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Fractional Simplification of Linear Fractional Order Models

Tavakoli-Kakhki, Mahsan | 2011

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 41891 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Haeri, Mohammad
  7. Abstract:
  8. In recent years, increasing attention has been paid to the fractional calculus as a powerful tool for more precise modeling of real world phenomena. Also, it has been shown that using this tool in designing control systems results in controllers that are more efficient in comparison with their traditional integer order counterparts. In spite of the advantages of fractional order models, the difficulties in the implementation of this type of models are still the main concern of the control system community. Clearly, as a model becomes simpler, its implementation becomes more convenient. Therefore, one way to rectify the implementation problems is to model the intended system as simple as possible. Paying attention to the importance of model simplification problem in the area of fractional order systems, in this thesis some methods are preseneted for simplifying fractional order models. To this end, firstly the problem of simplification of fractional order models is defined and then two different viewpoints are presented which help to have a more systematic study on this problem. These two viewpoins are simplification of a fractional order transfer function based on the retention, and based on the approximation of the main transfer function. The simplification problem considered in the first viewpoint is in fact the problem of finding a minimal realization for a fractional order transfer function which to the best of our knowledge no research has been done before on this subject. The simplification problem in the second viewpoint is studied in three separate sections. In the first section, some existing methods of model order reduction for approximating integer order models are extened for simplifying fractional order models. In the second section, the concept of dominant dynamics is defined for a fractional order model. Then, a simplification algorithm based on the retention of the dominant dynamics of a fractional order model in its approximated model is presented. In the third section, two simple fractional order models are presented for describing those systems having an S-shaped step response. These models are useful in those methodologies of designing fractional order controllers where a simple model of the process is utilized. In each of these three sections, the efficiency of the presented simplification methods is shown in designing different control systems. The problems presented and the methods proposed in this thesis can be considered as pioneering works for doing future researches in the field of simplification of fractional order models
  9. Keywords:
  10. Model Simplification ; Fractional Order Controller ; Fractional Order Model ; Minimal Realization

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