References
- Atherton, D.P., Tan, N. and Yüce, A. (2014). Methods for computing the time response of fractional-order systems, IET Control Theory & Applications9(6): 817–830.
- Balas, G., Chiang, R., Packard, A. and Safonov, M. (2007). Robust Control Toolbox 3: User’ Guide, MathWorks, Natick, MA.
- Bingi, K., Ibrahim, R., Karsiti, M.N., Hassan, S.M. and Harindran, V.R. (2018a). A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems, Archives of Control Sciences28(4): 635–682.
- Bingi, K., Ibrahim, R., Karsiti, M.N., Hassan, S.M. and Harindran, V.R. (2018b). Real-time control of pressure plant using 2DOF fractional-order PID controller, Arabian Journal for Science and Engineering44(3): 2091–2102.
- Caponetto, R. (2010). Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore.
- Das, S. (2011). Functional Fractional Calculus, Springer, Berlin/Heidelberg.
- de Oliveira Valério, D.P.M. (2005). Fractional Robust System Control, PhD thesis, Universidade Técnica de Lisboa, Lisboa.
- Deniz, F.N., Alagoz, B.B., Tan, N. and Atherton, D.P. (2016). An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators, ISA Transactions62: 154–163.
- Djouambi, A., Charef, A. and Besançon, A.V. (2007). Optimal approximation, simulation and analog realization of the fundamental fractional order transfer function, International Journal of Applied Mathematics and Computer Science17(4): 455–462, DOI: 10.2478/v10006-007-0037-9.10.2478/v10006-007-0037-9
- Du, B., Wei, Y., Liang, S. and Wang, Y. (2017). Rational approximation of fractional order systems by vector fitting method, International Journal of Control, Automation and Systems15(1): 186–195.
- Joice Nirmala, R. and Balachandran, K. (2017). The controllability of nonlinear implicit fractional delay dynamical systems, International Journal of Applied Mathematics and Computer Science27(3): 501–513, DOI: 10.1515/amcs-2017-0035.10.1515/amcs-2017-0035
- Kaczorek, T. (2018). Decentralized stabilization of fractional positive descriptor continuous-time linear systems, International Journal of Applied Mathematics and Computer Science28(1): 135–140, DOI: 10.2478/amcs-2018-0010.10.2478/amcs-2018-0010
- Khanra, M., Pal, J. and Biswas, K. (2011). Rational approximation and analog realization of fractional order differentiator, 2011 International Conference on Process Automation, Control and Computing (PACC), Coimbatore, India, pp. 1–6.
- Khanra, M., Pal, J. and Biswas, K. (2013). Rational approximation and analog realization of fractional order transfer function with multiple fractional powered terms, Asian Journal of Control15(3): 723–735.
- Kishore, B., Ibrahim, R., Karsiti, M.N. and Hassan, S.M. (2017). Fractional-order filter design for set-point weighted PID controlled unstable systems, International Journal of Mechanical & Mechatronics Engineering17(5): 173–179.
- Kishore, B., Ibrahim, R., Karsiti, M.N. and Hassan, S.M. (2018). Fractional order set-point weighted PID controller for pH neutralization process using accelerated PSO algorithm, Arabian Journal for Science and Engineering43(6): 2687–2701.
- Krajewski, W. and Viaro, U. (2011). On the rational approximation of fractional order systems, 16th International Conference on Methods and Models in Automation and Robotics (MMAR), Międzyzdroje, Poland, pp. 132–136.
- Krajewski, W. and Viaro, U. (2014). A method for the integer-order approximation of fractional-order systems, Journal of the Franklin Institute351(1): 555–564.
- Krishna, B. (2011). Studies on fractional order differentiators and integrators: A survey, Signal Processing91(3): 386–426.
- Li, Z., Liu, L., Dehghan, S., Chen, Y. and Xue, D. (2017). A review and evaluation of numerical tools for fractional calculus and fractional order controls, International Journal of Control90(6): 1165–1181.
- Liang, S., Peng, C., Liao, Z. and Wang, Y. (2014). State space approximation for general fractional order dynamic systems, International Journal of Systems Science45(10): 2203–2212.
- Meng, L. and Xue, D. (2012). A new approximation algorithm of fractional order system models based optimization, Journal of Dynamic Systems, Measurement, and Control134(4): 044504.
- Merrikh-Bayat, F. (2012). Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PIλDμ controller, Communications in Nonlinear Science and Numerical Simulation17(4): 1852–1861.
- Mitkowski, W. and Oprzedkiewicz, K. (2016). An estimation of accuracy of Charef approximation, in S. Domek and P. Dworak (Eds.), Theoretical Developments and Applications of Non-Integer Order Systems, Springer, Berlin/Heidelberg, pp. 71–80.
- Monje, C.A., Chen, Y., Vinagre, B.M., Xue, D. and Feliu-Batlle, V. (2010). Fractional-Order Systems and Controls: Fundamentals and Applications, Springer, Berlin/Heidelberg.
- Oprzedkiewicz, K. (2014). Approximation method for a fractional order transfer function with zero and pole, Archives of Control Sciences24(4): 447–463.
- Oustaloup, A., Levron, F., Mathieu, B. and Nanot, F.M. (2000). Frequency-band complex noninteger differentiator: characterization and synthesis, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications47(1): 25–39.
- Pachauri, N., Singh, V. and Rani, A. (2018). Two degrees-of-freedom fractional-order proportional-integral-derivative-based temperature control of fermentation process, Journal of Dynamic Systems, Measurement, and Control140(7): 071006.
- Petráš, I. (2011a). Fractional derivatives, fractional integrals, and fractional differential equations in Matlab, in A. Assi (Ed.), Engineering Education and Research Using MAT-LAB, InTech, London, pp. 239–264.
- Petráš, I. (2011b). Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Berlin/Heidelberg.
- Poinot, T. and Trigeassou, J.-C. (2003). A method for modelling and simulation of fractional systems, Signal processing83(11): 2319–2333.
- Shah, P. and Agashe, S. (2016). Review of fractional PID controller, Mechatronics38: 29–41.
- Sheng, H., Chen, Y. and Qiu, T. (2011). Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications, Springer, Berlin/Heidelberg.
- Shi, G. (2016). On the nonconvergence of the vector fitting algorithm, IEEE Transactions on Circuits and Systems II: Express Briefs63(8): 718–722.
- Tepljakov, A., Petlenkov, E. and Belikov, J. (2012). Application of Newton’s method to analog and digital realization of fractional-order controllers, International Journal of Microelectronics and Computer Science2(2): 45–52.
- Valério, D., Trujillo, J.J., Rivero, M., Machado, J.T. and Baleanu, D. (2013). Fractional calculus: A survey of useful formulas, The European Physical Journal Special Topics222(8): 1827–1846.
- Vinagre, B., Podlubny, I., Hernandez, A. and Feliu, V. (2000). Some approximations of fractional order operators used in control theory and applications, Fractional Calculus and Applied Analysis3(3): 231–248.
- Wei, Y., Gao, Q., Peng, C. and Wang, Y. (2014a). A rational approximate method to fractional order systems, International Journal of Control, Automation and Systems12(6): 1180–1186.
- Wei, Y., Gao, Q., Peng, C. and Wang, Y. (2014b). A rational approximate method to fractional order systems, International Journal of Control, Automation and Systems12(6): 1180–1186.
- Xue, D. (2017). Fractional-order Control Systems: Fundamentals and Numerical Implementations, Walter de Gruyter GmbH, Berlin.
- Xue, D., Chen, Y. and Attherton, D.P. (2007). Linear Feedback Control: Analysis and Design with MATLAB, SIAM, Philadelphia, PA.
- Xue, D., Zhao, C. and Chen, Y. (2006). A modified approximation method of fractional order system, Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation, Luoyang, China pp. 1043–1048.
- Yüce, A., Deniz, F.N. and Tan, N. (2017). A new integer order approximation table for fractional order derivative operators, IFAC-PapersOnLine50(1): 9736–9741.