Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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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)
  • Published : 2004.07.01
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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

References

  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
  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. 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
  4. Franklin, G. F., Powell, J. D. and Workman, M. L., 1998, Digital Control of Dynamic Systems, Addison-Wesley, New York
  5. Henk Nijmeijer and Arjan van der Schaft, 1990, Nonlinear dynamical control systems. Springer-Verlag, New York
  6. 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 https://doi.org/10.1007/BF02953237
  7. 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
  8. 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 https://doi.org/10.1007/BF03184567
  9. 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 https://doi.org/10.1080/002071797223901
  10. Kazantzis, N. and Kravaris, C., 1999, 'Time Discretization of Nonlinear Control Systems via Taylor Methods,' Comp. Chem. Engn., Vol. 23, pp. 763-784 https://doi.org/10.1016/S0098-1354(99)00007-1
  11. 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
  12. 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 https://doi.org/10.3795/KSME-A.2002.26.6.1035
  13. 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 https://doi.org/10.1007/BF03186445
  14. 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
  15. 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 https://doi.org/10.1016/0009-2509(94)00141-3
  16. Vaccaro, R. J., 1995, Digital Control. McGraw-Hill, New York
  17. Vidyasagar, M., 1978, Nonlinear Systems Analysis. Prentice Hall, Englewood Cliffs