, affirming the viability of integrating deep neural networks with fractional order control for advanced robotic applications. This study contributes to the field by showcasing a novel methodology that not only achieves precise and robust control of worm robot locomotion but also sets a foundation for future research in adaptive and intelligent robotic systems.

Neural learning fault-tolerant control of fuel cell–battery–ultracapacitor-based hybrid electric vehicle

This article investigates the energy management and control of a fuel cell hybrid electric vehicle (FCHEV) with parametric uncertainties and sensor faults. The FCHEV in this study consists of a fuel cell, battery, and ultracapacitor connected to the DC-bus via DC–DC power converters, while the DC-bus is connected to the AC motor which drives the electric vehicle via a DC–AC converter. To control the power transfer from the energy sources to the drivetrain, a finite-time fractional-order control is proposed to coordinate the DC–DC power converters. A radial basis function neural network (RBFNN) is employed to estimate and compensate for sensor faults and parametric uncertainties. A minimum learning parameter scheme is used to minimize the computational burden on the RBFNN. The main tasks of the proposed scheme are; tolerating faults and parametric uncertainties, delivering the required power to the load, voltage regulation of the DC-bus, tracking the reference currents for the battery, fuel cell, and ultracapacitor in a short finite time. The closed-loop system is guaranteed to be stable in finite time using the Lyapunov function. The simulation results highlight the validity of the presented control.

Optimal design of fractional-order proportional integral derivative controllers for structural vibration suppression

In designing control systems, it is known that fractional-order proportional integral derivative (FOPID) controllers often provide greater flexibility than conventional proportional integral derivative (PID) controllers. This higher level of flexibility has proven to be extremely valuable for various applications such as vibration suppression in structural engineering. In this paper, we study the optimization of FOPID controllers using twelve well-established algorithms to minimize structural responses under seismic excitations. The algorithms include crystal structure algorithm (CryStAl), stochastic paint optimizer, particle swarm optimization, krill herd, harmony search, ant colony optimization, genetic algorithm, grey wolf optimizer, Harris hawks optimization, sparrow search algorithm, hippopotamus optimization algorithm, and duck swarm algorithm. In addition to highlighting the benefits of fractional calculus in structural control, this study provides a detailed analysis of FOPID controllers as well as a brief description of the algorithms used to optimize them. To evaluate the efficiency of the proposed techniques, two building models with different numbers of stories are examined. FOPID controllers are designed based on oustaloup’s approximation and the El Centro earthquake data. Using five well-known metrics, the performances of the developed methods are evaluated against five earthquake scenarios, including the recent earthquake in Turkey. A non-parametric (Friedman) test is also employed to compare the algorithms based on their corresponding vibration reduction. The findings of this analysis show that CryStAl consistently performs better than the other algorithms for both building models, thus resulting in superior vibration suppression.

Fractional-Order Robust Control Design under parametric uncertain approach

This paper presents a novel methodology that combines fractional-order control theory with robust control under a parametric uncertainty approach to enhance the performance of linear time-invariant uncertain systems with integer or fractional order, referred to as Fractional-Order Robust Control (FORC). In contrast to traditional approaches, the proposed methodology introduces a novel formulation of inequalities-based design, thus expanding the potential for discovering improved solutions through linear programming optimization. As a result, fractional order controllers are designed to guarantee desired transient and steady-state performance in a closed-loop system. To enable the digital implementation of the designed controller, an impulse response invariant discretization of fractional-order differentiators (IRID-FOD) is employed to approximate the fractional-order controllers to an integer-order transfer function. Additionally, Hankel’s reduction order method is applied, thus making it suitable for hardware deployment. Experimental tests carried out in a thermal system and the assessment results, based on time-domain responses and robustness analysis supported by performance indices and set value analysis in a thermal system test-bed, demonstrate the improved and robust performance of the proposed FORC methodology compared to classical robust control under parametric uncertainty.

Speed Control of Sensorless Induction motor based on Grey Wolf Optimizer Fractional Order Controller using MRAS based Speed Estimation

Speed Control of Sensorless Induction motor based on Grey Wolf Optimizer Fractional Order Controller using MRAS based Speed Estimation

Robust fractional-order PID controller assisted by active disturbance rejection control for the first-order plus time-delay systems

Time-delay characteristics of various industrial processes may degrade the stability and dynamic performance of the control systems. Aiming at the problems of the existing methods in dealing with the time delay plant, a modified fractional-order proportional–integral–derivative (FOPID) controller for the first-order plus time-delay (FOPTD) system is developed. Assisted by a modified active disturbance rejection control (ADRC) scheme with increased observer bandwidth, the proposed FOPID controller inherently obtains good robustness to time-delay uncertainties and external disturbances. In addition, taking advantage of the fractional-order operator, the proposed controller can provide larger stability margin over the proportional–integral–derivative (PID) controller. By suitably establishing the relation between ADRC and FOPID controller parameters, the proposed controller can be analytically tuned based on the common design indices. A practical tuning guideline is developed according to frequency-domain characteristic analysis, making the proposed controller more acceptable to industrial application. The performance of the ADRC-based FOPID controller is tested by the control simulation of some typical FOPTD systems and a diesel engine speed regulation system. The efficiency of the ADRC-based FOPID controller is demonstrated by the comparisons with some existing controllers.

A novel fractional-order boundary layer fast terminal sliding mode controller for permanent magnet linear synchronous motor

This paper presents a novel fractional-order boundary layer fast terminal sliding mode (FBLFTSM) control method for high-precision tracking tasks of the permanent magnet linear synchronous motor (PMLSM). Specifically, a dynamic model of PMLSM with lumped uncertainty is established by considering the tracking task involving parameter variations, disturbance load, etc. Then, based on the dynamic model, a FBLFTSM control law is designed to guarantee higher tracking accuracy of the surface motion than the classical terminal sliding mode control even if the system suffers from unknown disturbance. Meanwhile, the fractional-order boundary layer control has the feature of “large error turns into large gain, small error turns into small gain,” which solves the contradiction between weak chattering and fast convergence in the integer-order boundary layer control and improves the dynamic performance of the system. Finally, the effectiveness of the control approach is verified by conducting tracking experiments on the cSPACE-based motor platform.

A graphical method to determine robust stabilizing region of FOPID controllers for stable/unstable fractional-order plants with interval uncertainties of a fractional order and model coefficients

This paper focuses on robustly stabilizing stable and unstable fractional-order plants with one uncertain fractional-order term and interval uncertainties using fractional order P I μ D λ controllers. Two necessary and sufficient conditions are provided to check the robust stability of the closed-loop control system. Moreover, the D-decomposition technique is utilized to determine the robust stability region of the system. Subsequently, evolutionary algorithms, such as the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE), can be utilized to discover a fractional-order controller within the region of robust stability. This work introduces three primary contributions, outlined as follows: (1) Utilizing a graphical approach, a set of stabilizing controller is obtained. (2) Rather than employing just a single stabilizing fractional-order controller, a collection of controllers is provided for the control system. (3) Employing evolutionary algorithms to find an optimal fractional-order controller. Finally, four numerical examples are presented to validate the results.

Practical one-shot data-driven design of fractional-order PID controller: Fictitious reference signal approach

This study proposes a one-shot data-driven tuning method for a fractional-order proportional-integral-derivative (FOPID) controller. The proposed method tunes the FOPID controller in the model-reference control formulation. A loss function is defined to evaluate the match between a given reference model and the closed-loop response while explicitly considering the closed-loop stability. A loss function value is based on the fictitious reference signal computed using the input/output data. Model matching is achieved via loss function minimization. The proposed method is simple and practical: it needs only one-shot input/output data of a plant (no plant model required), considers the bounded-input bounded-output stability of the closed-loop system from a bounded reference input to a bounded output, and automatically determines the appropriate parameter value via optimization. Numerical simulations show that the proposed approach facilitates good control performance, and destabilization can be avoided even if perfect model matching is unachievable.

Optimization of fractional-order PI-PID controllers for MIMO systems using artificial bee colony algorithm

Optimization of fractional-order PI-PID controllers for MIMO systems using artificial bee colony algorithm

Development and Experiment of Semi-Physical Simulation Platform for Space Manipulator.

To address the extended development cycle, high costs, and maintenance difficulties associated with existing microgravity simulation methods, this study has developed a semi-physical simulation platform for robotic arms tailored to different gravity environments and loading conditions. The platform represents difficult-to-model joints as physical objects, while the easily modeled components are simulated based on principles of similarity. In response to the strong coupling, nonlinearity, and excess force disturbance issues in the electric variable load loading system, a fractional-order linear active disturbance rejection control algorithm was employed. The controller parameters were tuned using an improved particle swarm algorithm with modified weight coefficients, and experimental results demonstrate that a fractional-order linear active disturbance rejection control improves response speed and disturbance rejection performance compared to linear sliding mode control. The study investigated the differences in the drive force of joint motors in space robotic arms under varying gravity environments and loading conditions. Experimental results indicate that load torque is the primary influencing factor on joint motor drive force, while radial force serves as a secondary influencing factor. Additionally, when the axis of the joint motor is perpendicular to the ground, it can, to some extent, simulate microgravity conditions on the ground.

Optimized coordinated control method with virtual inertia based on fractional impedance model for charging stations

Due to the EV (Electric Vehicles) charging stations are characterized by weak damping and low inertia, the EV with a high degree of uncertainty can easily have an impact on the stability of the charging station system. Therefore, this paper proposes an optimization control method to improve the system inertia effect based on the fractional order impedance model of the charging station. This paper presents a study on establishing a fractional impedance model for charging stations, using the deviation between theoretical impedance spectra and actual measurements as a criterion. The goal is to enhance system inertia and optimize the parameters of the fractional-order controller to improve the supporting capacity of the charging station system and enhance its dynamic response. Initially, considering the fractional characteristics of the EV load, a fractional impedance model of the charging station is established. The analysis demonstrates that the fractional-order capacitor provides inertia to the system, enhancing its inertia support capability. In addition, a virtual inertia control strategy based on fractional-order PID (FOPID) is designed. Finally, an improved particle swarm optimization algorithm is utilized to optimize the control parameters. Through experimental verification under different operating conditions, it has been demonstrated that the fractional-order control strategy can achieve a dynamic response time of approximately 0.025s and limit the voltage deviation within 5%. Furthermore, the rotational inertia can rapidly increase to the maximum value satisfying the objective function within 0.05s. The results indicate that this control method effectively suppresses the DC voltage and power oscillations in the distribution grid.

Optimal control and bifurcation analysis of a delayed fractional-order SIRS model with general incidence rate and delayed control

A fractional-order generalized SIRS model considering incubation period is established in this paper for the transmission of emerging pathogens. The corresponding Hopf bifurcation is discussed by selecting time delay as the bifurcation parameter. In order to control the occurrence of Hopf bifurcation and achieve better dynamic behaviors, a delayed feedback control is adopted to the model. Further, the delayed fractional-order optimal control problem (DFOCP) is proposed and discussed. The parameters of the proposed model are identified through the measurement data of coronavirus disease 2019 (COVID-19). Based on the results of parameter identification, the corresponding DFOCP with delayed control is numerically solved.

Prescribed finite-time stabilization of fuzzy neural networks with time-varying controller

This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller. First, the constraints of boundedness and differentiability on time delays are simultaneously relaxed, the Lipschitz condition for activation function is also relaxed. Second, different from the traditional Lyapunov function, two different time-varying Lyapunov functions are respectively constructed to achieve the exponential and prescribed finite-time stabilization. Significantly, the exponential convergence rate and the settling time are constants that can be given in advance and are not affected by system parameters and initial states. In addition, the time-varying controllers have good tolerance for disturbance caused by discontinuous functions and the disturbance is perfectly resolved and does not affect the control performance. Especially, the form of controllers is relatively simple and there is not necessary to design the fractional-order controllers for prescribed finite-time stabilization. Furthermore, the exponential and prescribed finite-time stabilization for FNNs without delay are respectively established via continuous time-varying state feedback control. Finally, examples show the effectiveness of the proposed control methods.

Current Harmonic Suppression in Maritime Vessel Rudder PMSM Drive System Based on Composite Fractional-Order PID Repetitive Controller

To address the control performance and harmonic suppression issues in maritime vessel rudder permanent magnet servo systems, a fractional-order PID controller was introduced into the existing improved repetitive control strategy. We used the Oustaloup approximation algorithm and particle swarm optimization for tuning the fractional-order PID controller. The optimized parameters substantially improved the control performance. By integrating the fractional-order PID controller with the improved repetitive controller, a composite fractional-order PID repetitive control strategy was formed. Finally, MATLAB/Simulink simulations were conducted to compare and verify the disturbance rejection and harmonic suppression capabilities of the improved control strategy. The results demonstrate its superior control performance, thereby increasing the practicality of the control system in dealing with various situations.

Optimization of a fractional-order interval type-2 fuzzy PID controller based on BBO for real-time applications

This paper addresses the development of a robust controller for a nonlinear system to minimize the tracking errors and reduce the effects of external noise and disturbances. To achieve this, the biogeography-based optimization (BBO) algorithm is utilized for an optimally robust interval type 2 fractional-order fuzzy proportional integral derivative controller (BB0-IT2FO-FPID) is proposed. The proposed method offers several advantages. Firstly, the proposed controller is optimized to achieve robustness and minimize tracking errors. Secondly, it effectively handles external noise and disturbances, making it suitable for real-world applications. Thirdly, the use of the BBO algorithm enhances the controller's performance by dynamically adjusting its parameters based on system requirements. The performance of the proposed controller is validated by applying it to control a robotic manipulator, which presents challenges due to its nonlinear characteristics and interacting multi-input multi-output (MIMO) dynamics. Additionally, a real-time evaluation of the proposed controller is conducted by applying it to the speed control of a direct current (DC) machine. The effectiveness of the proposed controller is verified through simulation and practical experiments and comparisons with other optimized controllers, namely FO fuzzy type 1 PID (T1FO-FPID) and FOPID. The simulation and practical results demonstrate the superior performance of the BBO-IT2FO-FPID controller in the presence of system uncertainties and different types of disturbances.

Leader-following consensus tracking control for fractional-order multi-motor systems via disturbance-observer

Abstract The leader-following consensus tracking control of fractional-order (FO) multi-motor systems (FOMMSs) in the presence of exogenous disturbances is investigated. It is widely recognized that FO models are better than integer-order (IO) ones for representing systems with memory effects. Therefore, studying the consensus tracking control of FOMMSs is essential. In this paper, a consensus tracking protocol is developed using a disturbance-observer and state feedback to deal with unknown exogenous disturbances. The closed-loop system stability is analyzed via Lyapunov and graph theory. Novel sufficient conditions for the stabilization of each motor are derived in the form of linear matrix inequalities. Simulation results illustrate the validity and efficacy of the proposed consensus protocol, namely its strong synchronization ability and robustness.

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

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

Frequency Loop-Shaping and IMC-Based Integer-Order Robust PID Controller Design for Fractional-Order Processes with Time-Delay

It is well accepted that fractional-order calculus yields a more accurate description of complex physical processes compared to integer-order one. So, fractional-order modelling is getting a good attention in the process industry. On the other hand, to meet design goals accurately, control designers prefer fractional-order controllers over integer-order ones due to the availability of more parameters. However, the design of such controllers are complex. More often, the design faces the challenge in real-time implementations, and the problem is circumvented by higher order approximations of fractional-order operators. In the presented work, three methods for integer-order Proportional–Integral–Derivative (PID) controller design are proposed based on Frequency Loop-Shaping (FLS) and Internal Model Control (IMC). To prove the efficacy of the presented control law, simulations are conducted and included along with a performance measure based on ISE (Integral of Square Error), ITAE (Integral of Time Absolute Error) and IAE (Integral of Absolute Error).