The Fundamental Reliance of Iterative Learning Control on Stability Robustness
Iterative learning control aims to achieve zero tracking
error of a specific command. This is accomplished by iteratively
adjusting the command given to a feedback control system, based on
the tracking error observed in the previous iteration. One would like
the iterations to converge to zero tracking error in spite of any error
present in the model used to design the learning law. First, this need
for stability robustness is discussed, and then the need for robustness
of the property that the transients are well behaved. Methods of
producing the needed robustness to parameter variations and to
singular perturbations are presented. Then a method involving
reverse time runs is given that lets the world behavior produce the
ILC gains in such a way as to eliminate the need for a mathematical
model. Since the real world is producing the gains, there is no issue
of model error. Provided the world behaves linearly, the approach
gives an ILC law with both stability robustness and good transient
robustness, without the need to generate a model.
[1] Z. Bien and J.-X. Xu, editors, Iterative Learning Control: Analysis,
Design, Integration and Applications, Kluwer Academic Publishers,
Boston, 1998.
[2] J.-X. Xu and K. L. Moore, Guest Editors, Special Issue on Iterative
Learning Control, International Journal of Control, Vol. 73, No. 10,
July 2000.
[3] M. Phan and R. W. Longman, "A mathematical theory of learning
control for linear discrete multivariable systems," Proceedings of the
AIAA/AAS Astrodynamics Conference, Minneapolis, Minnesota, pp.
740-746, August 1988.
[4] R. W. Longman, "Iterative learning control and repetitive control for
engineering practice," International Journal of Control, Special Issue on
Iterative Learning Control, Bien and Xu, guest editors, vol. 73, no. 10,
pp. 930-954, July 2000.
[5] D. H. Owens and N. Amann, Norm-Optimal Iterative Learning Control,
Internal Report Series of the Centre for Systems and Control
Engineering, University of Exeter, 1994.
[6] J. A. Frueh and M. Q. Phan, "Linear quadratic optimal learning control
(LQL)," Proceedings of the 37th IEEE Conference on Decision and
Control, Tampa, FL, pp. 678-683, Dec. 1998.
[7] K. Åström, P. Hagander, and J. Strenby, "Zeros of sampled systems,"
Proceedings of the 19th IEEE Conference on Decision and Control, pp.
1077-1081, 1980.
[8] P. A. LeVoci and R. W. Longman, "Intersample error in discrete time
learning and repetitive control," Proceedings of the 2004 AIAA/AAS
Astrodynamics Specialist Conference, Providence, RI, August 2004.
[9] R. W. Longman, P. A. LeVoci, and T. Kwon, "Making the impossible
possible in iterative learning control," Proceedings of the Thirteenth
Yale Workshop on Adaptive and Learning Systems, Center for System
Science, Yale University, New Haven, CT, pp. 99-106, May-June 2005.
[10] R. W. Longman, T. Kwon, and P. A. LeVoci, "Making the learning
control problem well posed - stabilizing intersample error," Advances in
the Astronautical Sciences, vol. 123, pp. 1143-1162, 2006.
[11] Y. Li and R. W. Longman, "Addressing problems of instability in
intersample error in iterative learning control," Advances in the
Astronautical Sciences, vol. 129, pp. 1571-1591, 2008.
[12] R. W. Longman, C.-K. Chang, and M. Phan, "Discrete time learning
control in nonlinear systems," A Collection of Technical Papers, 1992
AIAA/AAS Astrodynamics Specialist Conference, Hilton Head, South
Carolina, pp. 501-511, August 1992.
[13] R. W. Longman and Y.-C. Huang, "Analysis and frequency response of
the alternating sign learning and repetitive control laws," Journal of the
Chinese Society of Mechanical Engineers, vol. 21, no. 1, pp. 107-118,
2000.
[14] H. Elci, R. W. Longman, M. Phan, J.-N. Juang, and R. Ugoletti,
"Discrete frequency based learning control for precision motion
control," Proceedings of the 1994 IEEE International Conference on
Systems, Man, and Cybernetics, San Antonio, TX, pp. 2767-2773, Oct.
1994.
[15] R. W. Longman and Y.-C. Huang, "The phenomenon of apparent
convergence followed by divergence in learning and repetitive control,"
Intelligent Automation and Soft Computing, Special Issue on Learning
and Repetitive Control, Guest Editor: H. S. M. Beigi, vol. 8, no. 2, pp.
107-128, 2002.
[16] N. Amman, D. H. Owens, W. Rogers, and A. Wahl, "An H-infinity
approach to linear iterative learning control design," International
Journal of Adaptive Control and Signal Processing, vol. 10, pp. 767-
681, 1996.
[17] K. Takanishi, M. Q. Phan, and R. W. Longman, "Multiple-model
probabilistic design of robust iterative learning controllers,"
Transactions of the North American Manufacturing Research
Institution, Society of Manufacturing Engineers, vol. 33, pp. 533-540,
May 2005.
[18] R. W. Longman and K. D. Mombaur, "Implementing linear iterative
learning control laws in nonlinear systems," Advances in the
Astronautical Sciences, to appear.
[19] H. Elci, M. Phan, R. W. Longman, J.-N. Juang, and R. Ugoletti,
"Experiments in the use of learning control for maximum precision
robot trajectory tracking," Proceedings of the 1994 Conference on
Information Sciences and Systems, Princeton, NJ, pp. 951-958, March
1994.
[20] R. W. Longman and W. Kang, "Issues in robustification of iterative
learning control using a zero-phase filter cutoff," Advances in the
Astronautical Sciences, vol. 127, pp. 1683-1702, 2007.
[21] K. Chen and R. W. Longman, "Creating short time equivalents of
frequency cutoff for robustness in learning control," Advances in the
Astronautical Sciences, vol. 114, pp. 95-114, 2003.
[22] Y. Ye and D. Wang, "Zero phase learning control using reversed time
input runs," ASME Journal of Dynamic Systems, Measurement, and
Control, vol. 127, pp. 133-139, March 2005.
[23] R. W. Longman, T. Kwon, D. Wang, and Y. Ye, "Practical, model-free,
completely robust learning control using reversed time input runs,"
Proceedings of the 2006 AIAA/AAS Astrodynamics Specialist
Conference, Keystone, CO, Aug. 2006.
[1] Z. Bien and J.-X. Xu, editors, Iterative Learning Control: Analysis,
Design, Integration and Applications, Kluwer Academic Publishers,
Boston, 1998.
[2] J.-X. Xu and K. L. Moore, Guest Editors, Special Issue on Iterative
Learning Control, International Journal of Control, Vol. 73, No. 10,
July 2000.
[3] M. Phan and R. W. Longman, "A mathematical theory of learning
control for linear discrete multivariable systems," Proceedings of the
AIAA/AAS Astrodynamics Conference, Minneapolis, Minnesota, pp.
740-746, August 1988.
[4] R. W. Longman, "Iterative learning control and repetitive control for
engineering practice," International Journal of Control, Special Issue on
Iterative Learning Control, Bien and Xu, guest editors, vol. 73, no. 10,
pp. 930-954, July 2000.
[5] D. H. Owens and N. Amann, Norm-Optimal Iterative Learning Control,
Internal Report Series of the Centre for Systems and Control
Engineering, University of Exeter, 1994.
[6] J. A. Frueh and M. Q. Phan, "Linear quadratic optimal learning control
(LQL)," Proceedings of the 37th IEEE Conference on Decision and
Control, Tampa, FL, pp. 678-683, Dec. 1998.
[7] K. Åström, P. Hagander, and J. Strenby, "Zeros of sampled systems,"
Proceedings of the 19th IEEE Conference on Decision and Control, pp.
1077-1081, 1980.
[8] P. A. LeVoci and R. W. Longman, "Intersample error in discrete time
learning and repetitive control," Proceedings of the 2004 AIAA/AAS
Astrodynamics Specialist Conference, Providence, RI, August 2004.
[9] R. W. Longman, P. A. LeVoci, and T. Kwon, "Making the impossible
possible in iterative learning control," Proceedings of the Thirteenth
Yale Workshop on Adaptive and Learning Systems, Center for System
Science, Yale University, New Haven, CT, pp. 99-106, May-June 2005.
[10] R. W. Longman, T. Kwon, and P. A. LeVoci, "Making the learning
control problem well posed - stabilizing intersample error," Advances in
the Astronautical Sciences, vol. 123, pp. 1143-1162, 2006.
[11] Y. Li and R. W. Longman, "Addressing problems of instability in
intersample error in iterative learning control," Advances in the
Astronautical Sciences, vol. 129, pp. 1571-1591, 2008.
[12] R. W. Longman, C.-K. Chang, and M. Phan, "Discrete time learning
control in nonlinear systems," A Collection of Technical Papers, 1992
AIAA/AAS Astrodynamics Specialist Conference, Hilton Head, South
Carolina, pp. 501-511, August 1992.
[13] R. W. Longman and Y.-C. Huang, "Analysis and frequency response of
the alternating sign learning and repetitive control laws," Journal of the
Chinese Society of Mechanical Engineers, vol. 21, no. 1, pp. 107-118,
2000.
[14] H. Elci, R. W. Longman, M. Phan, J.-N. Juang, and R. Ugoletti,
"Discrete frequency based learning control for precision motion
control," Proceedings of the 1994 IEEE International Conference on
Systems, Man, and Cybernetics, San Antonio, TX, pp. 2767-2773, Oct.
1994.
[15] R. W. Longman and Y.-C. Huang, "The phenomenon of apparent
convergence followed by divergence in learning and repetitive control,"
Intelligent Automation and Soft Computing, Special Issue on Learning
and Repetitive Control, Guest Editor: H. S. M. Beigi, vol. 8, no. 2, pp.
107-128, 2002.
[16] N. Amman, D. H. Owens, W. Rogers, and A. Wahl, "An H-infinity
approach to linear iterative learning control design," International
Journal of Adaptive Control and Signal Processing, vol. 10, pp. 767-
681, 1996.
[17] K. Takanishi, M. Q. Phan, and R. W. Longman, "Multiple-model
probabilistic design of robust iterative learning controllers,"
Transactions of the North American Manufacturing Research
Institution, Society of Manufacturing Engineers, vol. 33, pp. 533-540,
May 2005.
[18] R. W. Longman and K. D. Mombaur, "Implementing linear iterative
learning control laws in nonlinear systems," Advances in the
Astronautical Sciences, to appear.
[19] H. Elci, M. Phan, R. W. Longman, J.-N. Juang, and R. Ugoletti,
"Experiments in the use of learning control for maximum precision
robot trajectory tracking," Proceedings of the 1994 Conference on
Information Sciences and Systems, Princeton, NJ, pp. 951-958, March
1994.
[20] R. W. Longman and W. Kang, "Issues in robustification of iterative
learning control using a zero-phase filter cutoff," Advances in the
Astronautical Sciences, vol. 127, pp. 1683-1702, 2007.
[21] K. Chen and R. W. Longman, "Creating short time equivalents of
frequency cutoff for robustness in learning control," Advances in the
Astronautical Sciences, vol. 114, pp. 95-114, 2003.
[22] Y. Ye and D. Wang, "Zero phase learning control using reversed time
input runs," ASME Journal of Dynamic Systems, Measurement, and
Control, vol. 127, pp. 133-139, March 2005.
[23] R. W. Longman, T. Kwon, D. Wang, and Y. Ye, "Practical, model-free,
completely robust learning control using reversed time input runs,"
Proceedings of the 2006 AIAA/AAS Astrodynamics Specialist
Conference, Keystone, CO, Aug. 2006.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56092", author = "Richard W. Longman", title = "The Fundamental Reliance of Iterative Learning Control on Stability Robustness", abstract = "Iterative learning control aims to achieve zero tracking
error of a specific command. This is accomplished by iteratively
adjusting the command given to a feedback control system, based on
the tracking error observed in the previous iteration. One would like
the iterations to converge to zero tracking error in spite of any error
present in the model used to design the learning law. First, this need
for stability robustness is discussed, and then the need for robustness
of the property that the transients are well behaved. Methods of
producing the needed robustness to parameter variations and to
singular perturbations are presented. Then a method involving
reverse time runs is given that lets the world behavior produce the
ILC gains in such a way as to eliminate the need for a mathematical
model. Since the real world is producing the gains, there is no issue
of model error. Provided the world behaves linearly, the approach
gives an ILC law with both stability robustness and good transient
robustness, without the need to generate a model.", keywords = "Iterative learning control, stability robustness,
monotonic convergence.", volume = "5", number = "12", pages = "1945-6", }
