TEACHING FRACTIONAL ORDER CONTROL SYSTEMS USING INTERACTIVE TOOLS
Year 2016,
Volume: 4 , 554 - 563, 01.09.2016
Nusret Tan
Ali Yüce
Furkan Nur Deniz
Abstract
Much
of subjects being taught in a first course on control theory in Electrical and
Electronics Engineering appears to have changed little. Although the basic
theories, methods and applications on classical control in textbooks remain
unchanged, there have been many new developments in the field of control theory
in recent years. One of such topic is fractional order control systems which is
based on fractional order calculus and can be used to model physical system
more exactly than integer order systems. The purpose of this paper is to show
how fractional order control methods can be introduced into a first course on
classical control using interactive tools such as Matlab and LabView.
References
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Chen, Y. Q., Petras, I., & Xue, D. (2009). Fractional order control-a tutorial. In 2009 American Control Conference pp. 1397–1411.
Das, S. (2008). Functional Fractional Calculus for System Identification and Control. Springer-Verlag, Berlin Heidelberg, New York.
Dormido, S., (2002). Control learning: present and future. 15th IFAC World Congress on Automatic Control, Barcelona, Spain.
Deniz, F. N., Alagoz, B. B., Tan, N., & Atherton, D. P. (2016). An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators. ISA Transactions. http://doi.org/10.1016/j.isatra.2016.01.020.
Hamamci, S. E. (2008). Stabilization using fractional-order PI and PID controllers. Nonlinear Dynamics, 51, 329–343.
Matsuda, K., & Fujii, H. (1993). H (infinity) optimized wave-absorbing control-Analytical and experimental results. Journal of Guidance, Control, and Dynamics, 16(6), 1146–1153.
MathWorks, Inc. Using Simulink. Retrieved from http://www.mathworks.com/.
Monje C. A., Chen, Y. Q., Vinagre, B. M., Xue D., Feliu, V. (2010). Fractional-order Systems and Controls-“Fundamentals and Applications”. London: Springer-Verlag.
Oustaloup A., Levron F., Mathieu B., and Nanot F.M. (2000). Frequency- band complex noninteger differentiator: characterization and synthesis. 1410 IEEE Trans. on Circuit and Systems - I: Fundamental Theory and Application, vol. 47, no. 1, pp. 25–3.
Petras I. (1999). The fractional-order controllers: methods for their synthesis and application. J. of Electrical Engineering, vol. 50, no. 9-10, pp. 284–288.
Podlubny,I., (1999a). Fractional Differential Equation. Academic Press, San Diego.
Podlubny, I. (1999b). Fractional-order systems and PIλDµ -controllers. IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 208– 214.
Rodriguez, A. A., Metzger, R.P., Cifdaloz, O., & Dhirasakdanon, T. (2005). Description of a modeling, simulation, animation, and real-time control (MoSART) environment for a class of electromechanical systems. IEEE Transactions on Education, 48(3), 359-374.
Xue, D., Chen, Y. Q., & Atherton, D. P., (2007). Linear Feedback Control - Analysis and Design with Matlab. SIAM Press, ISBN: 978-0-898716-38-2. (348 pages) Chapter-8: Fractional-order Controller - An Introduction.
Xuejun, X., Ping, X., Sheng, Y., & Ping, L. (2007). Real-time Digital Simulation of Control System with LabVIEW Simulation Interface Toolkit. Proceedings of the 26th Chinese Control Conference, Zhangjiajie, Hunan, China, 318-322.
Vento, J. A. (1988). Application of Labview In Higher Education Laboratories. 1988 Frontiers In Education Conference Proceedings, 444-447.
Vinagre, B. M., Podlubny, I., Hernández A., Feliu, V. (2000). Some Approximations of Fractional Order Operators used in Control Theory and Applications. Fractional Calculus & Applied Analysis, 3(3), 231–248.
Year 2016,
Volume: 4 , 554 - 563, 01.09.2016
Nusret Tan
Ali Yüce
Furkan Nur Deniz
References
- Atherton, D. P., Tan, N., Yüce, A. (2015). Methods for Computing the Time Response of Fractional Order Systems. IET Control Theory & Application, 9(6), 817-830.
Chen, Y. Q., Petras, I., & Xue, D. (2009). Fractional order control-a tutorial. In 2009 American Control Conference pp. 1397–1411.
Das, S. (2008). Functional Fractional Calculus for System Identification and Control. Springer-Verlag, Berlin Heidelberg, New York.
Dormido, S., (2002). Control learning: present and future. 15th IFAC World Congress on Automatic Control, Barcelona, Spain.
Deniz, F. N., Alagoz, B. B., Tan, N., & Atherton, D. P. (2016). An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators. ISA Transactions. http://doi.org/10.1016/j.isatra.2016.01.020.
Hamamci, S. E. (2008). Stabilization using fractional-order PI and PID controllers. Nonlinear Dynamics, 51, 329–343.
Matsuda, K., & Fujii, H. (1993). H (infinity) optimized wave-absorbing control-Analytical and experimental results. Journal of Guidance, Control, and Dynamics, 16(6), 1146–1153.
MathWorks, Inc. Using Simulink. Retrieved from http://www.mathworks.com/.
Monje C. A., Chen, Y. Q., Vinagre, B. M., Xue D., Feliu, V. (2010). Fractional-order Systems and Controls-“Fundamentals and Applications”. London: Springer-Verlag.
Oustaloup A., Levron F., Mathieu B., and Nanot F.M. (2000). Frequency- band complex noninteger differentiator: characterization and synthesis. 1410 IEEE Trans. on Circuit and Systems - I: Fundamental Theory and Application, vol. 47, no. 1, pp. 25–3.
Petras I. (1999). The fractional-order controllers: methods for their synthesis and application. J. of Electrical Engineering, vol. 50, no. 9-10, pp. 284–288.
Podlubny,I., (1999a). Fractional Differential Equation. Academic Press, San Diego.
Podlubny, I. (1999b). Fractional-order systems and PIλDµ -controllers. IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 208– 214.
Rodriguez, A. A., Metzger, R.P., Cifdaloz, O., & Dhirasakdanon, T. (2005). Description of a modeling, simulation, animation, and real-time control (MoSART) environment for a class of electromechanical systems. IEEE Transactions on Education, 48(3), 359-374.
Xue, D., Chen, Y. Q., & Atherton, D. P., (2007). Linear Feedback Control - Analysis and Design with Matlab. SIAM Press, ISBN: 978-0-898716-38-2. (348 pages) Chapter-8: Fractional-order Controller - An Introduction.
Xuejun, X., Ping, X., Sheng, Y., & Ping, L. (2007). Real-time Digital Simulation of Control System with LabVIEW Simulation Interface Toolkit. Proceedings of the 26th Chinese Control Conference, Zhangjiajie, Hunan, China, 318-322.
Vento, J. A. (1988). Application of Labview In Higher Education Laboratories. 1988 Frontiers In Education Conference Proceedings, 444-447.
Vinagre, B. M., Podlubny, I., Hernández A., Feliu, V. (2000). Some Approximations of Fractional Order Operators used in Control Theory and Applications. Fractional Calculus & Applied Analysis, 3(3), 231–248.