Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Time-Discretization of Nonlinear Systems with Time Delayed Output via Taylor Series

  • Yuanliang Zhang (Faculty of Electronics and Information Engineering Chonbuk National University) ;
  • Chong Kil-To (Faculty of Electronics and Information Engineering Chonbuk National University)
  • Published : 2006.07.01
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Abstract

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.

Keywords

References

  1. Cho, H. C. and Park, J. H., 2004, 'Design and Stability Analysis of Impedance Controller for Bilateral Teleoperation under a Time Delay,' KSME International Journal, Vol. 18, No.7, pp. 1131-1139
  2. Choi, J. S. and Baek, Y. S., 2002, 'A Single DOF Magnetic Levitation System using Time Delay Control and Reduced-Order Observer,' KSME International Journal, Vol. 16, No. 12, pp.1643-1651
  3. Franklin, G. F., Powell, J. D. and Workman, M. L., 1998, Digital Control of Dynamic Systems. Addison-Wesley, New York
  4. Germani, A., Manes, C. and Pepe, P., 2002, 'A New Approach to State Observation of Nonlinear Systems with Delayed Output,' Automatic Control, IEEE Transactions, Vol. 47, Issue 1, pp. 96-101 https://doi.org/10.1109/9.981726
  5. Gudvanden, S., 1997, 'A Class of Sliding Fermat Number Transforms that Admit a Tradeoff Between Complexity and Input-Output Delay,' IEEE Transactions on Signal Processing, Vol. 45, No. 12, pp. 3094-3096 https://doi.org/10.1109/78.650272
  6. Higham, N. J., 2004, 'The Scaling and Squaring Method for the Matrix Exponential Revisited,' Numerical Analysis Report 452, Manchester Center for Computational Mathematics
  7. Huang, P. J., Chen, H. M. and Chang, R. C., 2004, 'A Novel Start-Controlled Phase/Frequency Detector for Multiphase-Output Delay-Locked Loops,' 2004 IEEE Asia-Pacific Conference on Advanced System Integrated Circuits (AP-ASIC2004), pp.68-71 https://doi.org/10.1109/APASIC.2004.1349408
  8. Kazantzis, N. and Kravaris, C., 1997, 'System-Theoretic Properties of Sampled-Data Representations of Nonlinear Systems Obtained via Taylor-Lie Series,' Int. J. of Control, Vol. 67, pp. 997 - 1020 https://doi.org/10.1080/002071797223901
  9. 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
  10. Kazantzis, N., Chong, K. T., Park, J. H. and Parlos, A. G., 2003, 'Control-Relevant Discretization of Nonlinear Systems with Time-Delay Using Taylor-Lie Series,' American Control Conference, pp. 149-154 https://doi.org/10.1109/ACC.2003.1238929
  11. Lee, H. and Kim, H., 2003, 'CVT Ratio Control for Improvement of Fuel Economy by Considering Powertrain Response Lag,' KSME International Journal, Vol. 17, No. 11, pp.1725-1731
  12. Park, J. H., Chong, K. T., Kazantzis, N. and Parlos, A. G., 2004a, 'Time-Discretization of Nonlinear Systems with Delayed Multi-Input using Taylor Series,' KSME International Journal, Vol. 18, No.7, pp. 1107-1120
  13. Park, J. H., Chong, K. T., Kazantzis, N. and Parlos, A. G., 2004b, 'Time-Discretization of Non-Affine Nonlinear Systems with Delayed Input using Taylor-Series,' KSME International Journal, Vol. 18, No.8, pp. 1297-1305
  14. Vaccaro, R. J., 1995, Digital Control. McGraw-Hill, New York
  15. Vydyasagar, M., 1978, Nonlinear Systems Analysis, Prentice Hall, Englewood Cliffs, New York
  16. Zhang, Y. and Chong, K. T., 2005, 'Discretization of Nonlinear Systems with Delayed Multi-Input via Taylor Series and Scaling and Squaring Technique,' KSME International Journal, Vol. 19, No. 11, pp. 1975-1987 https://doi.org/10.1007/BF02916490