簡易檢索 / 詳目顯示

回結果列表
研究生： 李澤漢
Lee, Cheh-Han
論文名稱： 雙線性系統識別
Bilinear system identification
指導教授： 莊哲男
Juang, Jer-Nan
學位類別： 博士
Doctor
系所名稱： 工學院 - 工程科學系
Department of Engineering Science
論文出版年： 2013
畢業學年度： 102
語文別： 英文
論文頁數： 119
中文關鍵詞： 系統識別 、雙線性系統 、非線性系統 、試驗系統建模
外文關鍵詞： system identification, bilinear system, nonlinear system, experimental system modeling
相關次數： 點閱：151  下載：5 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 系統識別利用系統之輸入訊號與輸出訊號間的關係，運用一定之程序建立系統模
    式。使用系統識別方法所建立之系統模式可精確地運用於及時控制或離線之控制設計領域。對線性非時變系統來說，現有系統識別方法已經發展的十分成熟。然而，各種自然、物理現象事實上都是非線性系統，因此發展非線性系統識別、對建立非線性系統的認知是相當重要的課題。
    雙線性系統是介於線性系統與廣義非線性系統間一種特殊的非線性系統模式，雙
    線性系統異於線性系統的是這類系統在原有線性系統模式外，加入了系統狀態與控制輸入的耦合項，因此雙線性系統可視為一種最簡單的非線性系統。雖然雙線性系統之組成單純，然而許多的物理、生物及經濟現象都可以這類模式來呈現。同時，一定類別的非線性系統可經過雙線性化後，以雙線性系統作為這類系統的簡化模式，也因此廣泛的提升了雙線性系統的運用範圍。
    莊哲男教授在2005 年發表的雙線性識別論文首度運用一系列不同脈衝的多次試
    驗方式，成功發展了無雜訊情形下雙線性系統的狀態空間精確的(exact) 系統識別方法。然而建立於多次試驗的系統識別方法是一種相對高成本、耗時的建模方式，因此本文嘗試結合現有的線性系統識別技術、雙線性系統的基本結構理論以及前述莊老師研究之基礎發展單一試驗的雙線性系統識別方法。本文描述的系統識別方法基於已發表或被接受發表的研究論文，僅運用單一試驗的雙線性系統識別方法大幅改善了多次試驗方式的缺點，提升了雙線性系統識別實際運用的可行性。

    System identification is the problem of building a dynamic system model from designed input and measured output data. Usually such an approach yields accurate-enough models and is often used by control area for the on/off-line applications. Methods for realizing linear time invariant (LTI) models of dynamical systems have been developed, but real world phenomena are always nonlinear in nature. Therefore, much work remains to be done to realize nonlinear models that represent the majority of physical systems.
    A special class, bilinear systems, exist as a gateway between the worlds of linear systems and of nonlinear systems. A bilinear plant model constituting a state and control-input coupling term in addition to a linear term forms the simplest model of nonlinear systems. In spite of their simple form, bilinear systems are widely applied to engineering, biology and economics. Indeed, the continuous-time bilinear system model is a universal approximater for a class of nonlinear systems and bi-linearizion procedures for nonlinear systems has widen the range of application of bilinear systems.
    In 2005, Juang presented a method using a combination of pulses via multiple experiments to identify the bilinear state-space matrices exactly for noise-free data, but multiple experiments usually consume money and time. Based on realization problem of LTI systems, the basic structure theory of continuous-time bilinear systems, and the above mentioned Juang's research results, this dissertation presents a series of methods to identify bilinear systems by a single experiment, which significantly advances the original version toward the real-time/on-line applications.

    摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 誌謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Continuous-time bilinear systems: An overview for system identification . . . . . . . . . . . 5 2.1 Basic system equations and classification of bilinear systems . . . . . . . . . . . . . . . 6 2.2 Reachability, observability, and assumptions . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Bi-linearize procedure for a nonlinear system . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Carleman linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Example of Euler's equation for rigid body rotation . . . . . . . . . . . . . . . . . . . 15 3 Continuous-time bilinear system identification using single experiment with multiple pulses . 19 3.1 Preliminary equations for system identification . . . . . . . . . . . . . . . . . . . . . . 20 3.2 SEMP identification method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2.1 Step 1: Identification of C and Ac . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.2 Step 2: Identification of Ai and bi . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.3 Step 3: Identification of x(0) and D . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.4 Step 4: Identification of Nc and Bc . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 ISEMP identification method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.1 Step 1: Identification of C and Ac . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3.2 Step 2: Identification of Ai and bi . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.3 Step 3: Identification of x(0) and D . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.4 Step 4: Identification of Nc and Bc . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4 System identification for a general class of observable and reachable bilinear systems . . . 39 4.1 Basic formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1 System equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.2 Specific input sequence definition and preliminary equations for identification . . . . . 44 4.2 SEARIS identification method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.1 Identification of C0, Xk, and Ac|wi . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.2 Coordinate transformation and identification of Ac, Nc, and C . . . . . . . . . . . . . . 52 4.2.3 Identification of system state, Bc, and D . . . . . . . . . . . . . . . . . . . . . . . . 55 5 Deterministic Bilinear System Identification . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 Bilinear system models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.2.1 Continuous-time model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.2.2 Discrete-time model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2.3 General discrete-time LTV model in block form31 . . . . . . . . . . . . . . . . . . . . . 61 5.3 System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.3.1 Input sequence design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.3.2 Preliminary equations for identification . . . . . . . . . . . . . . . . . . . . . . . . 65 5.3.3 Identification of system matrices related to the state vector . . . . . . . . . . . . . . 68 5.3.4 Identification of system matrices related to input only . . . . . . . . . . . . . . . . . 72 6 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.1 Automobile breaking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.2 Induction motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.3 A simple nonlinear system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.4 Euler's equation of rigid body rotation identified by ISEMP method . . . . . . . . . . . . 93 6.5 Bilinear system of homogeneous in the input . . . . . . . . . . . . . . . . . . . . . . . . 98 6.6 Euler's equation of rigid body rotation identified by SEARIS method . . . . . . . . . . . 100 6.7 Numerical results of DBSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.7.1 Example of DBS model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.7.2 Example of DBS model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.7.3 Example of CBS model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.7.4 Bilinearized approximation of Euler's equation of rigid body rotation . . . . . . . . . 106 7 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

    [1] Aganović, Z., and Gajić, Z. Linear Optimal Control of Bilinear Systems. Lecture Notes in Control and Information Sciences, vol. 206. London: Springer-Verlag London Limited, 1995.
    [2] Brewer, J., Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems, 25, pp. 772-781, 1978.
    [3] Brockett, R., Lie algebras and Lie groups in control theory. In Geometric Methods in Systems Theory, D. Q. Mayne and R. W. Brockett eds., Reidel Pub. Co., pp. 17-56, 1973.
    [4] Bruni, C., DiPillo, G., and Koch, G., On the Mathematical Models of Bilinear Systems, Ricerche Di Automatica, 2 (1), pp. 11-26, 1971.
    [5] Bruni, C., DiPillo, G., and Koch, G., Bilinear Systems: An Appealing Class of Nearly Linear Systems in Theory and Application, IEEE Transaction Automatic Control, AC-19, pp. 334-348, 1974.
    [6] Čelikovský, S. and Vaněček, J. C., Bilinear systems and chaos. Kybernetika (Prague), 30, 1994, pp. 403-424.
    [7] Chen, C.T., Linear System Theory and Design, 3rd Ed., Oxford University Press, 1999.
    [8] Chen, H. and Maciejowski, J., Subspace Identification of Deterministic Bilinear Systems, Proceedings of the American Control Conference, Chicago, IL, USA, 2000.
    [9] Cheng, B. and Hsu, N.-S., Analysis and parameter estimation of bilinear systems via block-pulse functions. International Journal of Control, 36, pp. 53-65, 1982.
    [10] Dai, H. and Naresh, K. S., Robust identification of systems using block-pulse functions. IEE Proceedings Part D: Control Theory and Applications, 139, pp. 308-316, 1992.
    [11] Daniel-Berhe, S. and Unbehauen, H., Bilinear continuous-time systems identification via Hartley-based modulating functions. Automatica 34, pp. 499-503, 1998.
    [12] Daniel-Berhe, S. and Unbehauen H., State space identification of bilinear continuous-time canonical systems via batch scheme Hartley modulating functions approach. In Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, pp. 4482-4487, December 1998.
    [13] Elliott, D. L., Bilinear Systems, in Encyclopedia of Electrical Engineering, Vol. II John Webster (ed.), John Wiley and Sons, New York, pp. 308-323, 1999.
    [14] Favoreel, W., De Moor, B., and Van Overschee, P., Subspace Identification of Bilinear Systems Subject to White Inputs, IEEE Transactions on Automatic Control, 44(6), pp. 1157-1165, 1999.
    [15] Grasselli, O. M. and Isidori, A., Deterministic state reconstruction and reachability of bilinear processes, Proceedings of IEEE joint automatic control conference, San Francisco, CA., pp. 1423-1427, June 1977.
    [16] Hara, S. and Furuta, K., Observability for bilinear systems. International Journal of Control 26(4), pp. 559-572, 1977.
    [17] Hermann, R., and Krener, A. J., Nonlinear controllability an observability, IEEE Trans. Aotom. Control, AC-22, pp. 728-740, 1977.
    [18] Hostetter, G. H., Digital Control System Design, Holt, Rinehart and Winston, Inc., New York, 1988.
    [19] Hwang, C. and Chen, M. Y., Analysis and parameter identification of bilinear systems via shifted Legendre polynomials. International Journal of Control, 44, pp. 351-362, 1986.
    [20] Isidori, A. and Ruberti, A., Realization theory of bilinear systems. In D. Q. Mayne and R. W. Brockett (Eds.), Geometric Methods in System Theory, pp. 83-130. Dordrecht, The Netherlands: D. Reidel Publishing Company. ISBN 90-277-0415-5, 1973.
    [21] Jha, A. N., Saxena, A. S., and Rajamani, V. S., Parameter estimation algorithms for bilinear and non-linear systems using Walsh functions: Recursive approach. International Journal of Systems Science 23, pp. 283-290, 1992.
    [22] Juang, J.-N., Applied System Identification, Prentice Hall, New Jersey, 1994.
    [23] Juang, J.-N., Continuous-Time Bilinear System Identification, Nonlinear Dynamics, Kluwer Academic Publishers, Special Issue 39(1-2), pp. 79-94, January 2005.
    [24] Juang, J.-N., Generalized Bilinear System Identification, The Journal of the Astronautical Sciences, January issue 2009.
    [25] Juang, J.-N. and Lee, C.-H., Continuous-time Bilinear System Identification using Single Experiment with Multiple Pulses, Nonlinear Dynamics, Vol. 69, No. 3, pp. 1009-1021, 2012, DOI: 10.1007/s11071-011-0323-9.
    [26] Juang, J-N. and Phan, M. Q., Identification and Control of Mechanical Systems, Cambridge University Press, New York, 2001.
    [27] Juang, J. N., Cooper, J. E., and Wright, J. R., An Eigensystem Realization Algorithm Using Data Correlations (ERA/DC) for Modal Parameter Identification, Journal of Control Theory and Advanced Technology, Vol. 4, No. 1, pp. 5-14, March 1988.
    [28] Juang, J. N., and Pappa, R. S., Effect of Noise on Modal Parameters Identified by the Eigensystem Realization Algorithm, Journal of Guidance, Control, and Dynamics, Vol. 9, No. 3, pp. 294-303, May-June 1986.
    [29] Juang, J.-N., Phan, M., Horta, L. G., and Longman, R. W., ”Identification of Observer/Kalman Filter Markov Parameters: Theory and Experiments,” Journal of Guidance, Control and Dynamics, Vol. 16, No. 2, pp. 320-329, Mar-Apr 1993.
    [30] Karanam, V. R., Frick, P.A, and Mohler, R. R., Bilinear system identification by Walsh functions. IEEE Transactions on Automatic Control, 23, pp. 709-713, 1973.
    [31] Kamen, E. W., Block-form observers for linear time-varying diecrete-time systems, Proceedings of the 32nd Conference on Decision and Control, pp. 355-356, 1993.
    [32] Karray, F. and Dwyer, T.A.W., III, On the nonlinear system identification of a class of bilinear dynamical models, Proceedings of the 30th IEEE Conference on Decision and Control, vol.1 , pp. 778-782, 1991.
    [33] Karray, F.; Dwyer, T. and Makrakis, D., Bilinear approximation and identification for nonlinear system modeling, Proceedings of the 35th IEEE Conference on Decision and Control, vol.1, pp. 1088-1093, 1996.
    [34] Kučera, J., Solution in large of control problem x’ = (A(1-u)+Bu)x. Czechoslovak Math. J, vol. 16, pp. 600-623, 1966.
    [35] Kučera, J., Solution in large of control problem x’ = (Au + Bv)x. Czechoslovak Math. J, vol. 17, pp. 91-96, 1967.
    [36] Kučera, J., On accessibility of bilinear systems., Czechoslovak Math. J, vol. 20, pp. 160-168, 1970.
    [37] Kvaternik, R. G., and Silva, W. A., A Computational Procedure for Identifying Bilinear Representations of Nonlinear Systems Using Volterra Kernels, NASA/TM-2008-215320, NASA Langley Research Center, Hampton, Virginia, June 2008.
    [38] Lee, C.-H. and Juang, J.-N., System Identification for A General Class of Observable and Reachable Bilinear, Journal of Vibration and Control published online 12 April 2013, DOI: 10.1177/1077546312473768.
    [39] Lee, C.-H. and Juang, J.-N., Nonlinear System Identification - A Continuous-Time Bilinear State Space Approach, The Journal of the Astronautical Sciences, Vol. 59, Nos. 1 & 2, pp. 409-431, January-June 2012.
    [40] Lee, C.-H. and Juang, J.-N., Deterministic Bilinear System Identification, The Journal of the Astronautical Sciences, Accepted.
    [41] Liu, C. C. and Shih, Y. P., Analysis and parameter estimation of bilinear systems via Chebyshev polynomials. Journal of the Franklin Institute, 317, pp. 373-382, 1984.
    [42] Lo, J. T.-H., Global Bilinearization of Systems with Control Appearing Linearly. SIAM J. Control Volume 13, Issue 4, pp. 879-885, 1975.
    [43] Majji, M., Juang, J.-N., and Junkins, J. L., Continuous-Time Bilinear System Identification Using Repeated Experiments, the AAS/AIAA Astrodynamics Specialist Conference, Pittsburgh, Pennsylvania, August 9-13, 2009.
    [44] Majji, M., Juang,J.-N., Junkins, J. L., Observer/Kalman-Filter Time-Varying System Identification, Journal of Guidance, Control, and Dynamics, Vol. 33, No. 3, pp. 13-28, 2010.
    [45] Majji, M., Juang, J.-N., and Junkins, J. L., Observer/Kalman Filter Time Varying System Identification, Journal of Guidance, Control, and Dynamics, Vol. 33, No. 3, pp. 887-900, 2010.
    [46] http://www.mathworks.com/access/helpdesk/help/techdoc/ref/colon.html (accessed 27 October 2013).
    [47] Mohler, R. R., Bilinear control processes: with applications to engineering, ecology, and medicine, New York, Academic Press, 1973.
    [48] Mohler, R. R., and Kolodziej, W. J., An Overview of Bilinear System Theory and Applications, IEEE Transactions on Systems, Man and Cybernetics, SMC-10, pp. 683-688, 1980.
    [49] Mohler, R. R., Nonlinear Systems: Vol. II, Applications to Bilinear Control, Prentice-Hall, New Jersey, 1991.
    [50] Paraskevopoulos, P., Tsirikos, A., and Arvanitis, K., A new orthogonal series approach to state space analysis of bilinear systems, IEEE Transactions on Automatic Control, 39, pp. 793-797, 1994.
    [51] Phan, M. Q. and Celik, H., A Superspace Method for Discrete-Time Bilinear Model Identification by Interaction Matrices, Paper AAS 10-330, Proceedings of the Kyle T. Alfriend Astrodynamics Symposium, Monterey, CA, May 2010.
    [52] Mohler, R. R. and Rink, R. E., Multivariable bilinear system control. In Advances in Control Systems, C. T. Leondes, Ed. New York: Academic Press, vol. 2, 1966.
    [53] Rugh, W. J., Nonlinear System Theory: The Volterra/Wiener Approach. Baltimore, Maryland: The John Hopkins University Press. ISBN 0-8018-2549-0, 1981.
    [54] Santina, M. S., Stubberud, A. R., Hostetter, G. H., Digital Control System Design, Oxford University Press, Second Edition, 1995.
    [55] Sen, P., On the choice of input for observability in bilinear systems, IEEE Transactions on Automatic Control, 26, pp. 451-454, 1981.
    [56] Sontag, E. D., Wang, Y., Megretski, A., Input Classes for Identification of Bilinear Systems, IEEE Transactions on Automatic Control, 54, pp. 195-207, 2009.
    [57] Svoronos, S., Stephanopoulos, G. and Aris, R., Bilinear approximation of general non-linear dynamic systems with linear inputs. International Journal of Control 31(1), pp. 109-126, 1980.
    [58] Van Overschee, P. and De Moor, B. , N4SID: Subspace Algorithms for the Identification of Combined Deterministic and Stochastic Systems, Automatica, vol. 30, no. 1, pp. 75-93, 1994.
    [59] Verdult, V., Nonlinear System Identification: A State-Space Approach, PhD thesis, University of Twente, Faculty of Applied Physics, Enschede, The Netherlands, 2002.
    [60] Verhaegen, M., Identification of the Deterministic Part of MIMO State Space Models Given in Innovations Form From Input-output Data, Automatica, vol. 30, no. 1, pp. 61-74, 1994.
    [61] Verhaegen, M and V. Verdult, Filtering and System Identification: A Least Squares Approach, Cambridge University Press, 2007.
    [62] Williamson, D., Observation of bilinear systems with application to biological control, Automatica, 13, pp. 243-254, 1977.

    下載圖示 校內：立即公開
    校外：立即公開
    QR CODE