Passivity-Based Tracking Control for Uncertain Nonlinear Feedback Systems

Ni Bu; Mingcong Deng

doi:10.20965/jrm.2016.p0837

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JRM Vol.28 No.6 pp. 837-841

doi: 10.20965/jrm.2016.p0837

(2016)

Paper:

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Passivity-Based Tracking Control for Uncertain Nonlinear Feedback Systems

Ni Bu^* and Mingcong Deng^**

^*College of Automation and Electronic Engineering, Qingdao University of Science and Technology
53 Zhengzhou Road, Qingdao, China

^**Graduate School of Engineering, Tokyo University of Agriculture and Technology
2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan

Received:

April 17, 2016

Accepted:

August 28, 2016

Published:

December 20, 2016

Keywords:

passivity-based control, robust right coprime factorization, isomorphism, uncertainty

Abstract

The tracking control problem for the uncertain nonlinear feedback systems is considered in this paper by using passivity-based robust right coprime factorization method. Concerned with the passivity for the nonlinear feedback system, two stable controllers are designed such that the nonlinear feedback system is robust stable and the plant output asymptotically tracks to the reference output. A numerical example is given to show the validity of the control scheme as well as the tracking performance.

The asymptotic tracking performance and the passivity property

Cite this article as:

N. Bu and M. Deng, “Passivity-Based Tracking Control for Uncertain Nonlinear Feedback Systems,” J. Robot. Mechatron., Vol.28 No.6, pp. 837-841, 2016.

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References

[1] R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-Ramirez, “Passivity-based control of Euler-Lagrange Systems,” London, Springer-Verlag, 1998.
[2] R. Ortega, A. J. van der Schaft, I. Mareels, and B. Maschke, “Putting energy back in control,” IEEE Control System Magazine, Vol.21, pp. 18-23, 2001.
[3] H. Kojima, T. Hashimoto, and S. Shimoyama, “Trajectory tracking control of a flexible mobile robot using disturbance Observer,” J. of Robotics and Mechatronics, Vol.10, No.3, pp. 272-277, 1998.
[4] I. Nagai and Y. Tanaka, “Mobile Robot with Floor Tracking Device for Localization and Control,” J. of Robotics and Mechatronics, Vol.19, No.1, pp. 34-41, 2007.
[5] N. Bu and M. Deng, “System design for nonlinear plants using operator-based robust right coprime factorization and isomorphism,” IEEE Trans. on Automatic Control, Vol.56, pp. 952-957, 2011.
[6] M. Deng, N. Bu, and A. Inoue, “Output tracking of nonlinear feedback systems with perturbation based on robust right coprime factorization,” Int. J. of Innovative Computing, Information and Control, Vol.5, pp. 3359-3366, 2009.
[7] A. Wang, D. Wang, H. Wang, S. Wen, and M. Deng, “Nonlinear Perfect Tracking Control for a Robot Arm with Uncertainties Using Operator-Based Robust Right Coprime Factorization Approach,” J. of Robotics and Mechatronics, Vol.27, No.1, pp. 49-56, 2015.
[8] R. J. P. de Figueiredo and G. R. Chen, “Nonlinear Feedback Control Systems-An Operator Theory Approach,” New York: Academic Press, Inc., 1993.
[9] M. Deng, A. Inoue, and K. Ishikawa, “Operator-based nonlinear feedback control design using robust right coprime factorization,” IEEE Trans. on Automatic Control, Vol.51, pp. 645-648, 2006.
[10] M. Deng and N. Bu, “Robust control for nonlinear systems with unknown perturbations using simplified robust right coprime factorization,” Int. J. of Control, Vol.85, pp. 842-850, 2012.
[11] N. Bu and M. Deng, “Operator-based robust right coprime factorization and nonlinear control scheme for nonlinear plant with unknown perturbations,” Proc. IMechE, Part I-J. Syst. Contr. Engineering, Vol.225, No.6, pp. 760-769, 2011.
[12] X. Chen, G. Zhai, and T. Fukuda, “An approximate inverse system for nonminimum-phase systems and its application to disturbance observer,” Syst. Control Lett., Vol.52, No.3-4, pp. 193-207, 2004.
[13] M. Deng and N. Bu, “Robust control for nonlinear systems using passivity-based robust right coprime factorization,” IEEE Trans. on Automatic Control, Vol.57, pp. 2599-2604, 2012.
[14] N. Bu and M. Deng, “Operator-based robust right coprime factorization and nonlinear control scheme for nonlinear plant with unknown perturbations,” Asian J. Control, Vol.14, No.6, pp. 1655-1661, 2012.
[15] M. Deng and N. Bu, “Isomorphism-based robust right coprime factorization of nonlinear unstable plants with perturbations,” IET Control Theory and Applications, Vol.4, pp. 2381-2390, 2010.
[16] N. Bu and X. Liu, “Passivity-based robust control for nonlinear feedback systems using robust right coprime factorization,” Proc. of the 33rd Chinese Control Conf., pp. 2261-2264, 2014.

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

[1] [1] R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-Ramirez, “Passivity-based control of Euler-Lagrange Systems,” London, Springer-Verlag, 1998.

[2] [2] R. Ortega, A. J. van der Schaft, I. Mareels, and B. Maschke, “Putting energy back in control,” IEEE Control System Magazine, Vol.21, pp. 18-23, 2001.

[3] [3] H. Kojima, T. Hashimoto, and S. Shimoyama, “Trajectory tracking control of a flexible mobile robot using disturbance Observer,” J. of Robotics and Mechatronics, Vol.10, No.3, pp. 272-277, 1998.

[4] [4] I. Nagai and Y. Tanaka, “Mobile Robot with Floor Tracking Device for Localization and Control,” J. of Robotics and Mechatronics, Vol.19, No.1, pp. 34-41, 2007.

[5] [5] N. Bu and M. Deng, “System design for nonlinear plants using operator-based robust right coprime factorization and isomorphism,” IEEE Trans. on Automatic Control, Vol.56, pp. 952-957, 2011.

[6] [6] M. Deng, N. Bu, and A. Inoue, “Output tracking of nonlinear feedback systems with perturbation based on robust right coprime factorization,” Int. J. of Innovative Computing, Information and Control, Vol.5, pp. 3359-3366, 2009.

[7] [7] A. Wang, D. Wang, H. Wang, S. Wen, and M. Deng, “Nonlinear Perfect Tracking Control for a Robot Arm with Uncertainties Using Operator-Based Robust Right Coprime Factorization Approach,” J. of Robotics and Mechatronics, Vol.27, No.1, pp. 49-56, 2015.

[8] [8] R. J. P. de Figueiredo and G. R. Chen, “Nonlinear Feedback Control Systems-An Operator Theory Approach,” New York: Academic Press, Inc., 1993.

[9] [9] M. Deng, A. Inoue, and K. Ishikawa, “Operator-based nonlinear feedback control design using robust right coprime factorization,” IEEE Trans. on Automatic Control, Vol.51, pp. 645-648, 2006.

[10] [10] M. Deng and N. Bu, “Robust control for nonlinear systems with unknown perturbations using simplified robust right coprime factorization,” Int. J. of Control, Vol.85, pp. 842-850, 2012.

[11] [11] N. Bu and M. Deng, “Operator-based robust right coprime factorization and nonlinear control scheme for nonlinear plant with unknown perturbations,” Proc. IMechE, Part I-J. Syst. Contr. Engineering, Vol.225, No.6, pp. 760-769, 2011.

[12] [12] X. Chen, G. Zhai, and T. Fukuda, “An approximate inverse system for nonminimum-phase systems and its application to disturbance observer,” Syst. Control Lett., Vol.52, No.3-4, pp. 193-207, 2004.

[13] [13] M. Deng and N. Bu, “Robust control for nonlinear systems using passivity-based robust right coprime factorization,” IEEE Trans. on Automatic Control, Vol.57, pp. 2599-2604, 2012.

[14] [14] N. Bu and M. Deng, “Operator-based robust right coprime factorization and nonlinear control scheme for nonlinear plant with unknown perturbations,” Asian J. Control, Vol.14, No.6, pp. 1655-1661, 2012.

[15] [15] M. Deng and N. Bu, “Isomorphism-based robust right coprime factorization of nonlinear unstable plants with perturbations,” IET Control Theory and Applications, Vol.4, pp. 2381-2390, 2010.

[16] [16] N. Bu and X. Liu, “Passivity-based robust control for nonlinear feedback systems using robust right coprime factorization,” Proc. of the 33rd Chinese Control Conf., pp. 2261-2264, 2014.

Passivity-Based Tracking Control for Uncertain Nonlinear Feedback Systems

Ni Bu* and Mingcong Deng**

Ni Bu^* and Mingcong Deng^**