Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Robust Stability of Two-Degrees-of-Freedom Servosystem with Stricture and Unstructured Uncertainties

  • Kim, Young-Bok (School of Transport Vechicle Engineering, Gyeongsang National University)
  • Published : 2000.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

A two-degrees-of-freedom servosystem for step-type reference signals has been preposed, in which the integral compensation is effective only when there is a modeling error or a disturbance input. this paper considers robust stability of the servosystem incorporating an observer against both structured and unstructured uncertainties of the plant. A condition is obtained as a linear matrix inequality, under which the servosystem is robustly stable independently of the gain of the integral compensator. This result implies that we can tune the gain to achieve a desirable transient response of the servpsystem preserving robust stability. An example is presented to demonstrate that under the robust stability condition, the transient response can be improved by increasing the gain of the integral compensator.

Keywords

References

  1. Cha I.H., Kweon T.J. and Han C.S., 2000, 'The Design of and Improved PID Controller by Using the Kalman Filter' Trans, of the KSME(A), Vol.24, No.1, pp.7-15
  2. Francis B.A. and Wonham W,M., 1975, 'The Inernal Model Principle for Linear Multivariable Regulators,' J,Applied Mathematics and Optimization, Vol.2, pp.170-194 https://doi.org/10.1007/BF01447855
  3. Fujisaki Y. and Ikeda M., 1991, 'Synthesis of Two-Degree-of Freedom Servosystems' Trans. of the SOCE, Vol.27, No.8, pp.907-914 (in Japanese)
  4. Fujisaki Y. and Ikeda M., 1992, 'Two-Degree-of-Freedom Design of Optimal Servosystems,' Proc.in 31st IEEE CDC, pp.3588-3598
  5. Gahinet P. and Apkarian P., 1994, 'A Linear Matrix Inequality Approach to $H{\infty}$ Control' International Journal of Robust and Nonlinear, Vol.4, pp.421-448 https://doi.org/10.1002/rnc.4590040403
  6. Hagiwara T., Ohtani Y. and Araki M., 1991, 'A Design Method of LQI Servo Systems with Two Degree of Freedom' Trans.of the ISICE, Vol.4, No.12, pp.501-510 (in Japanese)
  7. Hagiwara T., Furutani E. and Araki M., 1994, 'Two-Degree-of-Freedom Design Method of LQI Servo Systems-Performance Deterioration by the Introduction of an Observer Design-' Proc. in 33rd IEEE CDC, pp.4204-4209
  8. Kim Y.B., Ikeda M. and Fujisaki Y., 1995, 'Robust Stability and High-Gain Compensation of a Two-Degree-of-Freedom Desing of Optimal Servosystem', Proc.in 34th IEEE CDC, pp.1431-1436
  9. Kobayashi M., Kim Y.B., Ikeda M. and Fujisaki Y., 1995, 'On Robust Stability of a Two-Degree-of-Freedom Servosystem Incorporating an Observer', 39th Annual Conference of the ISCIE, pp.263-264