Fractional-order Control Method Research Articles

Fractional-Order Control Method Based on Twin-Delayed Deep Deterministic Policy Gradient Algorithm

In this paper, a fractional-order control method based on the twin-delayed deep deterministic policy gradient (TD3) algorithm in reinforcement learning is proposed. A fractional-order disturbance observer is designed to estimate the disturbances, and the radial basis function network is selected to approximate system uncertainties in the system. Then, a fractional-order sliding-mode controller is constructed to control the system, and the parameters of the controller are tuned using the TD3 algorithm, which can optimize the control effect. The results show that the fractional-order control method based on the TD3 algorithm can not only improve the closed-loop system performance under different operating conditions but also enhance the signal tracking capability.

Enhancing frequency stability in diverse power systems with conventional and renewable energy sources based on an innovative LFC and controlled energy storage integration

The rapid advancement of renewable energy sources (RESs) has led to a decrease in system inertia and an exacerbation of the instability issue. Hence, this study puts forward an approach to bolster the stability of the power grid amidst the presence of RESs and disturbances in load conditions. The strategy utilizes controlled energy storage systems, including plug-in electric vehicles and fuel cell systems, along with a secondary controller (SC). To improve the strategy's performance, novel controllers and an enhanced optimization technique are employed. The proposed controller combines proportional-integral-derivative (PID) and fractional order control methods, resulting in a new arrangement. The parameters of the controller are tuned using an improved optimization technique called an Enhanced Runge Kutta Optimizer. The effectiveness of the proposed algorithm is demonstrated through a performance comparison with conventional optimizers, using well-established mathematical equations. Additionally, the proposed controller's effectiveness is verified by comparing its performance with other controller arrangements, such as PID, combining TD-TI, and cascaded (1 + PD)-PID controllers. The performance of the system is enhanced by 66 % more with the proposed controller in SC compared to the (1 + PD)-PID controller, which is regarded as the most optimal among the controllers examined in this study. Additionally, the system's performance is improved by 44 % when the proposed strategy is implemented, as compared to the system's performance without the proposed strategy. Totally, the effectiveness of the proposed strategy is validated across various scenarios, including high penetration of RESs, significant load fluctuations, and system non-linearity.

Non-integer Order Control Scheme for Pressurized Water Reactor Core Power

Tracking load changes in a pressurized water reactor (PWR) with the help of an efficient core power control scheme in a nuclear power station is very important. The reason is that it is challenging to maintain a stable core power according to the reference value within an acceptable tolerance for the safety of PWR. To overcome the uncertainties, a non-integer-based fractional order control method is demonstrated to control the core power of PWR. The available dynamic model of the reactor core is used in this analysis. Core power is controlled using a modified state feedback approach with a non-integer integral scheme through two different approximations, CRONE (Commande Robuste d'Ordre Non Entier, meaning Non-integer order Robust Control) and FOMCON (non-integer order modeling and control). Simulation results are produced using MATLAB® program. Both non-integer results are compared with an integer order PI (Proportional Integral) algorithm to justify the effectiveness of the proposed scheme. Sate-space model Core power control Non-integer control Pressurized water reactor PI controller CRONE FOMCON.

Robust Synchronization Control of Uncertain Fractional-Order Chaotic Systems via Disturbance Observer

This paper studies the synchronization of two different fractional-order chaotic systems through the fractional-order control method, which can ensure that the synchronization error converges to a sufficiently small compact set. Afterwards, the disturbance observer of the synchronization control scheme based on adaptive parameters is designed to predict unknown disturbances. The Lyapunov function method is used to verify the appropriateness of the disturbance observer design and the convergence of the synchronization error, and then the feasibility of the control scheme is obtained. Finally, our simulation studies verify and clarify the proposed method.

Variable fractional order sliding mode control for seismic vibration suppression of building structure

Constant fractional order vibration control strategy has been one of research hotspots in recent decades. However, the variable fractional order control method is seldom concerned up to now. In this article, a novel variable fractional order sliding mode control (VOSMC) method is proposed to suppress the responses of building structure caused by seismic excitations, including El Centro, Hachinohe, Northridge, and Kobe earthquakes. Based on the proposed variable fractional order sliding mode surface, the control law of VOSMC is presented. The global asymptotic stability of the control system is analyzed and proved by utilizing variable fractional order Lyapunov stability theorem. Besides, the corresponding constant fractional order sliding mode control (COSMC) method is also given. The control effects of VOSMC and COSMC methods are discussed by four performance indices. Finally, the utilizability and reasonability of the proposed control method is verified by using two examples (include two-story and five-story shear buildings). Compared with the COSMC method, the proposed variable fractional order controller not only has a lesser control output, but also has a higher utilization of the output, which is conducive to energy saving.

Fractional-order adaptive fault-tolerant control for a class of general nonlinear systems

This paper proposes a series of fractional-order control methods (FOCMs) based on fractional calculus (FC) for a class of general nonlinear systems. In order to deal with the nonlinearities and uncertainties caused by both external and internal factors, the designed control schemes are adaptive, robust, fault-tolerant and do not involve detailed information of the system model. Besides, FC is combined to improve the control performance, especially in higher control accuracy, better anti-interference ability and stronger robustness. For a comprehensive consideration of the practical systems, three different actuator conditions are separately discussed, and the FOCMs are established aiming at these three different situations, respectively, and proved by theoretical analysis. The inverted pendulum system is adopted as simulation object, and the fractional-order schemes are verified and compared with integer-order controller and traditional PID controller. Simulation results make it clear that the proposed FOCMs are superior to other two schemes in control precision, robustness and anti-interference ability.

Recurrent neural network fractional-order sliding mode control of dynamic systems

In this study, a fractional-order sliding mode control (FSMC) scheme using a recurrent neural network (RNN) approximator is introduced to achieve better control performance for a class of dynamic systems. The proposed recurrent neural network fractional-order sliding mode control (RNNFSMC) scheme combines a fractional-order control method and a RNN structure. The primary objective of the proposed RNNFSMC scheme is to construct a fractional-order sliding mode controller. The RNN estimator is applied to approximate the unknown nonlinear part online. In the case study, the proposed RNNFSMC scheme is used for a dynamic model of an active power filter to realize the current harmonic compensation control. Simulation experiment proves that the proposed scheme is effective and robust and has a good tracking effect for dynamic system.

RBFNN-Based Fractional-Order Control of High-Speed Train With Uncertain Model and Actuator Failures

In this paper, the position/velocity tracking control problem of high speed train(HST) is investigated with considering some inevitable factors such as the input nonlinearity due to different notches of traction/braking forces, aerodynamic resistance, in-train force, external disturbance and unknown actuator failures, which lead to the uncertainty and nonlinearity of HST. Aiming at the system characteristics of HST, a set of integer-order control methods based on the excellent approximation ability of Radial Basis Function Neural Network(RBFNN) are established firstly, and motivated by them, a kind of RBFNN-based fractional-order control methods are proposed by utilizing the genetic attenuation properties of fractional calculus(FC) in order to improve the control performance in the work. It should be pointed out that all the developed methods are able to deal with uncertainties and nonlinearities as well as actuator failures without the need for any “trail and error” process. The feasibility and effectiveness of the proposed control methods are verified by Lyapunov theoretical analysis and numerical simulation studies. Besides, the control performance of integer-order control system and fractional-order control system is compared and analyzed, and the results show that the fractional-order control system is superior.

Performance comparison of wind turbine based doubly fed induction generator system using fault tolerant fractional and integer order controllers

Abstract A typical grid connected wind energy system is always associated with the nonlinear dynamics, uncertainties and external disturbances. Moreover as per the adopted grid codes and in the occurrence of specific faults the wind energy system should remain connected to the grid for a defined time period. Keeping in view all the effects this article proposes a high performance fault tolerant fractional order control system for the rotor side converter of a doubly fed induction generator (DFIG). The base line controller is formulated using novel fractional order sliding manifolds and the stability of the closed loop is ensured using fractional order Lyapunov theorem. As a case study the faults are introduced in the rotor current sensors and a model based fault tolerant rotor current estimation algorithm is proposed which is based on the stator measured currents and the voltages. Numerical results are presented to show the superiority of the proposed base line fractional order control method over the classical sliding mode control system in normal operating conditions. Finally the proposed algorithm is tested under the rotor current sensors fault and the results under faulty conditions are compared to that without faults.

Prescribed performance synchronization for fractional-order chaotic systems**Project supported by the National Natural Science Foundation of China (Grant Nos. 11401243 and 61403157), the Fundamental Research Funds for the Central Universities of China (Grant No. GK201504002), and the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China (Grant No. KJ2015A256).

In this paper the synchronization for two different fractional-order chaotic systems, capable of guaranteeing synchronization error with prescribed performance, is investigated by means of the fractional-order control method. By prescribed performance synchronization we mean that the synchronization error converges to zero asymptotically, with convergence rate being no less than a certain prescribed function. A fractional-order synchronization controller and an adaptive fractional-order synchronization controller, which can guarantee the prescribed performance of the synchronization error, are proposed for fractional-order chaotic systems with and without disturbances, respectively. Finally, our simulation studies verify and clarify the proposed method.

The Fractional-Order Control Method of Dynamic Elastoplastic Responses of Benchmark Buildings

The elastoplastic phenomenon of the structures will be advent under the action of the strong earthquakes, the presented research on the vibration control of the ones is chiefly concentrated on fuzzy and neuro-controller with the expense of bigger energy. In the paper, the 3-storey benchmark building is used as research object, the control strategy of vibration system with fractional-order is studied. The control method based on acceleration responses output is emphatically concerned as it is usually adopted in most actual application of active vibration control techniques. The concrete courses include the following three steps: the integer-order approximation of fraction-order, the transfer function reduction in frequency-domain which base on Pade approximation, the controller design and simulation. In the last, an example is used to show the feasibility of proposed method.

THE FRACTIONAL ORDER MODIFIED CHAOTIC n-SCROLL CHUA CIRCUIT AND FRACTIONAL CONTROL

A new fractional order chaotic n-scroll modified Chua circuit is introduced. It can generate n-scroll with a total order less than three. The equilibrium points are classified into two types according to the characteristics of the eigenvalues of the Jacobian matrix at the equilibrium points. To overcome some disadvantages of the traditional fractional order controller, a new fractional order control method is developed for stabilizing the system to any expected equilibrium point. Numerical examples are provided to verify the effectiveness of the proposed scheme.

Low Earth-orbit satellite attitude stabilization with fractional regulators

Fractional Order Control methods were applied to a three-axis reaction wheels satellite attitude control system. To show the advantages of this method, a comparative study between a Linear Quadratic Regulator and a Fractional Order Control was established through two principal fractional control laws. The aim is to establish an efficient control law which satisfies a given specification and maintains sufficient stability and accuracy even under the strong effects of intrinsic parameters uncertainties, and also external perturbations.