Tuning of a Pi x+iy D Fractional Complex Order Controller
01 Jul 2017-pp 643-648
TL;DR: In this article, a new structure of FCOC with the form PIx+iyD is presented, in which x and y are the real and imaginary parts of the integral complex order, respectively.
Abstract: This paper deals with Fractional Complex Order Controller FCOC tuning. The paper presents new structure of FCOC with the form PIx+iyD, in which x and y are the real and imaginary parts of the integral complex order, respectively. With the controller's five parameters, we can fulfil five design requirements. Design specifications are set to ensure robustness toward gain variations, noise on system output and disturbance. A tuning method for the Controller is presented to accomplish design requirements. The proposed design method is investigated with a Second Order Plus Time Delay resonant system. Frequency and time domain analysis are presented in this manuscript.
Citations
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TL;DR: It is shown with simulations that complex-order controllers, owing to their increased flexibility, give superior closed-loop time-domain performances for these systems.
Abstract: Use of fractional-order controllers for fractional-order systems is now a well established field. Recently, there have been attempts to extend the concept of fractional-order control to complex-order control involving derivative and integral operators with complex-order (
$$q=u+iv$$
). The paper presents the design of two new complex-order controllers using genetic algorithms. The performance of these two complex-order controllers is tested for various types of fractional-order plants. A comparative study between integer-order, fractional-order and the two new complex-order controllers is also presented. It is shown with simulations that complex-order controllers, owing to their increased flexibility, give superior closed-loop time-domain performances for these systems.
7 citations
27 Jul 2018
TL;DR: In this article, a novel form of PID controller termed as complex fractional order proportional integral derivative (CFOPID) controller of the form PIx+iyDa+ib was introduced.
Abstract: Proportional Integral Derivative order controller has been used in feedback mechanism since time immemorial. The paper introduces a novel form of proportional integral derivative (PID) controller termed as complex fractional order proportional integral derivative (CFOPID) controller of the form PIx+iyDa+ib. This variant of PID controller has more number of parameters than any of the PID and its derivatives. This work realizes a complex natured PID controller and exhibits the tuning of all the variants of PID controller utilizing Genetic Algorithm (starting from primitive Proportional controller to advanced CFOPID controller). It additionally relates the responses of each of the controllers and concludes the superior variant of PID controller.
3 citations
3 citations
TL;DR: Simulation results of the model-driven method applied to a nanopositioning system in atomic force microscopy suggest that the proposed method can be used for optimization of fractional-order controllers while enforcing closed-loop stability.
1 citations
01 Mar 2019
TL;DR: This research realizes CFOPID controller and synthesizes all the variants of PID controller’s parameter utilizing Genetic Algorithm by minimizing the weighted sum of error specifications and concludes the superior variant of PID controllers.
Abstract: Proportional Integral Derivative (PID) controller has been used in feedback mechanism since time immemorial. This work discusses about another hybrid of PID controller of the form PIx+iyDa+ib also termed as Complex Fractional order PID controller. This variant of PID controller has excess of tuning parameters, more than any of the PID and its other fractional order variant (also known as Fractional order PID controller). Henceforth, this research realizes CFOPID controller and synthesizes all the variants of PID controller’s parameter utilizing Genetic Algorithm (starting from primitive Proportional controller to advanced CFOPID controller) by minimizing the weighted sum of error specifications. It additionally relates the responses of each of the controllers and concludes the superior variant of PID controller.
1 citations
References
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TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.
Abstract: Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.
2,479 citations
TL;DR: A new tuning method for fractional order proportional and derivative (PD ¿) or FO-PD controller is proposed for a class of typical second-order plants and shows that the closed-loop system can achieve favorable dynamic performance and robustness.
Abstract: In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), specially PI ? D ? controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this paper, a new tuning method for fractional order proportional and derivative (PD ?) or FO-PD controller is proposed for a class of typical second-order plants. The tuned FO-PD controller can ensure that the given gain crossover frequency and phase margin are fulfilled, and furthermore, the phase derivative w. r. t. the frequency is zero, i.e., the phase Bode plot is flat at the given gain crossover frequency. Consequently, the closed-loop system is robust to gain variations. The FOC design method proposed in the paper is practical and simple to apply. Simulation and experimental results show that the closed-loop system can achieve favorable dynamic performance and robustness.
378 citations
TL;DR: This paper deals with the application of fractional system identification to lead acid battery state of charge estimation and a new fractional model of the battery is proposed based on parameter variations of this model.
285 citations
TL;DR: An overview of the main simulation methods of fractional systems is presented in this paper, where some improvements are proposed based on Oustaloup's recursive poles and zeros approximation of a fractional integrator in a frequency band, taking into account boundary effects around outer frequency limits.
Abstract: An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band, some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters.
122 citations