Model Reference Adaptive Controller for LTI Systems with Time-variant Delay

Authors

  • G. Keltoum Department of Electrical Engineering, University Ferhat Abbas Setif 1, Algeria

Abstract

In this paper, a new Direct Model Reference Adaptive Control Procedure (DMRAC) for Linear Time-Invariant (LTI) delay systems is presented with the use of the concept of the command generator tracker which expands the class of processes that can now be controlled with zero output error. The stability of the error between the system and the model is guaranteed by the Lyapunov theory. The new algorithm is applied to control a perturbed delay system. Matlab simulation examples are given to demonstrate the usefulness of the algorithm.

Keywords:

adaptive control, asymptotic stability, time delay systems, dynamical uncertainties

Downloads

Download data is not yet available.

References

E. Fridman, “Tutorial on Lyapunov-based methods for time-delay systems”, European Journal of Control, Vol. 20, No. 6, pp. 271–283, 2014 DOI: https://doi.org/10.1016/j.ejcon.2014.10.001

K. Gu, V. L. Kharitonov, J. Chen, Stability of time-delay systems, Springer, 2003 DOI: https://doi.org/10.1007/978-1-4612-0039-0

M. Wu, Y. He, J. H. She, Stability analysis and robust control of time-delay systems, Springer, 2010 DOI: https://doi.org/10.1007/978-3-642-03037-6

X. P. Chen, H. Dai, “Stability analysis of time-delay systems using a contour integral method”, Applied Mathematics and Computation, Vol. 273, pp. 390–397, 2016 DOI: https://doi.org/10.1016/j.amc.2015.09.094

M. Hashemi, J. Ghaisari, J. Askari, “Adaptive control for a class of MIMO nonlinear time delay systems against time varying actuator failures”, ISA Transactions, Vol. 57, pp. 23–42, 2015 DOI: https://doi.org/10.1016/j.isatra.2015.02.012

Z. Zhang, C. Lin, B. Chen, “New stability and stabilization conditions for T–S fuzzy systems with time delay”, Fuzzy Sets Systems, Vol. 263, pp. 82–91, 2015 DOI: https://doi.org/10.1016/j.fss.2014.09.012

J. Song, S. He, “Finite-time robust passive control for a class of uncertain Lipschitz nonlinear systems with time-delays”, Neurocomputing, Vol. 159, pp. 275–281, 2015 DOI: https://doi.org/10.1016/j.neucom.2015.01.038

S. H. Tsai, Y. A. Chen, J. C. Lo, “A novel stabilization condition for a class of T–S fuzzy time-delay systems”, Neurocomputing, Vol. 175, pp. 223-232, 2015 DOI: https://doi.org/10.1016/j.neucom.2015.10.054

Y. D. Song, H. Zhou, X. Su, L. Wang, “Pre-specified performance based model reduction for time-varying delays systems in fuzzy frame work”, Information Sciences, Vol. 328, pp. 206–221, 2016 DOI: https://doi.org/10.1016/j.ins.2015.08.031

D. J. Wang, “A PID controller set of guaranteeing stability and gain and phase margins for time-delay systems”, Journal of Process Control, Vol. 22, No. 7, pp. 1298–1306, 2012 DOI: https://doi.org/10.1016/j.jprocont.2012.05.019

D. B. Pietri, J. Chauvin, N. Petit, “Adaptive control scheme for uncertain time-delay systems”, Automatica, Vol. 48, No. 8, pp. 1536–1552, 2012 DOI: https://doi.org/10.1016/j.automatica.2012.05.056

J. Na, X. Ren, Y. Xia, “Adaptive parameter identification of linear SISO systems with unknown time-delay”, Systems & Control Letters, Vol. 66, pp. 43–50, 2014 DOI: https://doi.org/10.1016/j.sysconle.2014.01.005

M. C. Pai, “Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity”, Applied Mathematics and Computation, Vol. 271, pp. 757–767, 2015 DOI: https://doi.org/10.1016/j.amc.2015.09.058

Y. Zhang, Q. Wang, C. Dong, Y. Jiang, “H∞ output tracking control for flight control systems with time-varying delay”, Chinese Journal of Aeronautics, Vol. 26, No. 5, pp. 1251–1258, 2013 DOI: https://doi.org/10.1016/j.cja.2013.07.024

L. Frezzatto, M. J. Lacerda, R. C. L. F. Oliveira, P. L. D. Peres, “Robust H2 and H∞ memory filter design for linear uncertain discrete-time delay systems”, Signal Processing, Vol. 117, pp. 322-332, 2015

V. Andrieu, L. Praly, L. Astolfi, “Homogeneous approximation, recursive observer design, and output feedback”, SIAM Journal on Control and Optimization, Vol. 47, No. 4, pp. 1814–1850, 2008 DOI: https://doi.org/10.1137/060675861

A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems”, IEEE Transactions on Automatic Control, Vol. 57, No. 8, pp. 2106–2110, 2012 DOI: https://doi.org/10.1109/TAC.2011.2179869

D. Efimov, A. Polyakov, E. Fridman, W. Perruquetti, J. P. Richard, “Comments on finite-time stability of time-delay systems”, Automatica, Vol. 50, No. 7, pp. 1944–1947, 2014 DOI: https://doi.org/10.1016/j.automatica.2014.05.010

J. Lin, Z. Gao, “Observers design for switched discrete-time singular time-delay systems with unknown inputs”, Nonlinear Analysis: Hybrid Systems, Vol. 18, pp. 85–99, 2015 DOI: https://doi.org/10.1016/j.nahs.2015.06.004

G. Zheng, F. J. Bejarano, W. Perruquetti, J. P. Richard, “Unknown input observer for linear time-delay systems”, Automatica, Vol. 61, pp. 35–43, 2015 DOI: https://doi.org/10.1016/j.automatica.2015.07.029

C. Hua, G. Liu, L. Zhang, X. Guan, “Output feedback tracking control for nonlinear time-delay systems with tracking errors and input constraints”, Neurocomputing, Vol. 173, pp. 751-758, 2016 DOI: https://doi.org/10.1016/j.neucom.2015.08.026

Y. Q. Wu, Z. G. Liu, “Output feedback stabilization for time-delay nonholonomic systems with polynomial conditions”, ISA Transactions, Vol. 58, pp. 1–10, 2015 DOI: https://doi.org/10.1016/j.isatra.2015.03.008

K. Sobel, H. Kaufman, L. Mabius, “Implicit adaptive control for a class of MIMO systems”, IEEE Transactions on Aerospace and Electronic Systems, Vol. 18, No. 5, pp. 576-590, 1982 DOI: https://doi.org/10.1109/TAES.1982.309270

S. Ozcelik, H. Kaufman, “Robust direct model reference adaptive controllers”, 34th IEEE Conference on Decision and Control, New Orleans, USA, December 13-15, 1995

G. W. Neat, H. Kaufman, R. Steinvorth, “Comparison and extension of a direct model reference adaptive control procedure”, International Journal of Control, Vol. 55, No. 4, pp. 945-967, 1992 DOI: https://doi.org/10.1080/00207179208934266

I. Bar-kana, “Positive-realness in multivariable stationary linear systems”, Journal of the Franklin Institute, Vol. 328, No. 4, pp. 403-417, 1991 DOI: https://doi.org/10.1016/0016-0032(91)90016-V

I. Barkana, M. C. M. Teixeira, L. Hsu, “Mitigation of symmetry condition in positive realness for adaptive control”, Automatica, Vol. 42, No. 9, pp. 1611-1616, 2006 DOI: https://doi.org/10.1016/j.automatica.2006.05.013

I. Barkana, “Gain conditions and convergence of simple adaptive control”, International Journal of Adaptive Control and Signal Processing, Vol. 19, No. 1, pp. 13-40, 2005 DOI: https://doi.org/10.1002/acs.830

J. Broussard, M. O’Brien, “Feedforward control to track the output of a forced model”, IEEE Transactions on Automatic Control, Vol. 25, No. 4, pp. 851-853, 1980 DOI: https://doi.org/10.1109/TAC.1980.1102409

D. A. Torrey, Y. Sozer, H. Kaufman, “Direct model reference adaptive control of permanent magnet brushless DC motors”, IEEE International Conference on Control Applications, Hartford, USA, October 5-7, 1997

H. Kaufman, G. W. Neat, “Asymptotically stable multiple-input multiple-output direct model reference adaptive controller for processes not necessarily satisfying a positive real constraint”, International Journal of Control, Vol. 58, No. 5, pp. 1011-1031, 1993 DOI: https://doi.org/10.1080/00207179308923041

M. Darouach, “Linear functional observers for systems with delays in state variables”, IEEE Transactions on Automatic Control, Vol. 46, No. 3, pp. 491-496, 2001 DOI: https://doi.org/10.1109/9.911430

K. Behih, K. Benmahammed, Z. Bouchama, M. N. Harmas, “Real-time investigation of an adaptive fuzzy synergetic controller for a DC-DC buck converter”, Engineering, Technology & Applied Science Research, Vol. 9, No. 6, pp. 4984-4989, 2019 DOI: https://doi.org/10.48084/etasr.3172

Z. R. Labidi, H. Schulte, A. Mami, “A model-based approach of DC-DC converters dedicated to controller design applications for photovoltaic generators”, Engineering, Technology & Applied Science Research, Vol. 9, No. 4, pp. 4371-4376, 2019 DOI: https://doi.org/10.48084/etasr.2829

K. Mokhtari, A. Elhadri, M. Abdelaziz, “A passivity-based simple adaptive synergetic control for a class of nonlinear systems”, International Journal of Adaptive Control and Signal Processing, Vol. 33, No. 9, pp. 1359-1373, 2019 DOI: https://doi.org/10.1002/acs.3035

Y. Su, C. Zheng, P. Mercorelli, “Global finite-time stabilization of planar linear systems with actuator saturation”, IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 64, No. 8, pp. 947-951, 2017 DOI: https://doi.org/10.1109/TCSII.2016.2626199

P. Mercorelli, “An adaptive and optimized switching observer for sensorless control of an electromagnetic valve actuator in camless internal combustion engines”, Asian Journal of Control, Vol. 16, No. 4, pp. 959–973, 2014 DOI: https://doi.org/10.1002/asjc.772

P. Mercorelli, “Robust adaptive soft landing control of an electromagnetic valve actuator for camless engines”, Asian Journal of Control, Vol. 18, No. 4, pp. 1299–1312, 2016 DOI: https://doi.org/10.1002/asjc.1250

Downloads

How to Cite

[1]
G. Keltoum, “Model Reference Adaptive Controller for LTI Systems with Time-variant Delay”, Eng. Technol. Appl. Sci. Res., vol. 10, no. 3, pp. 5619–5626, Jun. 2020.

Metrics

Abstract Views: 704
PDF Downloads: 543

Metrics Information