Fractional Order Adaptive Control Research Articles

State Space Model Reference Adaptive Control for a Class of Second-Degree Fractional Order Systems with Different Eigenvalues

This study proposes an adaptive control synthesis for a class of second-degree fractional order systems with different eigenvalues in the state-space domain. The proposed fractional order adaptive controller is a generalization of the MRAC controller for the class of scalar fractional order systems. In order to control the fractional order plant, an adaptive state space feedback controller is applied based on the error between the system output and a chosen reference model using a fractional adaptation law to make the fractional order plant track the fractional order reference model. We show that the resulting adaptive regulator is able to stabilize the fractional order second degree system with a satisfying performance. A simulation example illustrating these performance properties is provided along with a comparison with a fractional order sliding mode control (FOSMC) to demonstrate the superiority of the proposed control scheme.

Enhancing the Pitch-Rate Control Performance of an F-16 Aircraft Using Fractional-Order Direct-MRAC Adaptive Control

This study presents a comparative analysis of classical model reference adaptive control (IO-DMRAC) and its fractional-order counterpart (FO-DMRAC), which are applied to the pitch-rate control of an F-16 aircraft longitudinal model. The research demonstrates a significant enhancement in control performance with fractional-order adaptive control. Notably, the FO-DMRAC achieves lower performance indices such as the Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) and eliminates system output oscillations during transient periods. This study marks the pioneering application of FO-DMRAC in aircraft pitch-rate control within the literature. Through simulations on an F-16 short-period model with a relative degree of 1, the FO-DMRAC design is assessed under specific flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the study ensures the boundedness of all signals, including internal ones such as ω(t).

Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

Fractional-Order Model-Free Adaptive Control with High Order Estimation

This paper concerns an improved model-free adaptive fractional-order control with a high-order pseudo-partial derivative for uncertain discrete-time nonlinear systems. Firstly, a new equivalent model is obtained by employing the Grünwald–Letnikov (G-L) fractional-order difference of the input in a compact-form dynamic linearization. Then, the pseudo-partial derivative (PPD) is derived using a high-order estimation algorithm, which provides more PPD information than the previous time. A discrete-time model-free adaptive fractional-order controller is proposed, which utilizes more past input–output data information. The ultimate uniform boundedness of the tracking errors are demonstrated through formal analysis. Finally, the simulation results demonstrate the effectiveness of the proposed method.

An adaptive fractional order controller design: A realization for liquid level regulation in liquid level plant

In this paper, an adaptive FO − IλD1−λ controller design is proposed using a frequency domain approach. The proposed adaptive controller parameters are tuned based on the frequency domain specifications. To realize the velocity error constant for the proposed controller, Oustaloup Recursive Approximation (ORA) method is employed. The proposed controller is realized for liquid level regulation in the Liquid Level Plant (LLP). An identification technique is proposed to identify a linear adaptable parameter transfer function (LAPTF) model of LLP. The performance of the proposed controller is compared with the existing works. It is observed that the proposed controller outperforms the existing controllers in the literature.

Finite-time synchronization of fractional-order delayed memristive fuzzy neural networks

This paper deals with the finite-time synchronization (FTS) for a class of fractional-order memristive fuzzy neural networks (FOMFNNs) with leakage and transmission delays. Two types of discontinuous control schemes with leakage and transmission delays are designed: one is the state feedback control and the other is the fractional-order adaptive control. Based on differential inclusion theory and fractional-order differential inequalities, several new delay-independent algebraic conditions are derived to guarantee the FTS of drive-response FOMFNNs with leakage and transmission delays. Moreover, the estimation of the upper bound of the settling time for the FTS is given as well. Ultimately, two numerical examples with simulations are furnished to demonstrate the feasibility and availability of the theoretical results.

Decision support system for managing multi-echelon supply chain networks against disruptions using adaptive fractional order control algorithm

Managing highly evolving supply chains can be challenging, especially when vulnerable to disruptions and risks. This paper deals with a supply chain system’s dynamical analysis and efficient management strategy using a four-stage hyperchaotic Lorenz–Stenflo equation under disruptive events. Nonlinear behaviors are intensely investigated by eigenvalue and bifurcation analysis to identify supply chain risks. Then phase portraits are presented to illustrate the bullwhip effect negatively influencing the performance of various stages of multi-echelon supply chains. Resilient supply chains have been developed along with dynamic identification by realizing an adaptive fractional-order controller. An efficient control algorithm can optimize the management system while reducing potential risks by employing control theory in a decision support system. Performance criteria have been exploited to validate the control methodology. Using digital management algorithms, decision-makers might effectively cope with chaos suppression and synchronization problems, ensuring productivity and sustainability. Finally, the novel decision-making strategy can offer new insights into effectively managing digital supply chain networks against market volatility.

Synchronization analysis of fractional-order inertial-type neural networks with time delays

This paper is dedicated to the global Mittag-Leffler synchronization (GMLS) of fractional-order inertial-type neural networks (FOITNNs) with time delays. To begin with, based on the semigroup property of the Caputo fractional derivative (CFD), an appropriate variable substitution is chosen to transform the original fractional-order inertial system into a traditional fractional-order system. Secondly, two types of discontinuous control schemes with delays and only a control input are proposed: one is the state feedback control and the other is the fractional-order adaptive control. On the basis of Lyapunov stability theory and fractional-order differential inequalities, some new sufficient criteria for the GMLS of two FOITNNs are established. Furthermore, the control gains here can be selected more widely, which makes the results more applicative and less conservative. Finally, two numerical examples validate the efficacy of the obtained results.

Fractional order robust adaptive control design for actuator failure compensation in dual ball-beam system

This paper is to proposes a fractional order adaptive control scheme design for actuator failure compensation in order to balance of a ball-beam system with redundant actuators. The proposed controller is based on a fractional order sliding surface from which an adaptive actuator failure compensation control scheme is obtained. In order to control the dual ball-beam system with redundant motors, a linearized model is derived, which is subjected to actuator failures. A set of numerical simulation tests representing few selected types of actuator failures scenarios are carried out to assess the output tracking performance of the proposed controller design when dealing with such failures

Design and Experimental Results of an Adaptive Fractional-Order Controller for a Quadrotor

The use of multi-copter systems started to grow over the last years in various applications. The designed solutions require high stability and maneuverability. To fulfill these specifications, a robust control strategy must be designed and integrated. Focusing on this challenge, this research proposes an adaptive control design applied to a physical model of a quadrotor prototype. The proposed adaptive structure guarantees robustness, control flexibility, and stability to the whole process. The prototype components, structure, and laboratory testing equipment that are used to run the experiments are presented in this paper. The study is focused on the performance comparison of a classical PID controller and a fractional-order controller, which are both integrated into the adaptive scheme. Fractional-order controllers are preferred due to their recognized ability to increase the robustness of the overall closed-loop system. Furthermore, this work covers the design and the tuning method of this control approach. The research concludes with the actual results obtained for this comparative study that highlights the advantages of the fractional-order controller.

Robust control of congestion in computer networks: An adaptive fractional-order approach

In this study, the congestion problem of computer networks is solved by introducing an adaptive fractional-order controller. The controller is designed to enhance the efficiency of nonlinear transmission control protocol/active queue management (TCP/AQM) in these networks. External disturbances can perturb the data transmission. Moreover, factors such as undetermined link capacity can affect the congestion control problem. Hence, the proposed controller should guarantee robustness against disturbances and uncertainties. Besides, small elapsed time to reach the desired queue length as well as convergence of tracking error to zero are essential in queue management. These objectives are fulfilled by designing a fractional-order controller. High tracking capability and robustness make the controller an effective method for TCP/AQM networks. Furthermore, asymptotic stability of the network is precisely proven based on the fractional-order Lyapunov lemma. A variety of simulations are performed to examine capability of the proposed method confronting disturbances and uncertainties while providing a fast and stable response with zero tracking error. The results are also compared with the results of two recently developed control approaches for congestion problem, using performance indices, which confirm the efficiency and superiority of the introduced controller.

Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems

• The global Mittag–Leffler ultimate bounds and synchronization for fractional order plasma chaotic systems are studied. • Some new ellipsoid and cylindrical domains as well as a rotatory paraboloid of the bounds are derived via generalized Lyapunov function theory. • Linear feedback control tactics with two inputs or one input as well as fractional order adaptive control with one input are proposed. • The boundaries and feedback gain constants are easier to be calculated and the controller structures are simpler. This paper focuses on the Mittag–Leffler ultimate bounds (MLUBs) and synchronization of fractional-order plasma chaotic systems (FOPCSs). For one thing, by choosing some appropriate generalized Lyapunov functions and combining fractional-order differential inequalities, some new estimates on the 3D ellipsoid and cylindrical domains as well as a rotatory paraboloid of the bounds for the FOPCS are acquired according to system parameters, which perfect the previous studies and may infer a few new estimates. For another, linear feedback control tactics with two inputs or one input as well as fractional-order adaptive control with one input and a single variable are presented to realize the synchronization of two FOPCSs. Several new sufficient conditions for synchronization are analytically obtained by using inequality methods. The boundaries and feedback gain constants are easier to be calculated and the controller structures are simpler. Finally, numerical simulations are shown to confirm the correctness of the presented synchronization schemes.

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.

Fractional adaptive SMC fault tolerant control against actuator failures for wing rock supervision

This article presents a new fractional order adaptive control scheme design based on sliding mode configuration for actuator failure compensation applied to a wing rock system with redundant actuators. The main objective of this work is to establish an adaptive control law that compensates faulty actuators by taking into account actuator redundancy and introducing fractional calculus. First, a non-integer sliding mode surface is defined. Next, an adaptive scheme is derived from the ideal control law to accommodate for the occurring failures during operation. Then, the stability analysis of the closed loop system is performed using the Lyapunov theory under certain assumptions on the system and the failures. Finally, simulations were carried out on a wing rock system subjected to various actuator failures scenarios in order to illustrate the effectiveness of the proposed control law.

A 6DOF Virtual Environment Space Docking Operation with Human Supervision

In this work, we present a synchronous co-simulation of a 6DOF (six degree of freedom) ball and plate platform and its 3D computer model. The co-simulation in the virtual environment is intended to mimic the rendezvous between a cargo vehicle such as the Falcon 9 from SpaceX and the ISS (International Space Station). The visual feedback sensing of the position of the 6DOF platform is implemented using a Kinect RGB-D device. The human in the loop acts as supervisory control for initiating the docking mechanism. This paper delivers an adaptive fractional order control solution which is easily tunable, implementable and validated on a laboratory benchmark. The results indicate that fractional order control can tackle large variability in the system dynamics and deliver specified performance at all times.

A new fractional-order developed type-2 fuzzy control for a class of nonlinear systems

In this paper, a novel fractional-order adaptive controller is presented for a class of nonlinear systems with unknown dynamics. The dynamics of the system is considered to be fully unknown. The multi-layer perceptron (MLP) neural network using restricted Boltzmann machine (RBMs) is employed for online dynamic identification. A deep learning method on the basis of contrastive divergence (CD) algorithm combined with the extended Kalman filter (EKF) is proposed for online optimisation. The proposed controller has two parts. The first part is a simple error feedback controller and the second one is the suggested DT2-FLS. The parameters of DT2-FLS are tuned such that a cost function of tracking error to be minimised and the closed-loop system to be stable. For the best knowledge of the authors, for the first time the tuning rules for the membership function and rule parameters of DT2-FLS are derived by error feedback learning method. The closed-loop stability is demonstrated with Lyapunov method and the well performance of the schemed controller is shown by applying on the induction motor and brushless DC motors. In addition to unknown dynamics, some disturbances are also considered such as abruptly changes in load torque and time-varying rotor resistance. Furthermore, the performance of the suggested scheme is compared with some popular controllers and FLSs.

Adaptive fractional order controller with Smith predictor-based propofol dosing in intravenous anaesthesia automation

Adaptive fractional order controller with Smith predictor-based propofol dosing in intravenous anaesthesia automation

Using the fractional order calculus in the combination of the MIT and Lyapunov stability method

AbstractThe main idea of the current paper consists in introducing the fractional order calculus in a control system. To control the system, an adaptive control technique with reference model is used. The fractional order models for the plant and reference model are obtained. To achieve the performances imposed by the fractional order reference model, a fractional order adaptive control law is proposed, which is a combination of two methods (MIT and Lyapunov stability). The original contribution in this paper is the use of fractional order calculus in the combined MIT and Lyapunov stability method and showing the dynamic behavior of the system. Several simulations are used to emphasize the effectiveness and benefits of the proposed method.

Observer-based adaptive fractional-order control of flexible-joint robots using the Fourier series expansion: theory and experiment

In this paper, fractional-order observer/controller design for flexible-joint robots is developed. In order to eliminate the need for obtaining the regressor matrix, the Fourier series expansion is applied for uncertainty estimation. Voltage saturation nonlinearities are compensated in the control law; hence, knowledge of the actuator/manipulator dynamics model is not required in the proposed method. Uniformly ultimately boundedness of observer estimation error and joint position tracking error are guaranteed through Lyapunov stability concept. The case study is a single-link flexible-joint robot actuated by permanent magnet DC motors. Experimental results are presented to emphasize the successful practical implementation of the proposed algorithm. Based on the experimental results, the proposed controller considerably outperforms some previous related works using various criteria.

Direct fractional order MRAC adaptive control design for a class of fractional order commensurate linear systems

In this paper, we introduce a direct fractional order adaptive control design based on model reference adaptive control (MRAC) structure for a class of commensurate fractional order linear systems with an arbitrary relative degree, and whose parameters are unknown. By generalising the application of standard direct MRAC strategy to plants described by fractional order models, we develop a fractional adaptive control scheme (FOMRAC) based on the output feedback. We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory. The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem. Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.