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Practical Design Issues in a Linear Feedback Control System with a Notch Filter

선형 피드백 제어계의 노치필터 설계에 대한 실제적 문제

  • Published : 2010.01.01

Abstract

This paper presents some practical design issues that should be carefully considered when a notch filter is included in a linear feedback controller. A notch filter is generally used to compensate the effects of resonant modes that may result in poor performance. It is very common that the practical engineers prefer to add such a notch filter after having previously designed a feedback controller without the filter. It is known that the resulting performance by this approach is not seriously different from when a feedback controller is designed for a plant previously compensated by a notch filter. However, we will point out that there are some cases where both approaches have different performances. In order to show this, a low-order controller design using the partial model matching method has been applied to a linear time invariant (L Tn model. The results suggest that there is a tendency to achieve much better time responses in terms of reducing the overshoot and shortening the settling time, and in the frequency domain characteristics such as the sensitivity function and the stability margins when the design of a feedback controller after including a notch filter is carried out.

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References

  1. H. Prochazka and I.D. Landau, "Pole Placement with Sensitivity Function Shaping using 2nd order Digital Notch Filters," Automatica, Vol. 39, No.6, pp. 1103-1107, 2003. https://doi.org/10.1016/S0005-1098(03)00067-0
  2. W. Messner and R. Oboe, "Phase Stabilized Design of a Hard Disk Drive Servo using The Complex Lag Compensator," Proc. of the 2004 American Control Conference, Vol. 2, pp. 1165-1170, 2004.
  3. Karl J. Astrom, Bjorn Wittenmark, Computer -Controlled Systems, Prentice-Hall, Third Edition, pp. 208-213, 1997.
  4. P. Katz, Digital Control using Microprocessors, Prentice Hall International, pp. 216-238, 1981.
  5. C.H. Cai, Z.Y. Xu, W.B. Xu and B. Feng; "Notch Filter Feedback Control in A Class of Chaotic Systems," Automatica, Vol. 38, pp. 695-701, 2002. https://doi.org/10.1016/S0005-1098(01)00239-4
  6. Lihua Jin and Y.C. Kim, "Fixed, low-order controller design with time response specifications using non-convex optimization," ISA Transactions, Vol. 47, pp. 429-438, 2008. https://doi.org/10.1016/j.isatra.2008.05.001
  7. G.F. Franklin, J.D. Powell, and A. Emani-Naeini, Feedback Control of Dynamic Systems, Addison -Wesley, Fifth Edition, pp. 579-587, 2006.
  8. Y.C. Kim, L.H. Keel, and S.P. Bhattacharyya, "Transient Response Control via Characteristic Ratio Assignment," IEEE Trans. on Automatic Control, Vol. 48, No. 12, pp. 2238-2244, 2003. https://doi.org/10.1109/TAC.2003.820153
  9. L.H. Keel, Y.C. Kim, and S.P. Bhattacharyya, "Ch.6 Transient response control via characteristic ratio assignment," in Lecture note of the 17th IFAC World Congress Tutorial Workshop: Advances in Three Term Control, Seoul, July, 2008.
  10. R.H. Middleton and S.F. Graebe, "Slow Stable Open-Loop Poles: to Cancel or Not to Cancel," Automatica, Vol. 35, No 5, pp. 877-886, 1999. https://doi.org/10.1016/S0005-1098(98)00220-9