# System identification from multiple-trial data corrupted by non-repeating periodic disturbances

Minh Phan; Richard Longman; Soo Lee; Jae-Won Lee

International Journal of Applied Mathematics and Computer Science (2003)

- Volume: 13, Issue: 2, page 185-192
- ISSN: 1641-876X

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topPhan, Minh, et al. "System identification from multiple-trial data corrupted by non-repeating periodic disturbances." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 185-192. <http://eudml.org/doc/207634>.

@article{Phan2003,

abstract = {Iterative learning and repetitive control aim to eliminate the effect of unwanted disturbances over repeated trials or cycles. The disturbance-free system model, if known, can be used in a model-based iterative learning or repetitive control system to eliminate the unwanted disturbances. In the case of periodic disturbances, although the unknown disturbance frequencies may be the same from trial to trial, the disturbance amplitudes, phases, and biases do not necessarily repeat. Furthermore, the system may not return to the same initial state at the end of each trial before starting the next trial. In spite of these constraints, this paper shows how to identify the system disturbance-free dynamics from disturbance-corrupted input-output data collected over multiple trials without having to measure the disturbances directly. The system disturbance-free model can then be used to identify the disturbances as well, for use in learning or repetitive control. This paper represents the first extension of the interaction matrix approach to the multiple-trial environment of iterative learning control.},

author = {Phan, Minh, Longman, Richard, Lee, Soo, Lee, Jae-Won},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {interaction matrix; iterative learning control; disturbance identification; system identification; repetitive control; linear system; multiple-trial approach; periodic disturbances},

language = {eng},

number = {2},

pages = {185-192},

title = {System identification from multiple-trial data corrupted by non-repeating periodic disturbances},

url = {http://eudml.org/doc/207634},

volume = {13},

year = {2003},

}

TY - JOUR

AU - Phan, Minh

AU - Longman, Richard

AU - Lee, Soo

AU - Lee, Jae-Won

TI - System identification from multiple-trial data corrupted by non-repeating periodic disturbances

JO - International Journal of Applied Mathematics and Computer Science

PY - 2003

VL - 13

IS - 2

SP - 185

EP - 192

AB - Iterative learning and repetitive control aim to eliminate the effect of unwanted disturbances over repeated trials or cycles. The disturbance-free system model, if known, can be used in a model-based iterative learning or repetitive control system to eliminate the unwanted disturbances. In the case of periodic disturbances, although the unknown disturbance frequencies may be the same from trial to trial, the disturbance amplitudes, phases, and biases do not necessarily repeat. Furthermore, the system may not return to the same initial state at the end of each trial before starting the next trial. In spite of these constraints, this paper shows how to identify the system disturbance-free dynamics from disturbance-corrupted input-output data collected over multiple trials without having to measure the disturbances directly. The system disturbance-free model can then be used to identify the disturbances as well, for use in learning or repetitive control. This paper represents the first extension of the interaction matrix approach to the multiple-trial environment of iterative learning control.

LA - eng

KW - interaction matrix; iterative learning control; disturbance identification; system identification; repetitive control; linear system; multiple-trial approach; periodic disturbances

UR - http://eudml.org/doc/207634

ER -

## References

top- Amann N., Owens D.H. and Rogers E. (1994): 2D systems theory applied to learning control systems. - Proc. 33-rd Conf. Decision and Control, Lake Buena, Florida.
- Bien Z. and Xu J. (Eds.) (1998): Iterative Learning Control: Analysis, Design, Integration, and Applications. -Boston, MA: Kluwer, pp. 107-146.
- Elci H., Longman R.W., Phan M.Q., Juang J.N. and Ugoletti R. (2002): Simple learning control made practical by zero-phase filtering: Applications to robotics. - IEEE Trans. Circ. Syst., I: Fund. Theory Applic.(Special issue on Multidimensional Signals and Systems), Vol. 49, No. 6, pp. 753-767.
- Franklin G.F., Powell J.D. and Workman M. (1998): Digital Control of Dynamic Systems. - Menlo Park, CA: Addison-Wesley, pp. 535-539.
- Goodzeit N.E. and Phan M.Q. (2000a): System and disturbance identification for feedforward-feedback control applications. - J. Guid. Contr. Dyn., Vol. 23, No. 2, pp. 260-268.
- Goodzeit N.E. and Phan M.Q. (2000b): System identification in the presence of completely unknown periodic disturbances. - J.Guid. Contr. Dyn., Vol. 23, No. 2, pp. 251-259.
- Hsin Y.P., Longman R.W., Solcz E.J. and de Jong J. (1997): Experiments bridging learning and repetitive control.- Adv. Astr. Sci., Vol. 95, pp. 671-690.
- Hsin Y.P., Longman R.W., Solcz E.J. and de Jong J. (1998): A repetitive control law designed to eliminate periodic measurement disturbances. - Adv. Astr. Sci., Vol. 97, pp. 837-849.
- Juang J.-N. (1994): Applied System Identification. -Englewood Cliffs, NJ: Prentice-Hall.
- Juang J.-N. and Phan M. (1994): Identification of system, observer, and controller from closed-loop experimental data. - J. Guid. Contr. Dyn., Vol. 17, No. 1, pp. 91-96. Zbl0800.93266
- Juang J.-N. and Phan M.Q. (2001): Identification and Control of Mechanical Systems. - Cambridge: Cambridge University Press.
- Juang J.-N., Phan M.Q., Horta L.G. and Longman R.W. (1993): Identification of observer Kalman filter Markov parameters: Theory and experiments. - J. Guid. Contr. Dyn., Vol. 16, No. 2, pp. 320-329. Zbl0775.93259
- Lim R.K. and Phan M.Q. (1997): Identification of a multistep-ahead observer and its application to predictive control. - J. Guid. Contr. Dyn., Vol. 20, No. 6, pp. 1200-1206. Zbl0916.93018
- Moore K.L. (1993): Iterative Learning Control for Deterministic Systems. - London: Springer. Zbl0773.93002
- Van Overschee P. and De Moor B. (1996): Subspace Identification For Linear Systems: Theory, Implementation, Applications.- Boston: Kluwer. Zbl0888.93001
- Phan M.Q. and Frueh J.A. (1998): System identification and learning control, In: Iterative Learning Control: Analysis, Design, Integration, and Applications (Z. Bien and J. Xu, Eds.). - Norwell, MA: Kluwer, pp. 285-306.
- Phan M.Q., Juang J.-N., Horta L.G. and Longman R.W. (1994): System identification from closed-loop data with known output feedback dynamics. - J. Guid. Contr. Dyn., Vol. 17, No. 4, pp. 661-669. Zbl0925.93935
- Phan M.Q., Horta L.G., Juang J.-N. and Longman R.W. (1995): Improvement of observerKalman filter identification (OKID) by residual whitening. - J. Vibr. Acoust., Vol. 117, No. 2, pp. 232-238.
- Phan M.Q., Goodzeit N.E. and Juang J.-N. (1997): Identification of system and periodic disturbances. - Proc. ASME Design Engineering Technical Conferences, Sacramento, CA, Paper DETC97VIB-4256.
- Phan M.Q., Juang J.-N. and Longman R.W. (1997): Markov parameters in system identification: Old and new concepts, Chapter 16, In: Structronic Systems: Smart Structures, Devices, and Systems (H.S. Tzou and A. Guran, Eds.). - Singapore: World Scientific, Vol. 2, pp. 263-293.
- Phan M.Q., Lim R.K. and Longman R.W. (1998): Unifying input-output and state-space perspectives of predictive control. - Submitted for publication (pre-print available at http://www.dartmouth.edu/~mqphan).
- Phan M.Q., Juang J.N. and Eure K. (1999): Design of predictive controllers for simultaneous feedback stabilization and disturbance rejection from disturbance-corrupted data. - Proc. 137-th ASA Meeting and the 2nd EAA Convention, Berlin, Germany.
- Tesfaye A., Lee H.S. and Tomizuka M. (1997): Discrete-time design of a disturbance observer for robust motion control systems. - Proc. 2-nd Asian Control Conference, Seoul, Korea, pp. 261-264.

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