Optimal Integer Order Approximation of Fractional Order Human Ear Simulator

Existing graph filters, polynomial or rational, are mainly of integer order forms. However, there are some frequency responses which are not easily achieved by integer order approximation. It will substantially increase the flexibility of the filters if we relax the integer order to fractional ones. Motivated by fractional order models, we introduce the fractional order graph filters (FOGF), and propose to design the filter coefficients by genetic algorithm. In order to implement distributed computation on a graph, an FOGF can be approximated by the continued fraction expansion and transformed to an infinite impulse response graph filter.

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Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

International Journal of Applied Mathematics and Computer Science ◽

10.2478/amcs-2019-0023 ◽

2019 ◽

Vol 29 (2) ◽

pp. 311-326 ◽

Cited By ~ 7

Author(s):

Kishore Bingi ◽

Rosdiazli Ibrahim ◽

Mohd Noh Karsiti ◽

Sabo Miya Hassam ◽

Vivekananda Rajah Harindran

Keyword(s):

Frequency Response ◽

Frequency Domain ◽

Fractional Order ◽

Curve Fitting ◽

Order Approximation ◽

Frequency Range ◽

Approximation Techniques ◽

Integer Order ◽

The Best Approximation ◽

Fractional Order Pid

Abstract Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results.

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Design Of Multivariable Fractional Order Pid Controller Using Covariance Matrix Adaptation Evolution Strategy

Archives of Control Sciences ◽

10.2478/acsc-2014-0014 ◽

2014 ◽

Vol 24 (2) ◽

pp. 235-251 ◽

Cited By ~ 5

Author(s):

Sudalaiandi Sivananaithaperumal ◽

Subramanian Baskar

Keyword(s):

Covariance Matrix ◽

Fractional Order ◽

Pid Controller ◽

Order Approximation ◽

Absolute Error ◽

Evolution Strategy ◽

Fractional Integrals ◽

Integer Order ◽

Covariance Matrix Adaptation ◽

Adaptation Evolution

Abstract This paper presents an automatic tuning of multivariable Fractional-Order Proportional, Integral and Derivative controller (FO-PID) parameters using Covariance Matrix Adaptation Evolution Strategy (CMAES) algorithm. Decoupled multivariable FO-PI and FO-PID controller structures are considered. Oustaloup integer order approximation is used for the fractional integrals and derivatives. For validation, two Multi-Input Multi- Output (MIMO) distillation columns described byWood and Berry and Ogunnaike and Ray are considered for the design of multivariable FO-PID controller. Optimal FO-PID controller is designed by minimizing Integral Absolute Error (IAE) as objective function. The results of previously reported PI/PID controller are considered for comparison purposes. Simulation results reveal that the performance of FOPI and FO-PID controller is better than integer order PI/PID controller in terms of IAE. Also, CMAES algorithm is suitable for the design of FO-PI / FO-PID controller.

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