Research Papers

Optimal Tuning for Fractional-Order Controllers: An Integer-Order Approximating Filter Approach

[+] Author and Article Information
Mohammad Saleh Tavazoei

e-mail: tavazoei@sharif.edu
Electrical Engineering Department,
Sharif University of Technology,
P.O. Box 11155-4363,
Tehran, Iran

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received July 8, 2010; final manuscript received October 6, 2012; published online February 21, 2013. Editor: J. Karl Hedrick.

J. Dyn. Sys., Meas., Control 135(2), 021017 (Feb 21, 2013) (11 pages) Paper No: DS-10-1192; doi: 10.1115/1.4023066 History: Received July 08, 2010; Revised October 06, 2012

This paper offers a systematic framework for the design of suboptimal integer-order controllers based on fractional-order structures. The proposed approach is built upon the integer-order approximations that are traditionally used to implement fractional-order controllers after they are designed. Accordingly, the fractional-order structures are exploited to derive a suitable parameterization for a fixed-structure integer-order controller. The parameters, which describe the structure of the fixed-order integer controller, are the same as those used to describe the original fractional structure. Optimal tuning is then performed in the parameter space of the fractional structure and the resultant set of optimum parameters will determine the optimal integer-order controller. The proposed approach outperforms traditional implementations of optimal fractional controllers and presents an alternative that attempts to capture merits of both fractional-order and integer-order structures.

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Grahic Jump Location
Fig. 1

A basic closed-loop control system. C(s) and G(s) denote compensator and plant transfer functions, respectively.

Grahic Jump Location
Fig. 2

Optimal tuning of a fixed-structure controller

Grahic Jump Location
Fig. 3

Fractional-order controller design paradigm

Grahic Jump Location
Fig. 4

Optimization of the parameterized integer-order controller that is derived as a result of approximating the fractional-order structure

Grahic Jump Location
Fig. 5

Three paradigms are distinguishable in the study of optimal fractional controllers: The fractional control design paradigm, the integer-order control paradigm and the newly introduced intermediate design paradigm. Using the intermediate design paradigm, we can still take advantage of a fractional structure while tuning and implementation are performed in the integer-order control paradigm.

Grahic Jump Location
Fig. 6

The feasible domain of parameters over which the fractional structure in (9) should be optimized

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Fig. 7

The phase margin γ is plotted for the admissible values of parameters over which the fractional structure in Eq. (9) should be optimized

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Fig. 8

The phase margin γ is plotted for the admissible values of parameters over which the integer-order structure in Eq. (34) should be optimized

Grahic Jump Location
Fig. 9

Step responses for the two controllers in Eqs. (32) and (37) are plotted

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Fig. 10

The ITAE index is plotted for the admissible values of parameters over which the integer-order structure in Eq. (34) should be optimized. The feasible domain of parameters is the same as that in Fig. 8. The values close to the stability boundary tend to be exceedingly large, since such points produce poorly damped closed-loop responses which are highly discriminated against by the ITAE index.




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