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Time-Discretization of Nonlinear Systems with Delayed Multi-Input Using Taylor Series  

Park, Ji-Hyang (Division of Electronics and Information Engineering Chonbuk National University)
Chong, Kil-To (Division of Electronics and Information Engineering Chonbuk National University)
Nikolaos Kazantzis (Department of Chemical Engineering, Worcester Polytechnic Institute Worceste)
Alexander G. Parlos (Department of Mechanical Engineering Texas A&M University College Station)
Publication Information
Journal of Mechanical Science and Technology / v.18, no.7, 2004 , pp. 1107-1120 More about this Journal
Abstract
This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.
Keywords
Nonlinear System; Time-Discretization; Time-Delay; Multi-Input; Taylor-Series;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
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1 Byeon, K. S. and Song, J. B., 1997, 'Control of Throttle Actuator System based on Time Delay Control,' KSMEA, Vol. 21, No. 12, pp. 2081-2090, in Korea   과학기술학회마을
2 Choi, B. H., Jung, W. J. and Choi, H. R., 1999, 'Study for Control of Master-Slave Teleoperation System with Time Delay,' KSMEA, Vol. 23, No. 1, pp. 57-65, in Korea
3 Hong, K. S. and Wu, J. W., 1994, 'Stability and Coefficients Properties of Polynomials of Linear Discrete Systems,' KSME Int. J., Vol. 8, No. 1, pp. 1-5, in Korea   DOI
4 Jeong, K. W. and Lee, S. H., 1995 'Design of Robust Controller Teleoperated Robot System with Time Delay,' KSME, Vol. 19, No. 12, pp. 3141-3150, in Korea
5 Kazantzis, N. Chong, K. T., Park, J. H. and Parlos, A. G., 2003, 'Control-relevant Discretizaiton of Nonlinear Systems with Time-Delay Using Taylor-Lie Series,' American Control Conference, pp. 149-154
6 Henk Nijmeijer and Arjan van der Schaft, 1990, Nonlinear dynamical control systems. Springer-Verlag, New York
7 Kazantzis, N. and Kravaris, C., 1997, 'System-Theoretic Properties of Sampled-Data Representations of Nonlinear Systems Obtained via Taylor-Lie Series,' Int. J. Control., Vol. 67, pp. 997-1020   DOI
8 Kazantzis, N. and Kravaris, C., 1999, 'Time Discretization of Nonlinear Control Systems via Taylor Methods,' Comp. Chem. Engn., Vol. 23, pp. 763-784   DOI   ScienceOn
9 Choi, J. S. and Baek, Y. S., 2002, 'A Single DOF Magnetic Levitation System using Time Delay Control and Reduced-Order Observer,' KSME Int. J., Vol. 16, No. 12, pp. 1643-1651, in Korea   과학기술학회마을
10 Franklin, G. F., Powell, J. D. and Workman, M. L., 1998, Digital Control of Dynamic Systems, Addison-Wesley, New York
11 Kang, S. J. and Park, K. S., 1999, 'Discretization-Based Analysis of Structural Electrodynamics,' KSME Int. J., Vol. 13, No. 11, pp. 842-850, in Korea   DOI
12 Park, J. H., 2004, 'Discretization of Nonlinear System with Time-Delay via Taylor Series,' M. S. Thesis, Chonbuk National University, Jeon-Ju, Feb, in Korea
13 Svoronos, S. A., Papageorgiou, D. and Tsiligiannis, C., 1994, 'Discretization of Nonlinear Control Systems via the Carleman Linearization,' Chem. Engin. Sci., Vol. 49, pp. 3263-3267   DOI   ScienceOn
14 Vaccaro, R. J., 1995, Digital Control. McGraw-Hill, New York
15 Kwon, O. S., Chang, P. H. and Jung, J. H., 2002, 'Stability Analysis of Time Delay Controller for General Plants,' KSMEA, Vol. 26, No. 6, pp. 1035-1046, in Korea   과학기술학회마을   DOI
16 Vidyasagar, M., 1978, Nonlinear Systems Analysis. Prentice Hall, Englewood Cliffs
17 Lee, J. W. and Chang, P. H., 1999, 'Input/Output Linearization using Time Delay Control and Time Delay Observer,' KSME Int. J., Vol. 13, No. 7, pp. 546-556, in Korea   DOI