Stability and Robust Performance Analysis of Fractional Order Controller over Conventional Controller Design


Electrical Engineering Department, SunRise University, Alwar, Rajasthan, India


In this paper, a new comparative approach has been proposed for reliable controller design. Scientists and engineers are often confronted with the analysis, design, and synthesis of real-life problems. The first step in such studies is the development of a 'mathematical model' which can be considered as a substitute for the real problem. The mathematical model is used here as a plant. Fractional integrals and derivatives have found wide application in the control of dynamical systems when the controlled system and the controller are described by a set of fractional order differential equations. Here the stability of fractional order system is checked at the different level and it is found that the stability region is large in the complex plane. This large stability region provides the more flexibility for system implementation in the control engineering. Generally, an analytically or experimentally approaches are used for designing the controller. If a fractional order controller design approach used for a given plant then the controlled parameter gives the better result.


1.     Gutman, P., Mannerfelt, C. and Molander, P., "Contributions to the model reduction problem", IEEE Transactions on Automatic Control,  Vol. 27, No. 2, (1982), 454-455.
2.     Bandyopadhyay, B., Rao, A. and Singh, H., "On pade approximation for multivariable systems", IEEE Transactions on Circuits and Systems,  Vol. 36, No. 4, (1989), 638-639.
3.     Smamash, Y., "Truncation method of reduction: A viable alternative", Electronics letters,  Vol. 17, No. 2, (1981), 97-99.
4.     Jamshidi, M., "An overview on the aggregation of large-scale systems", IFAC Proceedings Volumes,  Vol. 14, No. 2, (1981), 1309-1314.
5.     Shamash, Y., "Model reduction using the routh stability criterion and the pade approximation technique", International Journal of Control,  Vol. 21, No. 3, (1975), 475-484.
6.     Shahri, E.S.A., Alfi, A. and Machado, J.T., "Stabilization of fractional-order systems subject to saturation element using fractional dynamic output feedback sliding mode control", Journal of Computational and Nonlinear Dynamics,  Vol. 12, No. 3, (2017), 0310141-0310146.
7.     Alfi, A., Khosravi, A. and Lari, A., "Swarm-based structure-specified controller design for bilateral transparent teleoperation systems via μ synthesis", IMA Journal of Mathematical control and Information,  Vol. 31, No. 1, (2013), 111-136.
8.     Mousavi, Y. and Alfi, A., "A memetic algorithm applied to trajectory control by tuning of fractional order proportional-integral-derivative controllers", Applied Soft Computing,  Vol. 36, (2015), 599-617.
9.     Alfi, A. and Fateh, M.-M., "Intelligent identification and control using improved fuzzy particle swarm optimization", Expert Systems with Applications,  Vol. 38, No. 10, (2011), 12312-12317.
10.   Axtell, M. and Bise, M.E., "Fractional calculus application in control systems", in Aerospace and Electronics Conference, 1990. NAECON 1990., Proceedings of the IEEE 1990 National, IEEE., (1990), 563-566.
11.   Dorcak, L., "Numberical models for simulation the fractional order control systems [j/ol]. Uefsav, the academy of science institute of experimental physcics, kosice, slovak republic, 1994 [2009-12-19]", arXiv preprint math/0204108,  62–68.
12.   Hassanpour, H. and ROSTAMI, G.A., "Image enhancement via reducing impairment effects on image components",  International Journal of Engineering-Transactions B: Applications, Vol. 26, No. 11, (2013), 1267-1274.
13.   Soltani, J., Abjadi, N. and PAHLAVANI, N.M., "An adaptive nonlinear controller for speed sensorless PMSM taking the iron loss resistance into account (research note)",  International Journal of Engineering-Transactions B: Applications, Vol. 21, No. 2, (2008), 151-160.
14.   Oldham, K. and Spanier, J., "The fractional calculus theory and applications of differentiation and integration to arbitrary order, Elsevier,  Vol. 111,  (1974), ISBN: 9780080956206
15.   Podlubny, I., "Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier,  Vol. 198,  (1998).
16.   Miller, K.S. and Ross, B., "An introduction to the fractional calculus and fractional differential equations",  (1993).
17.   Samko, S., Kilbas, A. and Marichev, O., "Fractional integrals and derivatives and some of their applications", Science and Technica,  Vol. 1, (1987), ISBN: 2881248640 9782881248641
18.   Moghanloo, D. and Ghasemi, R., "Observer based fuzzy terminal sliding mode controller design for a class of fractional order chaotic nonlinear systems", International Journal of Engineering-Transactions B: Applications,  Vol. 29, No. 11, (2016), 1574-1581.
19.   Pilla, R., Tummala, A. and Chintala, M., "Tuning of extended kalman filter using self-adaptive differential evolution algorithm for sensorless permanent magnet synchronous motor drive", International Journal of Engineering-Transactions B: Applications,  Vol. 29, No. 11, (2016), 1565-1573.
20.   Chen, Y., Petras, I. and Xue, D., "Fractional order control-a tutorial", in American Control Conference, 2009. ACC'09., IEEE., (2009), 1397-1411.
21.   Bidan, P., "Commande diffusive d'une machine electrique: Une introduction", in ESAIM: Proceedings, EDP Sciences. Vol. 5, (1998), 55-68.
22.   Vinagre, B.M., Podlubny, I., Dorcak, L. and Feliu, V., "On fractional pid controllers: A frequency domain approach", IFAC Proceedings Volumes,  Vol. 33, No. 4, (2000), 51-56.
23.   Yan, Z., He, J., Li, Y., Li, K. and Song, C., "Realization of fractional order controllers by using multiple tuning-rules", International Journal of Signal Processing, Image Processing and Pattern Recognition,  Vol. 6, No. 6, (2013), 119-128.
24.   Tajbakhsh, H. and Balochian, S., "Robust fractional order pid control of a dc motor with parameter uncertainty structure", Int. J. of Innovative Science, Engineering & Technology,  Vol. 1, No. 6, (2014), 223-229.
25.   Yeroglu, C. and Tan, N., "Note on fractional-order proportional–integral–differential controller design", IET Control Theory&Applications,  Vol. 5, No. 17, (2011), 1978-1989.