Öz
In this paper, an optimization method is
proposed to design a fractional order system with PID controller by taking
Bode’s ideal transfer function as reference model. In the study, PID
controllers are preferred because of their simplicity, reliability and
robustness. PID controller parameters can be obtained by optimization method.
In order to obtain the desired time response, it is sufficient to set two
parameters in the Bode’s ideal transfer function. The Bode's ideal transfer
function was considered as the reference model and compared with the generated
model. The error in the output signal is minimized by the integral performance
criteria, and the PID controller parameters are optimized. Integral performance
criteria are frequently used in evaluating the performance of control systems.
In Simulink model, Matsuda's 4th order integer approximation model is used for
fractional order control system. Finally, the success of the optimization
method is seen in the given numerical example.
Anahtar Kelimeler
Controller design Optimization Fractional order control systems PID Controller
Kaynakça
- C. A. Monje, Y. Chen, B. M. Vinagre, D. Xue, and V. Feliu-Batlle, Fractional-order systems and controls: fundamentals and applications. Springer Science & Business Media, 2010.
- G. Carlson and C. Halijak, "Approximation of fractional capacitors (1/s)(1/n) by a regular Newton process," IEEE Transactions on Circuit Theory, vol. 11, no. 2, pp. 210-213, 1964.
- A. Charef, H. Sun, Y. Tsao, and B. Onaral, "Fractal system as represented by singularity function," IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1465-1470, 1992.
- B. Krishna, "Studies on fractional order differentiators and integrators: A survey," Signal Processing, vol. 91, no. 3, pp. 386-426, 2011.
- R. Matušů, "Application of fractional order calculus to control theory," International journal of mathematical models and methods in applied sciences, vol. 5, no. 7, pp. 1162-1169, 2011.
- A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, "Frequency-band complex noninteger differentiator: characterization and synthesis," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 47, no. 1, pp. 25-39, 2000.
- D. Atherton, Control engineering. Bookboon, 2009.
- K. J. Åström and T. Hägglund, "The future of PID control," Control engineering practice, vol. 9, no. 11, pp. 1163-1175, 2001.
- J. G. Ziegler and N. B. Nichols, "Optimum settings for automatic controllers," trans. ASME, vol. 64, no. 11, 1942.
- H. W. Bode, "Network Analysis and Feedback Amplifier Design," 1945.
- R. S. Barbosa, J. T. Machado, and I. M. Ferreira, "Tuning of PID controllers based on Bode’s ideal transfer function," Nonlinear dynamics, vol. 38, no. 1, pp. 305-321, 2004.
- O. Katsuhiko, "Modern control engineering," ed, 2010.
- T. Doğruer and N. Tan, "Bode’nin İdeal Transfer Fonksiyonunu Kullanarak Lag/Lead Kontrolör Tasarımı," presented at the TOK 2014 Otomatik Kontrol Ulusal Toplantısı, 2014.
- N. Tan, "Computation of stabilizing PI and PID controllers for processes with time delay," ISA transactions, vol. 44, no. 2, pp. 213-223, 2005.
Öz
Kaynakça
- C. A. Monje, Y. Chen, B. M. Vinagre, D. Xue, and V. Feliu-Batlle, Fractional-order systems and controls: fundamentals and applications. Springer Science & Business Media, 2010.
- G. Carlson and C. Halijak, "Approximation of fractional capacitors (1/s)(1/n) by a regular Newton process," IEEE Transactions on Circuit Theory, vol. 11, no. 2, pp. 210-213, 1964.
- A. Charef, H. Sun, Y. Tsao, and B. Onaral, "Fractal system as represented by singularity function," IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1465-1470, 1992.
- B. Krishna, "Studies on fractional order differentiators and integrators: A survey," Signal Processing, vol. 91, no. 3, pp. 386-426, 2011.
- R. Matušů, "Application of fractional order calculus to control theory," International journal of mathematical models and methods in applied sciences, vol. 5, no. 7, pp. 1162-1169, 2011.
- A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, "Frequency-band complex noninteger differentiator: characterization and synthesis," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 47, no. 1, pp. 25-39, 2000.
- D. Atherton, Control engineering. Bookboon, 2009.
- K. J. Åström and T. Hägglund, "The future of PID control," Control engineering practice, vol. 9, no. 11, pp. 1163-1175, 2001.
- J. G. Ziegler and N. B. Nichols, "Optimum settings for automatic controllers," trans. ASME, vol. 64, no. 11, 1942.
- H. W. Bode, "Network Analysis and Feedback Amplifier Design," 1945.
- R. S. Barbosa, J. T. Machado, and I. M. Ferreira, "Tuning of PID controllers based on Bode’s ideal transfer function," Nonlinear dynamics, vol. 38, no. 1, pp. 305-321, 2004.
- O. Katsuhiko, "Modern control engineering," ed, 2010.
- T. Doğruer and N. Tan, "Bode’nin İdeal Transfer Fonksiyonunu Kullanarak Lag/Lead Kontrolör Tasarımı," presented at the TOK 2014 Otomatik Kontrol Ulusal Toplantısı, 2014.
- N. Tan, "Computation of stabilizing PI and PID controllers for processes with time delay," ISA transactions, vol. 44, no. 2, pp. 213-223, 2005.
Ayrıntılar
| Bölüm | Makaleler |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 26 Aralık 2017 |
| Gönderilme Tarihi | 8 Ekim 2017 |
| Yayımlandığı Sayı | Yıl 2017 Cilt: 9 Sayı: 3 |
Cited By
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