Design and analysis of a universal model reference  adaptive controller based on extended state observer

LI Jie; QI Xiaohui; ZHEN Hongtao; LIU Xinhai

doi:10.3969/j.issn.0253-2778.2014.10.004

JUSTC > 2014 > 44(10): 818-827. > DOI: 10.3969/j.issn.0253-2778.2014.10.004 CSTR: 32290.14.j.issn.0253-2778.2014.10.004

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Open Access JUSTC Original Paper

Design and analysis of a universal model reference adaptive controller based on extended state observer

Department of Unmanned Aerial Vehicle Engineering, Ordance Engineering College, Shijiazhuang 050003, China

Cite this: JUSTC, 2014, 44(10): 818-827

https://doi.org/10.3969/j.issn.0253-2778.2014.10.004

CSTR: 32290.14.j.issn.0253-2778.2014.10.004

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Corresponding author:
LI Jie (corresponding author), male, born in 1988, PhD candidate. Research field: Nonlinear control.
Received Date: January 03, 2014
Revised Date: June 18, 2014
Accepted Date: June 18, 2014
Published Date: October 29, 2014

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Abstract

Abstract

A universal model reference adaptive control (MRAC) method based on extended state observer (ESO) was presented, which was used to directly estimate states and uncertainties and then compensate the uncertainties. Benefiting from the ESO, we only need to know the order of a system without distinction between linear and nonlinear system, time-varying and time-invariant system, the internal (parameter or structure) uncertainty and the external (disturbance) uncertainty etc. Furthermore, the reference model which meets desired performance index and has the same order with the system can be chosen arbitrarily largely independently of the system structure. Therefore, the controller design process is greatly simplified. After proposing the control architecture, the control law was designed and a strict stability analysis was given. The features mentioned above in addition to strong robustness, small control moment and high steady state accuracy are demonstrated by the simulation results.

Abstract

A universal model reference adaptive control (MRAC) method based on extended state observer (ESO) was presented, which was used to directly estimate states and uncertainties and then compensate the uncertainties. Benefiting from the ESO, we only need to know the order of a system without distinction between linear and nonlinear system, time-varying and time-invariant system, the internal (parameter or structure) uncertainty and the external (disturbance) uncertainty etc. Furthermore, the reference model which meets desired performance index and has the same order with the system can be chosen arbitrarily largely independently of the system structure. Therefore, the controller design process is greatly simplified. After proposing the control architecture, the control law was designed and a strict stability analysis was given. The features mentioned above in addition to strong robustness, small control moment and high steady state accuracy are demonstrated by the simulation results.

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References (27)

References

[1]	Monopoli R V. Model reference adaptive control with an augmented error signal[J]. IEEE Transactions on Automatic Control, 1974, 19: 474-484.
[2]	Narendra K S, Valavani L S. Direct and indirect adaptive control[J]. Automatica, 1979, 15(6): 653-664.
[3]	Wang C, Lin Y. Decentralised adaptive dynamic surface control for a class of interconnected non-linear systems[J]. IET Control Theory Applications, 2012, 6(9): 1 172-1 181.
[4]	Kamali M, Askari J. Output-feedback model reference adaptive control of linear continuous state delayed systems in the presence of actuator failures[C]// Proceedings of 8th IEEE International Conference on Control and Automation. Xiamen, China: IEEE Press, 2010: 2 126-2 131.
[5]	Hovakimyan N, Yang B J, Calise A J. Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems[J]. Automatica, 2006, 42 (4): 513-522.
[6]	Kim N, Calise A J. Neural network based adaptive output feedback augmentation of existing controllers[J]. Aerospace Science and Technology, 2008, 12(3): 248-255.
[7]	Rohrs C E, Valavani L, Athans M, et al. Robustness of adaptive control algorithms in the presence of unmodeled dynamics[C]// Proceedings of 21st IEEE Conference on Decision and Control. Orlando, USA: IEEE Press, 1982: 3-11.
[8]	Blaicˇ S, Matko D, krjanc I. Adaptive law with a new leakage term[J]. IET Control Theory & Applications, 2010, 4(9): 1 533-1 542.
[9]	Huh S H, Bien Z. Robust sliding mode control of a robot manipulator based on variable structure-model reference adaptive control approach[J]. IET Control Theory & Applications, 2007, 1(5): 1 355-1 363.
[10]	Yan L, Hsu L, Costa R R, et al. A variable structure model reference robust control without a prior knowledge of high frequency gain sign[J]. Automatica, 2008, 44(4): 1 036-1 044.
[11]	Calise A J, Hovakimyan N, Idan M. Adaptive output feedback control of nonlinear systems using neural networks[J]. Automatica, 2001, 37 (8): 1 201-1 211.
[12]	Cao C Y, Hovakimyan N. Design and analysis of a novel L1 adaptive controller[C]// American Control Conference. Minnesota, USA: IEEE Press, 2006: 3 397-3 402.
[13]	Cao C Y, Hovakimyan N. Design and analysis of a novel L1 adaptive controller[C]// American Control Conference. Minnesota, USA: IEEE Press, 2006: 3 403-3 408.
[14]	Cao C Y, Hovakimyan N. Guaranteed transient performance with L1 adaptive controller for systems with time-varying parameters and bounded disturbances[C]// American Control Conference. New York, USA: IEEE Press, 2007: 3 925-3 930.
[15]	Cao C Y, Hovakimyan N. L1 adaptive controller for systems in the presence of unmodelled actuator dynamics[C]// Proceedings of 46th IEEE Conference on Decision and Control. New Orleans, USA: IEEE Press, 2007: 891-896.
[16]	Cao C Y, Hovakimyan N. L1 adaptive controller for a class of systems with unknown nonlinearities[C]// American Control Conference. Baltimore, USA: IEEE Press, 2008: 4 093-4 098.
[17]	Cao C Y, Hovakimyan N. L1 adaptive controller for nonlinear systems in the presence of unmodelled dynamics[C]// American Control Conference. Baltimore, USA: IEEE Press, 2008: 4 099-4 104.
[18]	Kharisov E, Hovakimyan N, Wang J, et al. L1 adaptive controller for time-varying reference systems in the presence of unmodeled nonlinear dynamics[C]// American Control Conference. Baltimore, USA: IEEE Press, 2010: 886-891.
[19]	Hayakawa T, Haddad M M, Hovakimyan N. Neural network adaptive control for a class of nonlinear uncertain dynamical systems with asymptotic stability guarantees[J]. IEEE Transactions on Neural Networks, 2008, 19(1): 80-89.
[20]	Campa G, Fravolini M L, Mammarella M, et al. Bounding set calculation for neural network-based output feedback adaptive control systems[J]. Neural Computing and Applications, 2011, 20(3): 373-387.
[21]	Moreno-Valenzuela J, Santibaez V, Orozco-Manríquez E, et al. Theory and experiments of global adaptive output feedback tracking control of manipulators[J]. IET Control Theory & Applications, 2010, 4(9): 1 639-1 654.
[22]	Huang Y, Han J Q. A new synthesis method for uncertain systems the self-stable region approach[J]. International Journal of System Science, 1999, 30(1): 33-38.
[23]	Yang X X, Huang Y. Capabilities of extended state observer for estimating uncertainties[C]// American Control Conference. St. Louis, USA: IEEE Press, 2009: 3 700-3 705.
[24]	韩京清. 一类不确定对象的扩张状态观测器[J]. 控制与决策, 1995, 10(1): 85-88.
[25]	Gao Z Q. Scaling and bandwidth-parameterization based controller tuning[C]// American Control Conference. Denver, USA: IEEE Press, 2003: 4 989-4 996.
[26]	Yoo D, Yau S S T, Gao Z Q. On convergence of the linear extended state observer[C]// Proceedings of IEEE International Conference on Control Applications. Texas, USA: IEEE Press, 2006: 1 645-1 650.
[27]	Guo B Z, Zhao Z l. On the convergence of an extended state observer for nonlinear systems with uncertainty[J]. Systems & Control Letters, 2011, 60(6): 420-430.

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References

[1]	Monopoli R V. Model reference adaptive control with an augmented error signal[J]. IEEE Transactions on Automatic Control, 1974, 19: 474-484.
[2]	Narendra K S, Valavani L S. Direct and indirect adaptive control[J]. Automatica, 1979, 15(6): 653-664.
[3]	Wang C, Lin Y. Decentralised adaptive dynamic surface control for a class of interconnected non-linear systems[J]. IET Control Theory Applications, 2012, 6(9): 1 172-1 181.
[4]	Kamali M, Askari J. Output-feedback model reference adaptive control of linear continuous state delayed systems in the presence of actuator failures[C]// Proceedings of 8th IEEE International Conference on Control and Automation. Xiamen, China: IEEE Press, 2010: 2 126-2 131.
[5]	Hovakimyan N, Yang B J, Calise A J. Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems[J]. Automatica, 2006, 42 (4): 513-522.
[6]	Kim N, Calise A J. Neural network based adaptive output feedback augmentation of existing controllers[J]. Aerospace Science and Technology, 2008, 12(3): 248-255.
[7]	Rohrs C E, Valavani L, Athans M, et al. Robustness of adaptive control algorithms in the presence of unmodeled dynamics[C]// Proceedings of 21st IEEE Conference on Decision and Control. Orlando, USA: IEEE Press, 1982: 3-11.
[8]	Blaicˇ S, Matko D, krjanc I. Adaptive law with a new leakage term[J]. IET Control Theory & Applications, 2010, 4(9): 1 533-1 542.
[9]	Huh S H, Bien Z. Robust sliding mode control of a robot manipulator based on variable structure-model reference adaptive control approach[J]. IET Control Theory & Applications, 2007, 1(5): 1 355-1 363.
[10]	Yan L, Hsu L, Costa R R, et al. A variable structure model reference robust control without a prior knowledge of high frequency gain sign[J]. Automatica, 2008, 44(4): 1 036-1 044.
[11]	Calise A J, Hovakimyan N, Idan M. Adaptive output feedback control of nonlinear systems using neural networks[J]. Automatica, 2001, 37 (8): 1 201-1 211.
[12]	Cao C Y, Hovakimyan N. Design and analysis of a novel L1 adaptive controller[C]// American Control Conference. Minnesota, USA: IEEE Press, 2006: 3 397-3 402.
[13]	Cao C Y, Hovakimyan N. Design and analysis of a novel L1 adaptive controller[C]// American Control Conference. Minnesota, USA: IEEE Press, 2006: 3 403-3 408.
[14]	Cao C Y, Hovakimyan N. Guaranteed transient performance with L1 adaptive controller for systems with time-varying parameters and bounded disturbances[C]// American Control Conference. New York, USA: IEEE Press, 2007: 3 925-3 930.
[15]	Cao C Y, Hovakimyan N. L1 adaptive controller for systems in the presence of unmodelled actuator dynamics[C]// Proceedings of 46th IEEE Conference on Decision and Control. New Orleans, USA: IEEE Press, 2007: 891-896.
[16]	Cao C Y, Hovakimyan N. L1 adaptive controller for a class of systems with unknown nonlinearities[C]// American Control Conference. Baltimore, USA: IEEE Press, 2008: 4 093-4 098.
[17]	Cao C Y, Hovakimyan N. L1 adaptive controller for nonlinear systems in the presence of unmodelled dynamics[C]// American Control Conference. Baltimore, USA: IEEE Press, 2008: 4 099-4 104.
[18]	Kharisov E, Hovakimyan N, Wang J, et al. L1 adaptive controller for time-varying reference systems in the presence of unmodeled nonlinear dynamics[C]// American Control Conference. Baltimore, USA: IEEE Press, 2010: 886-891.
[19]	Hayakawa T, Haddad M M, Hovakimyan N. Neural network adaptive control for a class of nonlinear uncertain dynamical systems with asymptotic stability guarantees[J]. IEEE Transactions on Neural Networks, 2008, 19(1): 80-89.
[20]	Campa G, Fravolini M L, Mammarella M, et al. Bounding set calculation for neural network-based output feedback adaptive control systems[J]. Neural Computing and Applications, 2011, 20(3): 373-387.
[21]	Moreno-Valenzuela J, Santibaez V, Orozco-Manríquez E, et al. Theory and experiments of global adaptive output feedback tracking control of manipulators[J]. IET Control Theory & Applications, 2010, 4(9): 1 639-1 654.
[22]	Huang Y, Han J Q. A new synthesis method for uncertain systems the self-stable region approach[J]. International Journal of System Science, 1999, 30(1): 33-38.
[23]	Yang X X, Huang Y. Capabilities of extended state observer for estimating uncertainties[C]// American Control Conference. St. Louis, USA: IEEE Press, 2009: 3 700-3 705.
[24]	韩京清. 一类不确定对象的扩张状态观测器[J]. 控制与决策, 1995, 10(1): 85-88.
[25]	Gao Z Q. Scaling and bandwidth-parameterization based controller tuning[C]// American Control Conference. Denver, USA: IEEE Press, 2003: 4 989-4 996.
[26]	Yoo D, Yau S S T, Gao Z Q. On convergence of the linear extended state observer[C]// Proceedings of IEEE International Conference on Control Applications. Texas, USA: IEEE Press, 2006: 1 645-1 650.
[27]	Guo B Z, Zhao Z l. On the convergence of an extended state observer for nonlinear systems with uncertainty[J]. Systems & Control Letters, 2011, 60(6): 420-430.

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model reference adaptive control
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