Iterative Learning Control for Flexible Manipulator Using Fourier Basis Function

Li Zhang; Shan Liu

doi:10.1007/s11633-015-0932-8

December 2015

Article Contents

Li Zhang and Shan Liu. Iterative Learning Control for Flexible Manipulator Using Fourier Basis Function. International Journal of Automation and Computing, vol. 12, no. 6, pp. 639-647, 2015. doi: 10.1007/s11633-015-0932-8

Cite as: Li Zhang and Shan Liu. Iterative Learning Control for Flexible Manipulator Using Fourier Basis Function. International Journal of Automation and Computing, vol. 12, no. 6, pp. 639-647, 2015. doi: 10.1007/s11633-015-0932-8

Iterative Learning Control for Flexible Manipulator Using Fourier Basis Function

Li Zhang,
Shan Liu

College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China

Received: 2014-04-30

Fund Project:

This work was supported by National Natural Science Foundation of China (No. 61273133).

Abstract

Perfect tracking of the tip position of a flexible-link manipulator (FLM) is unable to be achieved by causal control because it is a typical non-minimum phase system. Combined with non-causal stable inversion, an adaptive iterative learning control scheme based on Fourier basis function is presented for the tip trajectory tracking of FLM performing repetitive tasks. In this method, an iterative identification algorithm is used to construct the Fourier basis function space model of the manipulator, and a pseudoinverse type iterative learning law is designed to approximate the stable inversion of the non-minimum phase system, which guarantees the convergence and robustness of the control system. Simulation results show the performance and effectiveness of the proposed scheme.
- Flexible-link manipulator (FLM),
- non-minimum phase system,
- adaptive iterative learning control,
- Fourier basis function,
- stable inversion

References

[1]	M. B. R. Neila, D. Tarak. Adaptive terminal sliding mode control for rigid robotic manipulators. International Journal of Automation and Computing, vol. 8, no. 2, pp. 215-220, 2011.
[2]	M. Moallem, R. V. Patel, K. Khorasani. An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators. Journal of Robotic Systems, vol. 14, no. 9, pp. 649-658, 1997.
[3]	B. Siciliano, W. J. Book. A singular perturbation approach to control of lightweight flexible manipulators. International Journal of Robotics Research, vol. 7, no. 4, pp. 79-90, 1988.
[4]	M. S. Alam, M. O. Tokhi. Designing feedforward command shapers with multi-objective genetic optimisation for vibration control of a single-link flexible manipulator. Engineering Applications of Artificial Intelligence, vol. 21, no. 2, pp. 229-246, 2008.
[5]	D.G. Wilson, R. D. Robinett III, G. G. Parker, G. P. Starr. Augmented sliding mode control for flexible link manipulators. Journal of Intelligent and Robotic Systems, vol. 34, no. 4, pp. 415-430, 2002.
[6]	H. C. Zhao. Stable Inversion Based Output Tracking Control of Robotic Systems, Ph. D. dissertation, Iowa State University, USA, 1997.
[7]	A. De Luca, S. Panzieri, G. Ulivi. Stable inversion control for flexible link manipulators. In Proceedings of International Conference on Robotics and Automation, IEEE, Leuven, Belgium, pp. 799-805, 1998.
[8]	S. Devasia, D. G. Chen, B. Paden. Nonlinear inversionbased output tracking. IEEE Transactions on Automatic Control, vol. 41, no. 7, pp. 930-942, 1996.
[9]	D. G. Chen, B. Paden. Stable inversion of nonlinear nonminimum phase systems. International Journal of Control, vol. 64, no. 1, pp. 81-97, 1996.
[10]	T. Sogo. On the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two-sided Laplace transform. Automatica, vol. 46, no. 1, pp. 122-126, 2010.
[11]	Q. Z. Zou. Optimal preview-based stable-inversion for output tracking of nonminimum-phase linear systems. Automatica, vol. 45, no. 1, pp. 230-237, 2009.
[12]	H. S. Ahn, Y. Q. Chen, K. L. Moore. Iterative learning control: Brief survey and categorization. IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews, vol. 37, no. 6, pp. 1099-1121, 2007.
[13]	W. S. Chen, R. H. Li, J. Li. Observer-based adaptive iterative learning control for nonlinear systems with timevarying delays. International Journal of Automation and Computing, vol. 7, no. 4, pp. 438-446, 2010.
[14]	K. Kinosita, T. Sogo, N. Adachi. Iterative learning control using adjoint systems and stable inversion. Asian Journal of Control, vol. 4, no. 1, pp. 60-67, 2002.
[15]	J. Ghosh, B. Paden. A pseudoinverse-based iterative learning control. IEEE Transactions on Automatic Control, vol. 47, no. 5, pp. 831-837, 2002.
[16]	M. Q. Phan, J. A. Frueh. Learning control for trajectory tracking using basis functions. In Proceedings of the 35th IEEE Conference on Decision and Control, IEEE, Kobe, Japan, pp. 2490-2492, 1996.
[17]	K. Hamamoto, T. Sugie. An iterative learning control algorithm within prescribed input-output subspace. Automatica, vol. 37, no. 11, pp. 1803-1809, 2001.
[18]	S. Liu, T. J. Wu. Stable-inversion based iterative learning control for non-minimum phase plants. Control Theory & Applications, vol. 20, no. 6, pp. 831-837, 2003. (in Chinese)
[19]	J. D. Ratcliffe, P. L. Lewin, E. Rogers, J. J. Hatonen, D. H. Owens. Norm-optimal iterative learning control applied to gantry robots for automation applications. IEEE Transactions on Robotics, vol. 22, no. 6, pp. 1303-1307, 2006.

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通讯作者: 陈斌, bchen63@163.com

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Iterative Learning Control for Flexible Manipulator Using Fourier Basis Function

College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China

Received: 2014-04-30

Fund Project:

This work was supported by National Natural Science Foundation of China (No. 61273133).

Key words:

Abstract: Perfect tracking of the tip position of a flexible-link manipulator (FLM) is unable to be achieved by causal control because it is a typical non-minimum phase system. Combined with non-causal stable inversion, an adaptive iterative learning control scheme based on Fourier basis function is presented for the tip trajectory tracking of FLM performing repetitive tasks. In this method, an iterative identification algorithm is used to construct the Fourier basis function space model of the manipulator, and a pseudoinverse type iterative learning law is designed to approximate the stable inversion of the non-minimum phase system, which guarantees the convergence and robustness of the control system. Simulation results show the performance and effectiveness of the proposed scheme.

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Reference (19)

[1]	M. B. R. Neila, D. Tarak. Adaptive terminal sliding mode control for rigid robotic manipulators. International Journal of Automation and Computing, vol. 8, no. 2, pp. 215-220, 2011.
[2]	M. Moallem, R. V. Patel, K. Khorasani. An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators. Journal of Robotic Systems, vol. 14, no. 9, pp. 649-658, 1997.
[3]	B. Siciliano, W. J. Book. A singular perturbation approach to control of lightweight flexible manipulators. International Journal of Robotics Research, vol. 7, no. 4, pp. 79-90, 1988.
[4]	M. S. Alam, M. O. Tokhi. Designing feedforward command shapers with multi-objective genetic optimisation for vibration control of a single-link flexible manipulator. Engineering Applications of Artificial Intelligence, vol. 21, no. 2, pp. 229-246, 2008.
[5]	D.G. Wilson, R. D. Robinett III, G. G. Parker, G. P. Starr. Augmented sliding mode control for flexible link manipulators. Journal of Intelligent and Robotic Systems, vol. 34, no. 4, pp. 415-430, 2002.
[6]	H. C. Zhao. Stable Inversion Based Output Tracking Control of Robotic Systems, Ph. D. dissertation, Iowa State University, USA, 1997.
[7]	A. De Luca, S. Panzieri, G. Ulivi. Stable inversion control for flexible link manipulators. In Proceedings of International Conference on Robotics and Automation, IEEE, Leuven, Belgium, pp. 799-805, 1998.
[8]	S. Devasia, D. G. Chen, B. Paden. Nonlinear inversionbased output tracking. IEEE Transactions on Automatic Control, vol. 41, no. 7, pp. 930-942, 1996.
[9]	D. G. Chen, B. Paden. Stable inversion of nonlinear nonminimum phase systems. International Journal of Control, vol. 64, no. 1, pp. 81-97, 1996.
[10]	T. Sogo. On the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two-sided Laplace transform. Automatica, vol. 46, no. 1, pp. 122-126, 2010.
[11]	Q. Z. Zou. Optimal preview-based stable-inversion for output tracking of nonminimum-phase linear systems. Automatica, vol. 45, no. 1, pp. 230-237, 2009.
[12]	H. S. Ahn, Y. Q. Chen, K. L. Moore. Iterative learning control: Brief survey and categorization. IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews, vol. 37, no. 6, pp. 1099-1121, 2007.
[13]	W. S. Chen, R. H. Li, J. Li. Observer-based adaptive iterative learning control for nonlinear systems with timevarying delays. International Journal of Automation and Computing, vol. 7, no. 4, pp. 438-446, 2010.
[14]	K. Kinosita, T. Sogo, N. Adachi. Iterative learning control using adjoint systems and stable inversion. Asian Journal of Control, vol. 4, no. 1, pp. 60-67, 2002.
[15]	J. Ghosh, B. Paden. A pseudoinverse-based iterative learning control. IEEE Transactions on Automatic Control, vol. 47, no. 5, pp. 831-837, 2002.
[16]	M. Q. Phan, J. A. Frueh. Learning control for trajectory tracking using basis functions. In Proceedings of the 35th IEEE Conference on Decision and Control, IEEE, Kobe, Japan, pp. 2490-2492, 1996.
[17]	K. Hamamoto, T. Sugie. An iterative learning control algorithm within prescribed input-output subspace. Automatica, vol. 37, no. 11, pp. 1803-1809, 2001.
[18]	S. Liu, T. J. Wu. Stable-inversion based iterative learning control for non-minimum phase plants. Control Theory & Applications, vol. 20, no. 6, pp. 831-837, 2003. (in Chinese)
[19]	J. D. Ratcliffe, P. L. Lewin, E. Rogers, J. J. Hatonen, D. H. Owens. Norm-optimal iterative learning control applied to gantry robots for automation applications. IEEE Transactions on Robotics, vol. 22, no. 6, pp. 1303-1307, 2006.

Iterative Learning Control for Flexible Manipulator Using Fourier Basis Function

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