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ANZIAM J. 47(EMAC2005) pp.C712--C732, 2007.

Continuous time system identification using subspace methods

Rosmiwati Mohd-Mokhtar

Liuping Wang

(Received 7 November 2005, revised 15 April 2007)

Abstract

System identification is a well known technique for developing mathematical models based on plant input and output data sequences. Models that describe the systems may be in various forms and one of the possibilities is a state space model formulation. The state space mathematical modelling involves vectors and matrices in a unique geometrical framework. It offers the key advantages on providing low parameter sensitivity with respect to perturbation for high order systems and also has shown its ability to present multi-input and multi-output systems with minimal state dimensions. We use a time domain subspace approach in conjunction with Laguerre filters and instrumental variables to develop a mathematical formulation of the state space model for identification of a continuous time system. The method aims at searching for accurate matrices of the state space model to ensure that the constructed model closely mimics the actual system as well as provide information for the purpose of control system design. The subspace identification algorithm provides state space models with better conditioning, improved quality and easily maintainable parametrisation. The algorithm is validated with identification of two systems: a simulated plant, and a magnetic bearing system. For both systems, the computer simulation results demonstrate that the obtained model describes the system closely.

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Authors

Rosmiwati Mohd-Mokhtar

School of Electrical & Computer Engineering, RMIT University, Melbourne, Australia. mailto:rosmiwati@ieee.org, mailto:rosmiwati.mohdmokhtar@student.rmit.edu.au

Liuping Wang

Published June 26, 2007. ISSN 1446-8735

References

1. L. Ljung, System Identification: Theory for the User, Prentice Hall, New Jersey, 1999.
2. G. C. Goodwin, S. T. Graebe and M. E. Salgado, Control System Design, Prentice Hall, New Jersey, 2001.
3. T. McKelvey, H. Akcay and L. Ljung, Subspace-based Multivariable System Identification from Frequency Response Data, IEEE Trans. on Automatic Control, 41(7), 960--979, 1996.
4. T. Gustafsson, M. Lovera and M. H. Verhaegen, A Novel Algorithm for Recursive Instrumental Variable Based Subspace Identification, in Proc. of IEEE Conf. on Decision and Control, 3920--3925, 1998.
5. F. Demourant and G. Ferreres, A Frequency Domain Identification-control Approach for A Flexible Aircraft, in Proc. of IEEE Int. Conf. on Control Applications, 126--137, 2002.
6. B. R. J. Haverkamp, C. T. Chou, M. H. Verhaegen and R. Johansson, Identification of continuous-time MIMO state space models from sampled data in the presence of process and measurement noise, in Proc. of 35th. Conf. on Decision and Control, 1539--1544, 1996.
7. H. Akcay, S. M. Islam and B. Ninnes, Subspace-based identification of power transformer models from frequency response data, IEEE Trans. on Inst. and Measurement, 48(3), 700--704, 1999.
8. H. L. Ari and A. J. Devancy, The time-reversal technique re-interpreted: Subspace-based signal processing for multi-static target location, in Proc. of IEEE on Sensor Array and Multi-channel Signal Processing Workshop, 509--513, 2000.
9. W. Favoreel, B. De Moor and P. Van Overschee, Subspace identification of bilinear systems subject to white inputs, IEEE Trans. on Automatic Control), 44(6), 1157--1165, 1999.
10. H. Kato, S. Wakui, T. Mayama, A. Toukairin, H. Takanashi and S. Adashi, System identification of anti-vibration units in semiconductor exposure apparatus, in Proc. of IEEE Int. Conf. on Control Applications, 1312--1317, 1999.
11. Z.J. Yang, Frequency domain subspace model identification with the aid of the w-operator, in Proc. of the SICE Annual Conf., 1077--1080, 1998.
12. B. J. R. Haverkamp, Subspace Method: Identification, Theory and Practice, Ph.D. Thesis, Faculty of Information Technology and Systems, Delft University, The Netherlands, 2000.
13. L. Wang and W. R. Cluett, From Plant Data to Process Control: Ideas for Process Identification and PID Design, Francis & Taylor, London, 2000.