Implementation of Fixed-Point Control Algorithms Based on the  Modified Delta Operator and Form for Intelligent Systems

Tatsu Aoki

doi:10.20965/jaciii.2007.p0709

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JACIII Vol.11 No.6 pp. 709-714

doi: 10.20965/jaciii.2007.p0709

(2007)

Paper:

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Implementation of Fixed-Point Control Algorithms Based on the Modified Delta Operator and Form for Intelligent Systems

Tatsu Aoki

Monozukuri Department, Tokyo Metropolitan College of Industrial Technology, 1-10-40 Higashi-Ohi, Shinagawa-ku, Tokyo 140-0011, Japan

Received:

January 15, 2007

Accepted:

March 19, 2007

Published:

July 20, 2007

Keywords:

digital control, delta operator, fixed-point arithmetic, PID control, simple adaptive control

Abstract

The methodology we propose for realizing energy- and space-saving adaptive control algorithms is based on pulse width modulation (PWM) with a modified delta operator. The dynamic calculation range is at least twice that of the conventional range, making it very useful in embedded real-time intelligent and micromechatronic systems because complex control algorithms can be implemented in fixed-point arithmetic with short words. Simulation results for PID control and simple adaptive control demonstrate the practicality and effectiveness of our proposal.

Cite this article as:

T. Aoki, “Implementation of Fixed-Point Control Algorithms Based on the Modified Delta Operator and Form for Intelligent Systems,” J. Adv. Comput. Intell. Intell. Inform., Vol.11 No.6, pp. 709-714, 2007.

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References

[1] N. Sureshbabu, B. K. Powell, and M. T. Dunn, “An Integrated Procedure for Fixed-Point Control Implementation,” Proc. of the 1998 American Control Conference, Vol.5, pp. 3096-3100, 1998.
[2] K. Kaneko, F. Kanehiro, S. Kajita, K. Yokoyama, K. Akachi, T. Kawasaki, S. Ota, and T. Isozumi, “Design of Prototype Humanoid Robotics Platform for HRP,” Proc. of the 2002 IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, pp. 2431-2436, 2002.
[3] S. Guccione and G. Muscato, “The Wheeleg Robot –Control Strategies, Comuting Architectures, and Experimental Results of the Hybrid Wheeled/Legged Robot–,” IEEE Robotics & Automation Magazine, Vol.10, No.4, pp. 33-43, 2003.
[4] S. Guccione and G. Muscato, “A True Walking Robot for the Comparative Study of Walking Machine Techniques,” IEEE Robotics & Automation Magazine, Vol.10, No.4, pp. 23-32, 2003.
[5] R. C. Agarwal and C. S. Burrus, “New recursive digital filter having very low sensitivity and round-off noise,” IEEE Trans. CAS, Vol.22, No.12, pp. 921-927, 1971.
[6] R. M. Goodall, “High-speed digital controllers using an 8bit microprocessor,” Software & Microsystems, Vol.4, No.5/6, pp. 246-250, 1985.
[7] R. H. Middleton and G. C. Goodwin,“Improved finite word length characteristics in digital control using delta operators,” IEEE Trans. on Automatic Control, Vol.31, No.11, pp. 1015-1021, 1986.
[8] R. M. Goodall, “Minimization of computation for digital controllers,” Trans. Inst MC, Vol.11, No.5, pp. 218-224, 1989.
[9] R. M. Goodall, “The delay operator z^-1 – inappropriate for use in recursive digital filters?” Trans. Inst MC, Vol.12, No.5, pp. 246-250, 1990.
[10] R. H. Middleton and G. C. Goodwin, “Digital Estimation and Control: A Unified Approach,” New Jersey:Prentice-Hall, 1990.
[11] G. C. Goodwin, R. H. Middleton, and H. V. Poor, “High-Speed Digital Signal Processing and Control,” Proc. The IEEE, Vol.80, No.2, pp. 240-259, 1992.
[12] T. Aoki and Y. Furukawa, “Proposal of Modified Delta Operation with V. M. M. and its Application to Controlling Algorithm in Fixed-Point Arithmetic,” Proc. of Fourth Int. Conf. Control, Automation, Robotics and Vision (ICARCV’96), pp. 2356-2360, 1996.
[13] T. Aoki, N. Moronuki, and Y. Furukawa, “A study on Controlling Algorithm to Realize High-Speed & High-Accuracy Control Systems –Proposal of Modified Delta Operator–,” J. of Robotics and Mechatronics, Vol.9, No.6, pp. 446-454, 1997.
[14] T. Aoki, “Implementation of Modified Delta Form for Microprocessors using Fixed-Point Arithmetic,” Proc. of the 1999 American Control Conference, Vol.5, pp. 4056-4060, 1999.
[15] K. Sobel, H. Kaufman, and L. Mebius, “Implicit Adaptive Control for a Class of MIMO Systems,” IEEE Trans. Aerospace & Electron. Syst., Vol.18, No.5, pp. 576-590, 1982.
[16] H. Kaufman, I. Barkana, and K. Sobel, “Direct adaptive control algorithms 2/e,” Springer, 1998.

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

[1] [1] N. Sureshbabu, B. K. Powell, and M. T. Dunn, “An Integrated Procedure for Fixed-Point Control Implementation,” Proc. of the 1998 American Control Conference, Vol.5, pp. 3096-3100, 1998.

[2] [2] K. Kaneko, F. Kanehiro, S. Kajita, K. Yokoyama, K. Akachi, T. Kawasaki, S. Ota, and T. Isozumi, “Design of Prototype Humanoid Robotics Platform for HRP,” Proc. of the 2002 IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, pp. 2431-2436, 2002.

[3] [3] S. Guccione and G. Muscato, “The Wheeleg Robot –Control Strategies, Comuting Architectures, and Experimental Results of the Hybrid Wheeled/Legged Robot–,” IEEE Robotics & Automation Magazine, Vol.10, No.4, pp. 33-43, 2003.

[4] [4] S. Guccione and G. Muscato, “A True Walking Robot for the Comparative Study of Walking Machine Techniques,” IEEE Robotics & Automation Magazine, Vol.10, No.4, pp. 23-32, 2003.

[5] [5] R. C. Agarwal and C. S. Burrus, “New recursive digital filter having very low sensitivity and round-off noise,” IEEE Trans. CAS, Vol.22, No.12, pp. 921-927, 1971.

[6] [6] R. M. Goodall, “High-speed digital controllers using an 8bit microprocessor,” Software & Microsystems, Vol.4, No.5/6, pp. 246-250, 1985.

[7] [7] R. H. Middleton and G. C. Goodwin,“Improved finite word length characteristics in digital control using delta operators,” IEEE Trans. on Automatic Control, Vol.31, No.11, pp. 1015-1021, 1986.

[8] [8] R. M. Goodall, “Minimization of computation for digital controllers,” Trans. Inst MC, Vol.11, No.5, pp. 218-224, 1989.

[9] [9] R. M. Goodall, “The delay operator z^-1 – inappropriate for use in recursive digital filters?” Trans. Inst MC, Vol.12, No.5, pp. 246-250, 1990.

[10] [10] R. H. Middleton and G. C. Goodwin, “Digital Estimation and Control: A Unified Approach,” New Jersey:Prentice-Hall, 1990.

[11] [11] G. C. Goodwin, R. H. Middleton, and H. V. Poor, “High-Speed Digital Signal Processing and Control,” Proc. The IEEE, Vol.80, No.2, pp. 240-259, 1992.

[12] [12] T. Aoki and Y. Furukawa, “Proposal of Modified Delta Operation with V. M. M. and its Application to Controlling Algorithm in Fixed-Point Arithmetic,” Proc. of Fourth Int. Conf. Control, Automation, Robotics and Vision (ICARCV’96), pp. 2356-2360, 1996.

[13] [13] T. Aoki, N. Moronuki, and Y. Furukawa, “A study on Controlling Algorithm to Realize High-Speed & High-Accuracy Control Systems –Proposal of Modified Delta Operator–,” J. of Robotics and Mechatronics, Vol.9, No.6, pp. 446-454, 1997.

[14] [14] T. Aoki, “Implementation of Modified Delta Form for Microprocessors using Fixed-Point Arithmetic,” Proc. of the 1999 American Control Conference, Vol.5, pp. 4056-4060, 1999.

[15] [15] K. Sobel, H. Kaufman, and L. Mebius, “Implicit Adaptive Control for a Class of MIMO Systems,” IEEE Trans. Aerospace & Electron. Syst., Vol.18, No.5, pp. 576-590, 1982.

[16] [16] H. Kaufman, I. Barkana, and K. Sobel, “Direct adaptive control algorithms 2/e,” Springer, 1998.