Velocity and Acceleration Estimation by a Nonlinear  Filter Based on Sliding Mode and Application to Control System

Takanori Emaru; Kazuo Imagawa; Yohei Hoshino; Yukinori Kobayashi

doi:10.20965/jrm.2009.p0590

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JRM Vol.21 No.5 pp. 590-596

doi: 10.20965/jrm.2009.p0590

(2009)

Paper:

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Velocity and Acceleration Estimation by a Nonlinear Filter Based on Sliding Mode and Application to Control System

Takanori Emaru, Kazuo Imagawa, Yohei Hoshino, and Yukinori Kobayashi

Graduate School of Engineering, Hokkaido University, N13W8, Kita-ku, Sapporo, Hokkaido, 060-8628 Japan

Received:

May 15, 2009

Accepted:

August 20, 2009

Published:

October 20, 2009

Keywords:

nonlinear filter, sliding mode, manipulator, nonlinear dynamics, attitude variation

Abstract

Proportional-integral-derivative (PID) control commonly used to operate mechanical systems has limited performance accuracy due to the influence of gravity, friction, and joint interaction caused by modeling error. Digital acceleration control is robust against modeling errors and superior to PID control, but the need for positioning, velocity, and acceleration knowledge constrains the development of digital acceleration control. To overcome this limitation, this report introduces the system which estimates the smoothed and differential values using sliding mode system (ESDS). Using ESDS enables digital acceleration control without increasing the number of sensors over that used in PID control. This paper focuses on the influence of gravity because digital acceleration control can, in principle, cancel its influence. This controls mechanical systems appropriately under attitude variations. Results of proposed control are demonstrated using 1- and 2-link manipulators.

Cite this article as:

T. Emaru, K. Imagawa, Y. Hoshino, and Y. Kobayashi, “Velocity and Acceleration Estimation by a Nonlinear Filter Based on Sliding Mode and Application to Control System,” J. Robot. Mechatron., Vol.21 No.5, pp. 590-596, 2009.

Data files:

References

[1] S. Y. Wang, K. Takahashi, Y. Hashimoto, K. Hori, T. Tsuchiya, and M. Nakatsuyama, “The Estimation Method Velocity and Acceleration Using Fuzzy Reasoning and its Application to Robot Manipulator Trajectory Control,” Fuzzy Theory and System, Vol.8, No.2, pp. 571-583, 1997.
[2] S. C. Pei and J. J. Shyu, “Eigenfilter Design of Higher-Order Digital Differentiators,” IEEE Trans. on Acoustics, Speech, and, Signal Processing, Vol.37, No.4, pp. 505-511, 1989.
[3] B. Carlsson, A. Ahlén, and M. Sternad, “Optimal Differentiation Based on Stochastic Signal Models,” IEEE Trans. on Signal Processing, Vol.39, No.2, pp. 341-353, 1991.
[4] T. Emaru and T. Tsuchiya, “Research on Estimating Smoothed Value and Differential Value By Using Sliding Mode System,” IEEE Trans. on Robotics and Automation, Vol.19, No.3, pp. 391-402, 2003.
[5] T. Emaru and T. Tsuchiya, “Research on Parameter Determination for Smoothed and Differential Value Estimator,” IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E86-A, No.7, pp. 1732-1741, 2003.
[6] A. Levant, “Sliding order and sliding accuracy in sliding mode control,” Int. J. of Control, Vol.58, No.6, pp. 1247-1263, 1993.
[7] A. Levant, “Robust exact differentiation via sliding mode technique,” Automatica, Vol.34, No.3, pp. 379-384, 1998.
[8] A. Levant, “Higher-order sliding modes, differentiation and output-feedback control,” Int. J. of Control, Vol.76, No.9/10, pp. 924-941, 2003.
[9] K. Imagawa, T. Emaru, Y. Hoshino, and Y. Kobayashi, “Estimation of velocity and acceleration by nonlinear filter based on sliding mode and application to control system,” Proc. of Asia Int. Symposium on Mechatronics, pp. 212-217, 2008.

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

[1] [1] S. Y. Wang, K. Takahashi, Y. Hashimoto, K. Hori, T. Tsuchiya, and M. Nakatsuyama, “The Estimation Method Velocity and Acceleration Using Fuzzy Reasoning and its Application to Robot Manipulator Trajectory Control,” Fuzzy Theory and System, Vol.8, No.2, pp. 571-583, 1997.

[2] [2] S. C. Pei and J. J. Shyu, “Eigenfilter Design of Higher-Order Digital Differentiators,” IEEE Trans. on Acoustics, Speech, and, Signal Processing, Vol.37, No.4, pp. 505-511, 1989.

[3] [3] B. Carlsson, A. Ahlén, and M. Sternad, “Optimal Differentiation Based on Stochastic Signal Models,” IEEE Trans. on Signal Processing, Vol.39, No.2, pp. 341-353, 1991.

[4] [4] T. Emaru and T. Tsuchiya, “Research on Estimating Smoothed Value and Differential Value By Using Sliding Mode System,” IEEE Trans. on Robotics and Automation, Vol.19, No.3, pp. 391-402, 2003.

[5] [5] T. Emaru and T. Tsuchiya, “Research on Parameter Determination for Smoothed and Differential Value Estimator,” IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E86-A, No.7, pp. 1732-1741, 2003.

[6] [6] A. Levant, “Sliding order and sliding accuracy in sliding mode control,” Int. J. of Control, Vol.58, No.6, pp. 1247-1263, 1993.

[7] [7] A. Levant, “Robust exact differentiation via sliding mode technique,” Automatica, Vol.34, No.3, pp. 379-384, 1998.

[8] [8] A. Levant, “Higher-order sliding modes, differentiation and output-feedback control,” Int. J. of Control, Vol.76, No.9/10, pp. 924-941, 2003.

[9] [9] K. Imagawa, T. Emaru, Y. Hoshino, and Y. Kobayashi, “Estimation of velocity and acceleration by nonlinear filter based on sliding mode and application to control system,” Proc. of Asia Int. Symposium on Mechatronics, pp. 212-217, 2008.