Fractional Gradient Descent RBFNN for Active Fault-Tolerant Control of Plant Protection UAVs

With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.

An Adaptive Neuro-Fuzzy Inference System to Improve Fractional Order Controller Performance

The design and analysis of a fractional order proportional integral deri-vate(FOPID)controller integrated with an adaptive neuro-fuzzy inference system(ANFIS)is proposed in this study.Afirst order plus delay time plant model has been used to validate the ANFIS combined FOPID control scheme.In the pro-posed adaptive control structure,the intelligent ANFIS was designed such that it will dynamically adjust the fractional order factors(λandµ)of the FOPID(also known as PIλDµ)controller to achieve better control performance.When the plant experiences uncertainties like external load disturbances or sudden changes in the input parameters,the stability and robustness of the system can be achieved effec-tively with the proposed control scheme.Also,a modified structure of the FOPID controller has been used in the present system to enhance the dynamic perfor-mance of the controller.An extensive MATLAB software simulation study was made to verify the usefulness of the proposed control scheme.The study has been carried out under different operating conditions such as external disturbances and sudden changes in input parameters.The results obtained using the ANFIS-FOPID control scheme are also compared to the classical fractional order PIλDµand conventional PID control schemes to validate the advantages of the control-lers.The simulation results confirm the effectiveness of the ANFIS combined FOPID controller for the chosen plant model.Also,the proposed control scheme outperformed traditional control methods in various performance metrics such as rise time,settling time and error criteria.

A Novel ANFIS Based SMC with Fractional Order PID Controller

Interacting The highest storage capacity of a circular tank makes it pop-ular in process industries.Because of the varying surface area of the cross-sec-tions of the tank,this two-tank level system has nonlinear characteristics.Controlling theflow rate of liquid is one of the most difficult challenges in the production process.This proposed effort is critical in preventing time delays and errors by managing thefluid level.Several scholars have explored and explored ways to reduce the problem of nonlinearity,but their techniques have not yielded better results.Different types of controllers with various techniques are implemented by the proposed system.Sliding Mode Controller(SMC)with Fractional Order PID Controller based on Intelligent Adaptive Neuro-Fuzzy Infer-ence System(ANFIS)is a novel technique for liquid level regulation in an inter-connected spherical tank system to avoid interferences and achieve better performance in comparison of rise time,settling time,and overshoot decrease.Evaluating the simulated results acquired by the controller yields the efficiency of the proposed system.The simulated results were produced using MATLAB 2018 and the FOMCON toolbox.Finally,the performance of the conventional controller(FOPID,PID-SMC)and proposed ANFIS based SMC-FOPID control-lers are compared and analyzed the performance indices.

ADRC FRACTIONAL ORDER PID CONTROLLER DESIGN OF HYPERSONIC FLIGHT VEHICLE

Active disturbance rejection controller（ADRC）uses tracking-differentiator（TD）to solve the contradiction between the overshoot and the rapid nature.Fractional order proportion integral derivative（PID）controller improves the control quality and expands the stable region of the system parameters.ADRC fractional order（ADRFO）PID controller is designed by combining ADRC with the fractional order PID and applied to reentry attitude control of hypersonic vehicle.Simulation results show that ADRFO PID controller has better control effect and greater stable region for the strong nonlinear model of hypersonic flight vehicle under the influence of external disturbance,and has stronger robustness against the perturbation in system parameters.

A Fractional Order Fast Repetitive Control Paradigm of Vienna Rectifier for Power Quality Improvement

Due to attractive features,including high efficiency,low device stress,and ability to boost voltage,a Vienna rectifier is commonly employed as a battery charger in an electric vehicle(EV).However,the 6k±1 harmonics in the acside current of the Vienna rectifier deteriorate theTHDof the ac current,thus lowering the power factor.Therefore,the current closed-loop for suppressing 6k±1 harmonics is essential tomeet the desired total harmonic distortion(THD).Fast repetitive control(FRC)is generally adopted;however,the deviation of power grid frequency causes delay link in the six frequency fast repetitive control to become non-integer and the tracking performance to deteriorate.This paper presents the detailed parameter design and calculation of fractional order fast repetitive controller(FOFRC)for the non-integer delay link.The finite polynomial approximates the non-integer delay link through the Lagrange interpolation method.By comparing the frequency characteristics of traditional repetitive control,the effectiveness of the FOFRC strategy is verified.Finally,simulation and experiment validate the steadystate performance and harmonics suppression ability of FOFRC.

An Artificial Approach for the Fractional Order Rape and Its Control Model

The current investigations provide the solutions of the nonlinear fractional order mathematical rape and its controlmodel using the strength of artificial neural networks(ANNs)along with the Levenberg-Marquardt backpropagation approach(LMBA),i.e.,artificial neural networks-Levenberg-Marquardt backpropagation approach(ANNs-LMBA).The fractional order investigations have been presented to find more realistic results of the mathematical form of the rape and its control model.The differential mathematical form of the nonlinear fractional order mathematical rape and its control model has six classes:susceptible native girls,infected immature girls,susceptible knowledgeable girls,infected knowledgeable girls,susceptible rapist population and infective rapist population.The rape and its control differential system using three different fractional order values is authenticated to perform the correctness of ANNs-LMBA.The data is used to present the rape and its control differential system is designated as 70%for training,14%for authorization and 16%for testing.The obtained performances of the ANNs-LMBA are compared with the dataset of the Adams-Bashforth-Moulton scheme.To substantiate the consistency,aptitude,validity,exactness,and capability of the LMBA neural networks,the obtained numerical values are provided using the state transitions(STs),correlation,regression,mean square error(MSE)and error histograms(EHs).

Digital implementation of fractional order PID controller and its application

A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.

Disturbance Observer Based Speed Control of PMSM Using Fractional Order PI Controller

In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM.All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer(NLDO) to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB/SIMULINK and results are presented.

Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System

The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.

Fractional Order [Proportional Integral] Controllers Parameters Algorithm Based on the Vector Method

A new calculation method of fractional order [proportional integral ]( FO [PI ]) controller parameters is proposed. And the systematic design schemes of fractional order [proportional integral ]( FO[PI]) controllers based on vector method are discussed in detail. The FO[PI]controller parameters algorithm based on the vector method can be programmed in MATLAB. According to MATLAB programs of the FO[PI]controller parameters algorithm,the FO[PI] controllers are designed following the different phase margins,different gain crossover frequency and different plants,respectively. From the simulation results,the calculated parameters based on MATLAB program is unique and the designed FO[PI] controllers work efficiently.

Design of Smith Predictor Based Fractional Controller for Higher Order Time Delay Process

Normally all real world process in a process industry will have time delay.For those processes with time delays,obtaining satisfactory closed loop performances becomes very difficult.In this work,three interacting cylindrical tank process is considered for study and the objective of the work is to compensate for time delays using smith predictor structure and to maintain the level in the third tank.Input/Output data is generated for the three interacting tank process.It is approximated as Integer First Order Plus Dead Time system(IFOPDT)and Fractional First Order Plus Dead Time system(FFOPDT).Smith predictor based fractional order Proportional Integral controller and Integer order Proportional Integral controller is designed for the IFOPDT and FFOPDT model using frequency response technique and their closed loop performance indices are compared and tabulated.The servo and regulatory responses are simulated using Matlab/Simulink.

Control of fractional chaotic and hyperchaotic systems based on a fractional order controller

We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate. The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method.

Analysis of the effect on control systems of order variation for fractional-orderPI~λD~μcontrollers

This paper is concerned with fractional-order PI~λD~μcontrollers. The definitions and properties of fractional calculus are introduced. The mathematical descriptions of a fractional-order controller and fractional-order control systems are outlined. The effects on control systems of order variation for fractional-order PI~λD~μ controllers are investigated by qualitative analysis and simulation. The conclusions and simulation examples are given. The results show the fractional-order PI~λD~μ controller is not sensitive to variation of its order.

Using Fractional-order PI^λD^μ Controller for Control of Aerodynamic Missile

A new type of PID controller is introduced and some properties are given. The novelty of the proposed controller consists in the extension of derivation and integration order from integer to non-integer order. The PIλDμ controller generally has three advantages when compared to the integerl-order controller: the first is that it has more degrees of freedom in the model; the second is that it has a memory in model,the memory insure the history and its impact to present and future,the third is it ensures the stability of missile. This approach provides a more flexible tuning strategy and therefore an easier achieving of control requirements. Flight dynamic model of an aerodynamic missile is taken into account in implementing the PIλDμ controller. Simulation results show that the PIλDμ controller is not sensitive to the changes of control parameters and the system parameters. Also,the controller has more flexible structure and stronger robustness.

Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 2~3 factorial experimental design for a fractional order proportional integral and derivative controller(FOPID), integer order proportional integral and derivative controller(IOPID)and the Skogestad internal model control controller(SIMC). The factors assumed in experiment are the presence of random noise,external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.

Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.

On Time-Constant Robust Tuning of Fractional Order [Proportional Derivative] Controllers

This paper deals with analyzing a newly introduced method for tuning of fractional order [proportional derivative](FO[PD]) controllers to be used in motion control. By using this tuning method, not only the phase margin and gain crossover frequency are adjustable, but also robustness to variations in the plant time-constant is guaranteed. Conditions on the values of control specifications(desired phase margin and gain crossover frequency) for solution existence in this tuning method are found. Also, the number of solutions is analytically determined in this study. Moreover, experimental verifications are presented to indicate the applicability of the obtained results.

Improving the Control Energy in Model Reference Adaptive Controllers Using Fractional Adaptive Laws

This paper presents the analysis of the control energy consumed in model reference adaptive control(MRAC)schemes using fractional adaptive laws, through simulation studies. The analysis is focused on the energy spent in the control signal represented by means of the integral of the squared control input(ISI). Also, the behavior of the integral of the squared control error(ISE) is included in the analysis.The orders of the adaptive laws were selected by particle swarm optimization(PSO), using an objective function including the ISI and the ISE, with different weighting factors. The results show that, when ISI index is taken into account in the optimization process to determine the orders of adaptive laws,the resulting values are fractional, indicating that control energy of the scheme might be better managed if fractional adaptive laws are used.

Fractional Order Proportional Integral Derivative Controller Design and Simulation for Bioengineering Systems

This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order mathematical model of bioengineering systems. The main contents include the design of FOPID controller and the simulation for bioengineering systems. The simulation results show that the tuning method of fractional order system based on the FOPID controller outperforms the fractional order system based on Fractional Order Proportional Integral( FOPI) controller. As it can enhance control character and improve the robustness of the system.