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Robust pole placement under structural constraints. (English) Zbl 1417.93142
Summary: A new controller synthesis technique is presented which allows the design of output feedback control systems achieving robust regional pole clustering in the presence of parametric uncertainties as well as satisfying prescribed structural constraints. Such features are rarely jointly present in currently available controller synthesis methods. The central idea in the proposed approach consists in reformulating the original robust pole placement problem into an equivalent robust stabilization problem involving highly structured controller and uncertainty. A numerical application corroborating the applicability of the proposed synthesis technique is also presented.

MSC:
 93B55 Pole and zero placement problems 93B35 Sensitivity (robustness) 93D21 Adaptive or robust stabilization 93B50 Synthesis problems 93B52 Feedback control
HIFOO
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 [1] Tapia, A.; Bernal, M.; Fridman, L., Nonlinear sliding mode control design: an LMI approach, Systems Control Lett., 104, 38-44, (2017) · Zbl 1370.93077 [2] Montanaro, U.; Olm, J. M., Integral MRAC with minimal controller synthesis and bounded adaptive gains: the continuous-time case, J. Franklin Inst. B, 353, 18, 5040-5067, (2016) · Zbl 1349.93223 [3] Chesi, G., Parameter and controller dependent Lyapunov functions for robust D-stability and robust performance controller design, IEEE Trans. Automat. Control, 62, 9, 4798-4803, (2017) · Zbl 1390.93312 [4] N. Sivashankar, I. Kaminer, P.P. Khargonekar, Optimal controller synthesis with regional stability constraints, in: Proceedings of the 32nd IEEE Conference on Decision and Control, 1993., Vol. 1, 1993, pp. 110-115. · Zbl 0800.93332 [5] Haddad, W. M.; Bernstein, D. S., Controller design with regional pole constraints, IEEE Trans. Automat. Control, 37, 1, 54-69, (1992) · Zbl 0747.93025 [6] Chilali, M.; Gahinet, P., H$${}_\infty$$ design with pole placement constraints: an LMI approach, IEEE Trans. Automat. Control, 41, 3, 358-367, (1996) · Zbl 0857.93048 [7] Chilali, M.; Gahinet, P.; Apkarian, P., Robust pole placement in LMI regions, IEEE Trans. Automat. Control, 44, 12, 2257-2270, (1999) · Zbl 1136.93352 [8] Peaucelle, D.; Arzelier, D.; Bachelier, O.; Bernussou, J., A new robust $$\mathcal{D}$$-stability condition for real convex polytopic uncertainty, Systems Control Lett., 40, 1, 21-30, (2000) · Zbl 0977.93067 [9] Lee, D. H.; Park, J. B.; Joo, Y. H.; Lin, K. C., Lifted versions of robust D-stability and D-stabilisation conditions for uncertain polytopic linear systems, IET Control Theory Appl., 6, 1, 24-36, (2012) [10] Henrion, D.; Sebek, M.; Kucera, V., Robust pole placement for second-order systems: an LMI approach, IFAC Proc. Vol., 36, 11, 419-424, (2003), 4th IFAC Symposium on Robust Control Design 2003, Milan, Italy, 25-27 June 2003 [11] Yang, F.; Gani, M.; Henrion, D., Fixed-order robust H$${}_\infty$$ controller design with regional pole assignment, IEEE Trans. Automat. Control, 52, 10, 1959-1963, (2007) · Zbl 1366.93165 [12] J.V. Burke, A.S. Lewis, M.L. Overton, A nonsmooth, nonconvex optimization approach to robust stabilization by static output feedback and low-order controllers, in: Proc. IFAC Symp. Robust Control Design, Milan, Italy, 2003. [13] Apkarian, P.; Noll, D., Nonsmooth H$${}_\infty$$ synthesis, IEEE Trans. Automat. Control, 51, 1, 71-86, (2006) · Zbl 1366.93148 [14] J.V. Burke, D. Henrion, A.S. Lewis, M.L. Overton, HIFOO - A MATLAB package for fixed-order controller design and H$${}_\infty$$ optimization, in: 5th IFAC Symposium on Robust Control Design, 2006. [15] Simões, A. M.; Apkarian, P.; Noll, D., Nonsmooth multi-objective synthesis with applications, Control Eng. Pract., 17, 11, 1338-1348, (2009) [16] Apkarian, P., Nonsmooth $$\mu$$ synthesis, Internat. J. Robust Nonlinear Control, 21, 13, 1493-1508, (2011) · Zbl 1227.93043 [17] Yaesh, I.; Shaked, U., H$${}_\infty$$ optimization with pole constraints of static output-feedback controllers - a non-smooth optimization approach, IEEE Trans. Control Syst. Technol., 20, 4, 1066-1072, (2012) [18] Apkarian, P.; Dao, M. N.; Noll, D., Parametric robust structured control design, IEEE Trans. Automat. Control, 60, 7, 1857-1869, (2015) · Zbl 1360.93213 [19] da Silva de Aguiar, R. S.; Apkarian, P.; Noll, D., Structured robust control against mixed uncertainty, IEEE Trans. Control Syst. Technol., PP, 99, 1-11, (2017) [20] Goh, K.-C.; Safonov, M. G.; Ly, J. H., Robust synthesis via bilinear matrix inequalities, Internat. J. Robust Nonlinear Control, 6, 9, 1079-1095, (1996) · Zbl 0861.93015 [21] V. Bompart, P. Apkarian, D. Noll, Non-smooth techniques for stabilizing linear systems, in: 2007 American Control Conference, 2007, pp. 1245-1250. · Zbl 1127.93326 [22] Simões, A. M.; Savelli, D. C.; Pellanda, P. C.; Martins, N.; Apkarian, P., Robust design of a TCSC oscillation damping controller in a weak 500-kv interconnection considering multiple power flow scenarios and external disturbances, IEEE Trans. Power Syst., 24, 1, 226-236, (2009) [23] M.A. Mammadov, R. Orsi, A nonsmooth optimization approach to H$${}_\infty$$ synthesis, in: Proceedings of the 44th IEEE Conference on Decision and Control, 2005, pp. 6893-6898. [24] Zhou, K.; Doyle, J. C.; Glover, K., Robust and optimal control, (1996), Prentice Hall Englewood Cliffs, New Jersey 07632 · Zbl 0999.49500 [25] J. Doyle, Analysis of feedback systems with structured uncertainties, in: IEE Proceedings D - Control Theory and Applications, Vol. 129 (6) 1982, pp. 242-250. [26] Davison, E.; Ramesh, N., A note on the eigenvalues of a real matrix, IEEE Trans. Automat. Control, 15, 2, 252-253, (1970) [27] Gutman, S.; Jury, E., A general theory for matrix root-clustering in subregions of the complex plane, IEEE Trans. Automat. Control, 26, 4, 853-863, (1981) · Zbl 1069.93518 [28] Menezes, E. F.M.; Aguiar, R. S.S.; Simões, A. M.; Apkarian, P., Structured robust controller design via non-smooth mixed $$\mu$$ synthesis, IET Control Theory Appl., 10, 17, 2186-2193, (2016) [29] K.M. Sobel, W. Yu, J.E. Piou, J. Cloutier, R. Wilson, Robust eigenstructure assignment with structured state space uncertainty and unmodelled dynamics, in: 1991 American Control Conference, 1991, pp. 3137-3141. · Zbl 0758.93059 [30] Young, P. M., Controller design with real parametric uncertainty, Internat. J. Control, 65, 3, 469-509, (1996) · Zbl 0857.93029
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