Browse > Article

Robust Controller Design of Non-Square Linear Systems and Its Applications  

Son Young-Ik (동아대 공대 전기전자컴퓨터공학부)
Shim Hyungbo (한양대 공대 전기전자컴퓨터공학부)
Jo Nam-Hoon (숭실대 공대 전기제어시스템공학부)
Publication Information
The Transactions of the Korean Institute of Electrical Engineers D / v.52, no.4, 2003 , pp. 189-197 More about this Journal
Abstract
The problem of designing a parallel feedforward compensator (PFC) is considered for a class of non-square linear systems such that the closed-loop system is strictly passive. If a given square system has (vector) relative degree one and is weakly minimum phase, the system can be rendered passive by a state feedback. However, when the system states are not always measurable and the given output is considered, passivation (i.e. rendering passive) of a non-minimum phase system or a system with high relative degree cannot be achieved by any other methodologies except by using a PFC. To passivate a non-square system we first determine a squaring gain matrix and design a PFC such that the composite system has relative degree one and is minimum phase. Then the system is rendered strictly passvie by a static output feedback law. Necessary and sufficient conditions for the existence of the PFC and the squaring gain matrix are given by the static output feedback formulation, which enables to utilize linear matrix inequality (LMI). As an application of the scheme, an alternative way of replacing the role of velocity measurements is provided for the PD-control law of a convey-crane system.
Keywords
Non-square System; (Feedback) Passivity; Parallel Feedforward Compensation; Static Output Feedback;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 C.I. Byrnes, A. Isidori, J.C. Willems, 'Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems,' IEEE Trans. Automat. Contr., vol. 36, no. 11, pp. 1228-1240, 1991   DOI   ScienceOn
2 H.K. Khalil, Nonlinear Systems, Prentice-Hall, 2nd Ed., 1996
3 R. Sepulchre, M. Jankovic, P.V. Kokotovic, Constructive Nonlinear Control, Springer-Verlag, 1997
4 R. Ortega, A. Loria, P.J. Nicklasson, H. Sira-Ramirez, Passivity-based Control of Euler-Lagrange Systems, Springer-Verlag, 1998
5 A.G. Kelker and S.M. Joshi, 'Robust control of non-passive systems via passification', In Proc. of ACC, 1997   DOI
6 Young I. Son, Hyungbo Shim, Jin H. Seo, 'Passification of nonlinear systems via dynamic output feedback', Journal of KIEE, pp. 23-28, 2000
7 Hyungbo Shim and Jin H. Seo, 'Passivity framework for nonlinear state observer', In Proc. of ACC, pp. 699-705, 2000   DOI
8 I. Bar-Kana, 'Parallel feedforward and simplified adaptive control,' Int. J. Adaptive Control and Signal Processing, vol. 1, no. 2, 95-109, 1987   DOI
9 A.L. Fradkov and D.J. Hill, 'Exponential feedback passivity and stabilizability of nonlinear systems,' Automatica, vol. 34, no. 6, pp. 697-703, 1998   DOI   ScienceOn
10 W. Sun, P.P. Khagonekar, and D. Shim, 'Solution to the positive real control problem for linear time-invariant systems,' IEEE Trans. Automat. Contr., vol. 39, pp. 2034-2046, 1994   DOI   ScienceOn
11 C.-H. Huang, P.A. Ioannou, J. Maroulas, and M.G. Safonov, 'Design of strictly positive real systems using constant output feedback,' IEEE Trans. Automat. Contr., vol. 44, no. 3, pp. 569-573, 1999   DOI   ScienceOn
12 J.C. Geromel, P.L.D. Peres, S.R. Souza, 'Convex analysis of output feedback control problems: robust stability and performance,' IEEE Trans. Automat. Contr., vol. 41, no. 7, pp. 997-1003, 1996   DOI   ScienceOn
13 H. Kaufman, I. Bar-Kana, and K. Sobel, Direct Adaptive Control Algorithms, Springer-Verlag, 2nd Ed., 1998
14 A. Saberi and P. Sannuti, 'Squaring down by static and dynamic compensators', IEEE Trans. Automat. Contr., vol. 33, no. 4, pp. 358-365, 1988   DOI   ScienceOn
15 Z. Iwai and I. Mizumoto, 'Realization of simple adaptive control by using parallel feedforward compensator,' Int. J. Control, vol. 59, no. 6, pp. 1543-1565, 1994   DOI   ScienceOn
16 M. Deng, Z. Iwai, I. Mizumoto, 'Robust parallel compensator design for output feedback stabilization of plants with structured uncertainty, Systems & Control Letters, vol. 36, pp. 193-198, 1999   DOI   ScienceOn
17 P. Akella and J.T. Wen, 'Synthesized passive feedback control of sensor-rich structures,' In Proc. of ACC, pp. 2652-2656, 1997   DOI
18 Y. Kawasaki, I. Mizumoto, R. Wakamiya, and Z. Iwai, 'Adaptive control of an inverted pendulum system,' In Proc. of Asia-Pacific Vibration Conference'93, Japan, vol. 3, pp. 1114-1119, 1993
19 F.C. Lee, H. Flashner, and M.G. Safonov, 'Positivity embedding for noncolocated and nonsquare flexible structures,' In Proc. of ACC, pp. 267-271, 1994   DOI
20 J. Collado, R. Lozano, and I. Fantoni, 'Control of convey-crane based on passivity,' In Proc. of ACC, pp. 1260-1264, 2000   DOI
21 V. Kuvcera and C.de Souza, 'A necessary and sufficient condition for output feedback stabilizability,' Automatica, vol. 31, no. 9, pp. 1357-1359, 1995   DOI   ScienceOn
22 Y.-Y. Cao, J. Lam, and Y.-X. Sun, 'Static output feedback stabilization: an ILMI approach,' Automatica, vol. 34, no. 12, pp. 1641-1645, 1998   DOI   ScienceOn
23 C.A.R. Crusius and A. Trofino, 'Sufficient LMI conditions for output feedback control problems,' IEEE Trans. Automat. Contr., vol. 44, no. 5, pp. 1053-1057, 1999   DOI   ScienceOn
24 Z.P. Jiang and D.J. Hill, 'Passivity and disturbance attenuation via output feedback for uncertain nonlinear systems,' IEEE Trans. Automat. Contr., vol. 43, no. 7, pp. 992-997, 1998   DOI   ScienceOn