Design Method for Improvement of Transient-State Intersample Output of Multirate Systems Including Integrators

Tomonori Kamiya; Takao Sato; Nozomu Araki; Yasuo Konishi

doi:10.20965/jrm.2016.p0702

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JRM Vol.28 No.5 pp. 702-706

doi: 10.20965/jrm.2016.p0702

(2016)

Paper:

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Design Method for Improvement of Transient-State Intersample Output of Multirate Systems Including Integrators

Tomonori Kamiya, Takao Sato, Nozomu Araki, and Yasuo Konishi

Graduate School of Engineering, University of Hyogo
2167 Shosha, Himeji, Hyogo 671-2280, Japan

Received:

March 17, 2016

Accepted:

July 28, 2016

Published:

October 20, 2016

Keywords:

multirate system, intersample output, integrator, difference operation

Abstract

This paper discusses a design method for a multirate system including integrators, where the update interval of the control input is shorter than the sampling interval of the plant output. In such a multirate control system, intersample output might oscillate between sampled outputs in the steady state even if the sampled output converges to the reference input. This is because the control input can be updated between the sampled outputs. In a conventional method, a predesigned control law is extended such that the steady-state ripples are eliminated independent of a discrete-time response. However, the conventional method is invalid when integrators are included in a controlled plant. In this study, a difference operation in discrete time is used to address this issue. Moreover, the transient-state intersample response is improved independent of a pre-designed discrete-time response.

Comparison of output responses

Cite this article as:

T. Kamiya, T. Sato, N. Araki, and Y. Konishi, “Design Method for Improvement of Transient-State Intersample Output of Multirate Systems Including Integrators,” J. Robot. Mechatron., Vol.28 No.5, pp. 702-706, 2016.

Data files:

References

[1] M. Araki and T. Hagiwara, “Pole Assignment by Multirate Sampled-data Output Feedback,” Int. J. Control, Vol.44, No.6, pp. 1661-1673, 1986.
[2] T. Chen and B. Francis, “Optimal Sampled-Data Control Systems,” Springer-Verlag, London, 1995.
[3] A. Tangirala, D. Li, R. Patwardhan, S. Shah, and T. Chen, “Issues in Multirate Process Control,” Proc. of American Control Conf., pp. 2771-2775, 1999.
[4] A. Inoue and M. Deng, “An optimal robust controller with multi-rate output feedback by using symbolic computation,” Proc. of the 2014 Int. Conf. on Advanced Mechatronic Systems, pp. 224-228, Luoyang, China, 2013.
[5] H. Werner, “Generalized sampled-data hold functions for robust multivariable tracking and disturbance rejection,” Optimal Control Applications and Methods, Vol.22, pp. 75-93, 2001.
[6] H. Fujioka and S. Hara, “Synthesis of sampled-data Hinfty servo controller with generalized hold,” Proc. of 42nd IEEE CDC, pp. 2302-2307, 2003.
[7] T. Sato, “Parametric Design of Dual-Rate Controller for Improvement in Steady-State Intersample Response,” SICE J. of Control, Measurement, and System Integration, Vol.1, No.4, pp. 329-334, 2008.
[8] B. M. Chen, T. H. Lee, and V. Venkataramanan, “Hard Disk Drive Servo Systems,” Springer, 2002.
[9] A. A. Mamun, G. X. Guo, and B. Bi, “Hard Disk Drive,” Automation and Control Engineering, CRC Press, 2007.
[10] T. Kamiya, T. Sato, N. Araki, and Y. Konishi, “Ripple rejection for a multirate control system including an integrator,” 5th Int. Symposium on Advanced Control of Industrial Processes (ADCONIP 2014), pp. 170-173, 2D.11, Hiroshima, 2014.
[11] A. T. Tangirala, D. Li, R. S. Patwardhan, S. L. Shah, and T. Chen, “Ripple-free conditions for lifted multirate control systems,” Automatica, Vol.37, No.10, pp. 1637-1645, 2001.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] M. Araki and T. Hagiwara, “Pole Assignment by Multirate Sampled-data Output Feedback,” Int. J. Control, Vol.44, No.6, pp. 1661-1673, 1986.

[2] [2] T. Chen and B. Francis, “Optimal Sampled-Data Control Systems,” Springer-Verlag, London, 1995.

[3] [3] A. Tangirala, D. Li, R. Patwardhan, S. Shah, and T. Chen, “Issues in Multirate Process Control,” Proc. of American Control Conf., pp. 2771-2775, 1999.

[4] [4] A. Inoue and M. Deng, “An optimal robust controller with multi-rate output feedback by using symbolic computation,” Proc. of the 2014 Int. Conf. on Advanced Mechatronic Systems, pp. 224-228, Luoyang, China, 2013.

[5] [5] H. Werner, “Generalized sampled-data hold functions for robust multivariable tracking and disturbance rejection,” Optimal Control Applications and Methods, Vol.22, pp. 75-93, 2001.

[6] [6] H. Fujioka and S. Hara, “Synthesis of sampled-data Hinfty servo controller with generalized hold,” Proc. of 42nd IEEE CDC, pp. 2302-2307, 2003.

[7] [7] T. Sato, “Parametric Design of Dual-Rate Controller for Improvement in Steady-State Intersample Response,” SICE J. of Control, Measurement, and System Integration, Vol.1, No.4, pp. 329-334, 2008.

[8] [8] B. M. Chen, T. H. Lee, and V. Venkataramanan, “Hard Disk Drive Servo Systems,” Springer, 2002.

[9] [9] A. A. Mamun, G. X. Guo, and B. Bi, “Hard Disk Drive,” Automation and Control Engineering, CRC Press, 2007.

[10] [10] T. Kamiya, T. Sato, N. Araki, and Y. Konishi, “Ripple rejection for a multirate control system including an integrator,” 5th Int. Symposium on Advanced Control of Industrial Processes (ADCONIP 2014), pp. 170-173, 2D.11, Hiroshima, 2014.

[11] [11] A. T. Tangirala, D. Li, R. S. Patwardhan, S. L. Shah, and T. Chen, “Ripple-free conditions for lifted multirate control systems,” Automatica, Vol.37, No.10, pp. 1637-1645, 2001.