Fractional Order Controller Parameters Research Articles

Pitch angle control of wind turbines using model-free auto-tuned fractional order proportional derivative ATFOPD controller

The nonlinear dynamics of wind power plants, in addition to uncertainties such as unknown nonlinear disturbances and parameter variations make the design of a robust controller a difficult task. This paper proposes a robust fractional-order controller for the pitch angle control of a variable-speed wind turbine system. An auto-tuned fractional order proportional-derivative controller ATFOPD is designed taking the objectives of reducing pitch actuator fatigue, limiting output mechanical power and speed at their rated values above the rated wind speed. The phase, phase slope and modulus of the pitch actuator process at the fixed gain crossover frequency are needed in order to tune the fractional order controller parameters. These values are usually derived using a mathematical model of the system, such as a transfer function. A model-free auto-tuning technique that can calculate the controller's parameters from measured variables is used in this work in order to design a robust FOPD controller. Simulation results of the ATFOPD controlled system are compared to integer order proportional-derivative IOPD and IOPID controllers, which show that the ATFOPD controller is more effective than the other controllers and its robustness is verified in the presence of disturbances in addition to system parameters and wind speed variations.

A new fractional order controller tuning method based on Bode’s ideal transfer function

A new tuning method for Fractional Order Controllers (FOC) based on Bode’s ideal transfer function as a reference model is proposed in this paper. The proposed fractional order controller parameters are obtained by a simple tuning technique in two steps. In the first step, the open loop reference fractional integrator is designed according to the desired performances, and then approximated by a rational transfer function using Charef’s or Oustaloup’s approximation method. In the second step, a standard pole placement technique is used to align each pole of the plant transfer function with the nearest one of the Rational Function Approximation (RFA). The FOC transfer function is then obtained by gathering the remained poles and zeros of the RFA. The most innovative character of the proposed method is its simplicity and its remarkable performances in terms of robustness towards the variation of the static gain. Simulation of some illustrative examples confirms and validates the proposed method.

Devising a procedure for the synthesis of electromechanical systems with cascade-enabled fractional-order controllers and their study

An approach to the synthesis of automatic control circuits has been proposed, based on a fractional characteristic polynomial, which makes it possible to ensure the desired quality of a transition process under condition for implementing a certain structure of the fractional controller, which depends on the transfer function of a control object. The use of fractional desirable forms extends the range of possible settings of fractional-order controllers in the synthesis of circuits for electrical-mechanical systems, ensures better quality of transients compared to the full-order controllers, and thereby improves the efficiency of synthesized systems. Based on the obtained results of research, it becomes possible to recommend, in order to adjust the circuits for electromechanical systems, using the proposed fractional desirable forms that could meet the desired requirements to the systems of control over electromechanical systems. Construction of electromechanical systems on the principle of control with sequential correction has a significant advantage over other systems, owing to the simplicity of setting each contour, as well as a possibility to implement control coordinate constraints. A procedure for the structural-parametric synthesis of fractional-order controllers has been devised, on condition of their cascading switching in multi-circuit electromechanical systems; the synthesis algorithm of fractional-order controllers for appropriate control circuits has been given. We have synthesized an electromechanical system with cascade switching of controllers by applying the improved method of the generalized characteristic polynomial to choose the structure and parameters of fractional-order controllers and applying the desired form of fractional order. A two-circuit system of subordinate regulation has been considered as an example, in which a control object is the electric drive "thyristor transducer (converter) – engine (motor)". The influence of the synthesized fractional-order controllers on dynamic properties of the electromechanical system "thyristor transducer – engine" has been examined. Our study has shown a possibility to implement the cascading activated controllers for the electromechanical systems where the contours with the transfer full- and fractional-order functions are combined, as well as for systems with fractional-order contours only

Input dependent Nyquist plot for limit cycle prediction and its suppression using fractional order controllers

In practical systems having separable hard nonlinearities, sustained oscillation is detected at the steady state response due to the presence of stable limit cycles. An optimization problem is proposed to tune the fractional order controller parameters for system with multiple-nonlinearity to suppress the limit cycle magnitude in addition to meet the desired closed loop specifications. To extend the applicability of the existing Nyquist plot for predicting this limit cycle, an input dependent Nyquist plot is proposed in this paper. A servo system with backlash and relay nonlinearities is considered as a case study for limit cycle prediction with obtained fractional order controllers using an input dependent Nyquist plot. The predicted limit cycle information is compared with optimization results, input dependent root locus and are validated through closed loop simulations. Further, the robustness of the designed controllers are tested under system parameter uncertainty, disturbance and measurement noise conditions.

An interactive design strategy for fractional order PI controllers in LabVIEW

This paper presents an interactive design for fractional order PI (FOPI) controller based on inverse Fourier transform method (IFTM) in accordance with stability region of a closed-loop control system in LabVIEW, which is a powerful graphical program. Stability boundary locus (SBL) method is used to obtain the stability region including all stabilising FOPI controller parameters in (Kp, Ki) plane. The time response of the closed-loop control system with FOPI controller is then obtained by IFTM using the stabilising controller parameters selected from stability region. Changing the selected fractional order controller parameters in stability region, users can observe the step response of the system interactively.

An interactive design strategy for fractional order PI controllers in LabVIEW

This paper presents an interactive design for fractional order PI (FOPI) controller based on inverse Fourier transform method (IFTM) in accordance with stability region of a closed-loop control system in LabVIEW, which is a powerful graphical program. Stability boundary locus (SBL) method is used to obtain the stability region including all stabilising FOPI controller parameters in (Kp, Ki) plane. The time response of the closed-loop control system with FOPI controller is then obtained by IFTM using the stabilising controller parameters selected from stability region. Changing the selected fractional order controller parameters in stability region, users can observe the step response of the system interactively.

Optimization of Fractional Order PID Controller Using Grey Wolf Optimizer

This paper presents a novel evolutionary technique to optimize the parameters of fractional order controller for controlling two classes of systems: time-delay and higher-order system. The evolutionary technique known as grey wolf optimizer is used to tune both integer and fractional order controllers. The grey wolf optimizer searches for the optimum solution in the following manner, i.e. encircling, hunting, attacking the prey and finally search for the new prey consecutively if exists. To certify these various procedure, the performance indices like integral square error, integral absolute error, integral time-weighted square error, and integral time-weighted absolute error are minimized for the authenticity. Moreover, the proposed algorithm is validated and compared with well-established techniques.

Design and implementation of fractional order PI<SUP align="right">λ</SUP>D<SUP align="right">μ</SUP> controller for thermal process using stability boundary locus

Fractional order control is a new technique that uses fractional order calculus in the control applications. By introducing the fractional terms in basic control equations, we can achieve more satisfactory results with high precision in the system response, like less overshoot, reduced settling time, less steady state error, etc. It gives better control over the operating region with the help of fractional terms. Initially, the range of system stability is determined based on a novel graphical method, stability boundary locus. This method is used for tuning the fractional order controller parameters, K p , K i and K d for the specified gain and phase margins. Stability of the system with controller is checked based on bode plot. This novel graphical method, stability boundary locus, in frequency domain uses less mathematical calculations and gives an idea about the system stability regions. Using this method, the gain and phase margin specification can be attained very easily without complex numerical analysis.

Optimization of Fractional Order Controller Parameters

A new training method is proposed, which could solve the problem of that parameters of fractional order controller are not easy to be selected. This method which based on the principle of gravity optimizes parameters. Random initial parameter based on step was set as coordinate form which in the midpoint of the multidimensional space. The error between the actual output and the target output was set as radius. This method had advantages which could not need to calculate the gradient and could randomly select initial. Through the simulation experiment, this method is successfully applied in the fractional order PID controller, which obtains the optimal parameters.

Design of Fractional Order Controllers Using Genetic Algorithms

This paper presents the development of fractional order PI λ D μ and fuzzy-controllers for control of dynamic plant. The fractional order derivative and integral are described. The designs of fractional order PI λ D μ -and fuzzy controllers have been done. The parameters of fractional order controllers are turned using a real coded Genetic Algorithm (GA). The performances of the proposed control systems are illustrated through application examples. Fractional calculus has shown improvement in time response characteristics of feedback control system through the use of non -integer order derivatives and integrals.

Gain and Order Scheduling of Optimal Fractional Order PID Controllers for Random Delay and Packet Dropout in Networked Control Systems

Application of fractional order (FO) PID controllers has been proposed over an unreliable network with random delays and packet dropouts. The gain and order of the controllers have been tuned offline to obtain optimal time domain performance for different network conditions with the help of Genetic Algorithm (GA). The FO controller parameters are then scheduled for time varying network conditions and the performance is compared with their integer order counterparts.

Research on High Precision and Stability of Three-Phase Rectifier Based on Fractional <i>PI<sup>λ</sup></i> Order Controller

According to the demand of transmitter for deep exploration, this paper presents a strategy of current double closed loop control based on fractional order controller, which used to improve the tracing performance and anti-interference capability of the current regulating loop, also the stability of load current. And also presents a modified GA-PSO algorithm to get the parameters of fractional order controller. Results show that modified GA-PSO algorithm has faster convergence speed and higher accuracy, new control strategy using in three-phase PWM voltage rectifier has remarkably improved the stability and anti-interference capability of system.