Stabilization of Switched Systems Using Only A Single Fractional Order PI Controller

Year 2014, Volume: 2 Issue: 3, 150 - 155, 01.09.2014

S. E. Hamamci İ. Işık

https://doi.org/10.17694/bajece.30482

Abstract

The infinite root boundary does not exist because of m < n . Finally, the complex root boundary (CRB) is obtained by equating the real and imaginary parts of Pi(jw) to zero. In this case, Equation (4) is returned to two equations

Keywords

-

References

• D. Liberzon, Switching in Systems and Control, Birkäuser, 2003.
• J. Daafouz, P. Riedinger, and C. Lung, “Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach,” IEEE Trans. on Automatic Control, vol. 47, no. 11, pp. 1883–1887, 2002.
• S.L. Chen, Y.Yao, and X. Di, “Robust Stabilization for a Class of Uncertain Discrete-time Switched Linear Systems,” In: Discrete Time Systems, edited by M.A. Jordán, InTech-Open Access Company.
• D.J. Leith, R.N. Shorten, W.E. Leithead, O. Mason, and P. Curran, “Issues in the design of switched linear control systems: A benchmark study,” Int. J. Adapt. Control Signal Process, vol. 17, no. 2, pp. 103– 118, 2003.
• S. Kim, S.A. Campbell, and X. Liu, “Stability of a Class of Linear Switching Systems With Time Delay,” IEEE Trans. on Circuits and Systems-I: Regular Papers, vol. 53, no. 2, pp. 384-393, 2006.
• Z. Sun, and S.S. Ge, “Analysis and synthesis of switched linear control systems,” Automatica, vol. 41, no. 2, pp. 181-195, 2005.
• K. Wulff, Quadratic and Non-Quadratic Stability Criteria for Switched Linear Systems, Ph.D Thesis, National University of Ireland, 2004.
• M.S. Branicky, “Stability of switched and hybrid systems,” in: Proc. the 33rd IEEE Conf. on Decision and Control, pp. 3498-3503, 1994.
• Z. Sun, S. S. Ge, and T. H. Lee, “Controllability and reachability criteria for switched linear systems,” Automatica, vol. 38, no. 5, pp. 775–786, 2002.
• J.P. Hespanha, D. Liberzon, D. Angeli, and E.D. Sontag, “Nonlinear norm-observability notions and stability of switched systems,” IEEE Trans. Automat. Control, vol. 52, no. 2, pp. 154–168, 2005.
• S. Solmaz, R. Shorten, K. Wulff ve F.Ó. Cairbre, “A design methodology for switched discrete time linear systems with applications to automotive roll dynamics control,” Automatica, vol. 44, no. 9, pp. 2358-2363, 2008.
• X. Xu and P. J. Antsaklis, “Optimal control of switched systems based on parameterization of the switching instants,” IEEE Trans. Automat. Control, vol. 49, no. 1, pp. 2–16, 2004.
• K. Wulff, F. Wirth, and R. Shorten, “A control design method for a class of switched linear systems,” Automatica, vol. 45, no. 11, pp. 2592-2596, 2009.
• C. Chen, S. Fei, K. Zhang, and Y. Lu, “Control of switched linear systems with actuator saturation and its applications,” Mathematical and Computer Modelling, vol. 56, no. 1-2, pp. 14-26, 2009.
• S.H. HosseinNia, I. Tejado, B.M. Vinagre, “Robust Fractional order PI Controller for Switching Systems,” in: Proc. the 5th Symp. on. Fractional Differentiation and its Applications (FDA'2012), Hohai University, 2012.
• Y.I. Neimark, “D-decomposition of the space of quasi-polynomials (on the stability of linearized distributive systems),” American Mathematical Society Translations, vol. 102, pp. 95-131, 1973.
• D. Liberzon, ve A.S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, pp. 59–70, 1999.
• S.H. HosseinNia, I. Tejado, B.M. Vinagre, “A method for the design of robust controllers ensuring the quadratic stability for switching systems,” J. of Vibration and Control, vol. 20, no. 7, pp. 1085-1098, 2014.
• I. Podlubny, “Fractional Order Systems and PID Controllers,” IEEE  Trans. on Automatic Control, vol. 44, no. 1, pp. 208-214, 1999.
• J. Hwang, J.-F. Leu, and S.-Y. Tsay, “A note on time-domain simulation of feedback fractional-order systems,” IEEE Trans. on Automatic Control, vol. 47, no. 4, pp. 625-631, 2002.
• J. Ackermann, D. Kaesbauer, “Design of robust PID controllers,” in: Proc. the European Control Conference, pp. 522-527, 2001.
• M.-T. Ho, A. Datta, and S.P. Bhattacharyya, “A new approach to feedback stabilization,” in: Proc. The 35th Conf. on Decision and Control, Kobe, Japan, 1996.
• İ. Işık, and S.E. Hamamci, "Anahtarlamalı Sistemleri Kararlı Yapan PI Kontrolör Setinin Hesabı," in: Proc. the TOK 2013 Turkish Automatic Control National Meeting, Malatya, Turkey, 2013, (in Turkish).
• Y.C. Cheng, and C. Hwang, “Stabilization of unstable Şrst-order time- delay systems using fractional-order PD controllers,” J. of the Chinese Inst. of Engineers, vol. 29, pp. 241-249, 2006.