2013, 3(3): 445-462. doi: 10.3934/naco.2013.3.445

Direct model reference adaptive control of linear systems with input/output delays

1. 

Department of Electrical and Computer Engineering, College of Engineering and Applied Science, University of Wyoming, Laramie, WY 82071, United States, United States

Received  April 2013 Revised  June 2013 Published  July 2013

In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for linear systems with unknown time varying input delays. This controller can also reject bounded disturbances of known waveform but unknown amplitude, e.g. steps or sinusoids. In this paper a robustness result is developed for DMRAC of linear systems with unknown small constant or time varying input delays using the concept of un-delayed ideal trajectories. We will show that the adaptively controlled system is globally stable, but the adaptive tracking error is no longer guaranteed to approach the origin. However, exponential convergence to a neighborhood can be achieved as a result of the control design. A simple example will be provided to illustrate this adaptive control method.
Citation: James P. Nelson, Mark J. Balas. Direct model reference adaptive control of linear systems with input/output delays. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 445-462. doi: 10.3934/naco.2013.3.445
References:
[1]

M. Balas, R. Erwin and R. Fuentes, Adaptive control of persistent disturbances for aerospace structures,, Proceedings of the AIAA Guidance, (2000).

[2]

M. Balas, S. Gajendar and L. Robertson, Adaptive tracking control of linear systems with unknown delays and persistent disturbances (or who you callin retarded?),, Proceedings of the AIAA Guidance, (2009).

[3]

M. Balas, J. Nelson, S. Gajendar and L. Robertson, Robust adaptive control of nonlinear systems with input/output delays,, Proceedings of the AIAA Guidance, (2011).

[4]

R. Fuentes and M. Balas, Direct adaptive rejection of persistent disturbances,, Journal of Mathematical Analysis and Applications, 251 (2000), 28. doi: 10.1006/jmaa.2000.7017.

[5]

R. Fuentes and M. Balas, Disturbance accommodation for a class of tracking control systems,, Proceedings of the AIAA Guidance, (2000).

[6]

R. Fuentes and M. Balas, Robust model reference adaptive control with disturbance rejection,, Proceedings of the American Control Conference, (2002).

[7]

K. Gu, V. L. Kharitonov and J. Chen, "Stability of Time Delay Systems,", Bikhauser, (2003).

[8]

M. Krstic, Compensation of infinite-dimensional actuator and sensor dynamics : nonlinear delay-adaptive systems,, IEEE Control Systems Magazine, 01 (2010), 22. doi: 10.1109/MCS.2009.934990.

[9]

J. Luna, Time delay systems and applications on satellite control,, University of New Mexico/ARFL Space Vechicles, ().

[10]

J. Nelson, M. Balas and R. Erwin, Direct model reference adaptive control of linear systems with unknown time varying input/output delays,, Proceedings of the AIAA Guidance, (2012).

[11]

S.-I. Niculescu, "Delay Effects on Stability,", Springer, (2001).

[12]

J.-P. Richard, Time delay systems: an overview of some recent advances and open problems,, Science Direct Automatica, 39 (2003), 1667. doi: 10.1016/S0005-1098(03)00167-5.

[13]

A. Seuret, Networked control under synchronization errors,, Proceedings of the American Control Conference, (2008).

[14]

R. Sipahi, S.-I. Nculescu, C. T. Abdallah, W. Michiels and K. Gu., Stability and stabalization of systems with time delay,, IEEE Control Systems Magazine, 31 (2001), 38.

[15]

J. Wen, Time domain and frequency domain conditions for strict positive realness,, IEEE Transactions on Automatic Control, 33 (1988), 988. doi: 10.1109/9.7263.

show all references

References:
[1]

M. Balas, R. Erwin and R. Fuentes, Adaptive control of persistent disturbances for aerospace structures,, Proceedings of the AIAA Guidance, (2000).

[2]

M. Balas, S. Gajendar and L. Robertson, Adaptive tracking control of linear systems with unknown delays and persistent disturbances (or who you callin retarded?),, Proceedings of the AIAA Guidance, (2009).

[3]

M. Balas, J. Nelson, S. Gajendar and L. Robertson, Robust adaptive control of nonlinear systems with input/output delays,, Proceedings of the AIAA Guidance, (2011).

[4]

R. Fuentes and M. Balas, Direct adaptive rejection of persistent disturbances,, Journal of Mathematical Analysis and Applications, 251 (2000), 28. doi: 10.1006/jmaa.2000.7017.

[5]

R. Fuentes and M. Balas, Disturbance accommodation for a class of tracking control systems,, Proceedings of the AIAA Guidance, (2000).

[6]

R. Fuentes and M. Balas, Robust model reference adaptive control with disturbance rejection,, Proceedings of the American Control Conference, (2002).

[7]

K. Gu, V. L. Kharitonov and J. Chen, "Stability of Time Delay Systems,", Bikhauser, (2003).

[8]

M. Krstic, Compensation of infinite-dimensional actuator and sensor dynamics : nonlinear delay-adaptive systems,, IEEE Control Systems Magazine, 01 (2010), 22. doi: 10.1109/MCS.2009.934990.

[9]

J. Luna, Time delay systems and applications on satellite control,, University of New Mexico/ARFL Space Vechicles, ().

[10]

J. Nelson, M. Balas and R. Erwin, Direct model reference adaptive control of linear systems with unknown time varying input/output delays,, Proceedings of the AIAA Guidance, (2012).

[11]

S.-I. Niculescu, "Delay Effects on Stability,", Springer, (2001).

[12]

J.-P. Richard, Time delay systems: an overview of some recent advances and open problems,, Science Direct Automatica, 39 (2003), 1667. doi: 10.1016/S0005-1098(03)00167-5.

[13]

A. Seuret, Networked control under synchronization errors,, Proceedings of the American Control Conference, (2008).

[14]

R. Sipahi, S.-I. Nculescu, C. T. Abdallah, W. Michiels and K. Gu., Stability and stabalization of systems with time delay,, IEEE Control Systems Magazine, 31 (2001), 38.

[15]

J. Wen, Time domain and frequency domain conditions for strict positive realness,, IEEE Transactions on Automatic Control, 33 (1988), 988. doi: 10.1109/9.7263.

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