Enhanced Composite Nonlinear Control Technique using Adaptive Control for Nonlinear Delayed Systems

Author(s): Sonal Singh*, Shubhi Purwar

Journal Name: Recent Advances in Electrical & Electronic Engineering
Formerly Recent Patents on Electrical & Electronic Engineering

Volume 13 , Issue 3 , 2020


Become EABM
Become Reviewer
Call for Editor

Graphical Abstract:


Abstract:

Background and Introduction: The proposed control law is designed to provide fast reference tracking with minimal overshoot and to minimize the effect of unknown nonlinearities and external disturbances.

Methods: In this work, an enhanced composite nonlinear feedback technique using adaptive control is developed for a nonlinear delayed system subjected to input saturation and exogenous disturbances. It ensures that the plant response is not affected by adverse effect of actuator saturation, unknown time delay and unknown nonlinearities/ disturbances. The analysis of stability is done by Lyapunov-Krasovskii functional that guarantees asymptotical stability.

Results: The proposed control law is validated by its implementation on exothermic chemical reactor. MATLAB figures are provided to compare the results.

Conclusion: The simulation results of the proposed controller are compared with the conventional composite nonlinear feedback control which illustrates the efficiency of the proposed controller.

Keywords: Nonlinear delayed system, input saturation, composite nonlinear feedback control, adaptive control, linear matrix inequality, lyapunov-krasovskii analysis.

[1]
W. Wu, "Robust linearising controllers for nonlinear time-delay systems", IEE Proceedings-Control Theory Application, vol. 146, no. 1, pp. 91-97, . 1999
[2]
S.S. Ge, F. Hong, and T.H. Lee, "Robust adaptive control of nonlinear systems with unknown time delays", Automatica, vol. 41, no. 7, pp. 1181-1190, 2005.
[http://dx.doi.org/10.1016/j.automatica.2005.01.011]
[3]
B.M. Mirkin, and P.O. Gutman, "Robust adaptive output-feedback tracking for a class of nonlinear time-delay systems", IEEE Trans. Automat. Contr., vol. 55, no. 10, pp. 2418-2424, 2010.
[http://dx.doi.org/10.1109/TAC.2010.2054970]
[4]
H. Pan, W. Sun, H. Gao, O. Kaynak, F. Alsaadi, and T. Hayat, "Robust adaptive control of non-linear time-delay systems with saturation constraints", IET Control Theory Appl., vol. 9, no. 1, pp. 103-113, 2014.
[http://dx.doi.org/10.1049/iet-cta.2014.0557]
[5]
X. Zhang, and Y. Lin, "Adaptive control of nonlinear time-delay systems with application to a two-stage chemical reactor", IEEE Trans. Automat. Contr., vol. 60, no. 4, pp. 1074-1079, 2015.
[http://dx.doi.org/10.1109/TAC.2014.2330436]
[6]
Y.T. Chang, and B.S. Chen, "A fuzzy approach for robust reference tracking control of nonlinear distributed parameter time-delayed systems and its biological application", In: IEEE International Conference on Systems, Man and Cybernetics, Istanbul, Turkey, 2010, pp. 1139-1146.
[http://dx.doi.org/10.1109/ICSMC.2010.5642363]
[7]
Z. Li, Z. Chen, C-Y. Su, and F. Sun, "Adaptive tracking control of a class of MIMO nonlinear systems with time-varying delay and dead-zone inputs", In: Proceeding of the 11th World Congress on Intelligent Control and Automation, Shenyang, China, 2014, pp. 3860-3865.
[8]
T.S. Wu, M. Karkoub, H. Wang, H.S. Chen, and T.H. Chen, "Robust tracking control of MIMO underactuated nonlinear systems with dead-zone band and delayed uncertainty using an adaptive fuzzy control", IEEE Trans. Fuzzy Syst., vol. 25, no. 4, pp. 905-918, 2017.
[http://dx.doi.org/10.1109/TFUZZ.2016.2586970]
[9]
H. Liu, J. Xi, and Y. Zhong, "Robust attitude stabilization for nonlinear quadrotor Systems with uncertainties and delays", IEEE Trans. Ind. Electron., vol. 64, no. 7, pp. 5585-5594, 2017.
[http://dx.doi.org/10.1109/TIE.2017.2674634]
[10]
J. Gomes da Silva, A. Fischman, S. Tarbouriech, J. Dion, and L. Dugard, "Synthesis of state feedback for linear systems subject to control saturation by an LMI-based approach", IFAC Proceed. Vol., vol. 30, no. 16, 1997, pp. 207-212, .
[http://dx.doi.org/10.1016/S1474-6670(17)42607-3]
[11]
E.B. Castelan, S. Tarbouriech, and I. Queinnec, "Control design for a class of nonlinear continuous-time systems", Automatica, vol. 44, no. 8, pp. 2034-2039, 2008.
[http://dx.doi.org/10.1016/j.automatica.2007.11.013]
[12]
S. Singh, and S. Purwar, "Two term composite nonlinear feedback controller design for nonlinear time-delay systems", Trans. Inst. Meas. Contr., vol. 40, no. 12, pp. 3424-3432, 2017.
[http://dx.doi.org/10.1177/0142331217723703]
[13]
S. Mondal, and C. Mahanta, "Adaptive second-order sliding mode controller for a twin rotor multi-input–multi-output system", IET Control Theory Appl., vol. 6, no. 14, pp. 2157-2167, 2012.
[http://dx.doi.org/10.1049/iet-cta.2011.0478]
[14]
J.Y. Lee, M. Jin, and P.H. Chang, "Variable PID Gain Tuning Method Using Backstepping control with time-delay estimation and nonlinear damping", IEEE Trans. Ind. Electron., vol. 61, no. 12, pp. 6975-6985, 2014.
[http://dx.doi.org/10.1109/TIE.2014.2321353]
[15]
J.W. Lee, and P.H. Chang, Input/output linearization using time delay control and time delay observerProceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), Philadelphia, PA, USA, Vol. 1, 1998, pp. 318-322, .
[http://dx.doi.org/10.1109/ACC.1998.694683]
[16]
A. Singh, V. Sharma, P. Dahiya, and R.N. Sharma, "Model predictive based load frequency control of interconnected power systems", Recent Adv. Electr. Electron. Eng., vol. 11, no. 3, pp. 322-333, 2018.
[http://dx.doi.org/10.2174/2352096511666180117152541]
[17]
Y. Li, "Non-fragile passive filtering for sampled-data system with long time delay subject to nonlinearity", Recent Adv. Electr. Electron. Eng., vol. 6, pp. 196-202, 2013.
[18]
L. Yu, M. Chen, F. Yang, and X. Liu, "A fuzzy control strategy for pumped storage system of the microgrid with wind power", Recent Adv. Electr. Electron. Eng., vol. 7, no. 1, pp. 37-46, 2014.
[http://dx.doi.org/10.2174/2213111607666140516234304]
[19]
S.S. Ge, and K.P. Tee, "Approximation-based control of nonlinear MIMO time-delay systems", Automatica, vol. 43, no. 1, pp. 31-43, 2007.
[http://dx.doi.org/10.1016/j.automatica.2006.08.003]
[20]
L.A.M. Martinez, and C.H. Moog, "Input-output feedback linearization of nonlinear time-delay systems", In: 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), Maui, HI, USA, 2003, pp. 4557-4562.
[http://dx.doi.org/10.1109/CDC.2003.1272273]
[21]
K. Ichikawa, "Adaptive control of delay system", Int. J. Control, vol. 43, no. 6, pp. 1653-1659, 1986.
[http://dx.doi.org/10.1080/00207178608933565]
[22]
I. Kanellakopoulos, Adaptive Control of Nonlinear Systems: A Tutorial., Adapt. Cont., Filter. Sig. Process, pp. 89-133. 1995
[23]
H. Yue, and J. Li, "Output-feedback adaptive fuzzy control for a class of nonlinear systems with input delay and unknown control directions", J. Franklin Inst., vol. 350, no. 1, pp. 129-154, 2013.
[http://dx.doi.org/10.1016/j.jfranklin.2012.10.010]
[24]
T-C. Lin, and H-C. Huang, "Uncertain nonlinear time-delay system adaptive fuzzy PI sliding tracking control", In: CACS International Automatic Control Conference (CACS 2014) Kaohsiung, Taiwan, 2014, pp. 17-22.
[http://dx.doi.org/10.1109/CACS.2014.7097155]
[25]
H. Deng, H-X. Li, and Y-H. Wu, "Feedback-linearization-based neural adaptive control for unknown nonaffine nonlinear discrete-time systems", IEEE Trans. Neural Netw., vol. 19, no. 9, pp. 1615-1625, 2008.
[http://dx.doi.org/10.1109/TNN.2008.2000804] [PMID: 18779092]
[26]
S.S. Ge, F. Hong, T.H. Lee, and C.C. Hang, "Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients", In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, USA, 2002, pp. 961-966.
[http://dx.doi.org/10.1109/CDC.2002.1184633]
[27]
B.M. Chen, T.H. Lee, K. Peng, and V. Venkataramanan, "Composite nonlinear feedback control for linear systems with input saturation: Theory and an application", IEEE Trans. Automat. Contr., vol. 48, no. 3, pp. 427-439, 2003.
[http://dx.doi.org/10.1109/TAC.2003.809148]
[28]
M.Z. Oliveira, J.M. Gomes da Silva, D. Coutinho, and S. Tarbouriech, "Design of anti-windup compensators for a class of nonlinear control systems with actuator saturation", J. Cont.Autom. Electric. Syst., vol. 24, no. 3, pp. 212-222, 2013.
[http://dx.doi.org/10.1007/s40313-013-0031-4]
[29]
S. Mobayen, "Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback", Nonlinear Dyn., vol. 76, no. 1, pp. 827-838, 2014.
[http://dx.doi.org/10.1007/s11071-013-1172-5]
[30]
T. Wang, J. Qiu, and H. Gao, "Adaptive neural control of stochastic nonlinear time-delay systems with multiple constraints", IEEE Trans. Syst. Man Cybern. Syst., vol. 47, no. 8, pp. 1875-1883, 2017.
[http://dx.doi.org/10.1109/TSMC.2016.2562511]
[31]
R. Dey, S. Ghosh, G. Ray, and A. Rakshit, "H∞ load frequency control of interconnected power systems with communication delays", Int. J. Electr. Power Energy Syst., vol. 42, no. 1, pp. 672-684, 2012.
[http://dx.doi.org/10.1016/j.ijepes.2012.03.035]
[32]
S. Roy, I.N. Kar, J. Lee, and M. Jin, "Adaptive-robust time-delay control for a class of uncertain Euler–Lagrange systems", IEEE Trans. Ind. Electron., vol. 64, no. 9, pp. 7109-7119, 2017.
[http://dx.doi.org/10.1109/TIE.2017.2688959]
[33]
J-P. Richard, "Time-delay systems: An overview of some recent advances and open problems", Automatica, vol. 39, no. 10, pp. 1667-1694, 2003.
[http://dx.doi.org/10.1016/S0005-1098(03)00167-5]
[34]
J. Shen, and J. Yan, "Razumikhin type stability theorems for impulsive functional differential equations", Nonlinear Analysis Theory Methods & Applications, vol. 33, no. 5, pp. 519-531, 1998.
[http://dx.doi.org/10.1016/S0362-546X(97)00565-8]
[35]
S. Boyd, "L. El~Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities in System and Control Theory", SIAM Stud. Appl. Math., vol. 5, 1994.
[http://dx.doi.org/10.1137/1.9781611970777]
[36]
Y. Lofberg, "A toolbox for modeling and optimization in MATLAB", In: 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), New Orleans, LA, USA, 2004, pp. 284-289.
[http://dx.doi.org/10.1109/CACSD.2004.1393890]
[37]
R. Yang, and F. Zang, "Observer-based robust control for a class of secondary regulation rotate speed systems", Recent Adv. Electr. Electron. Eng., vol. 10, no. 1, pp. 81-87, 2017.
[http://dx.doi.org/10.2174/2352096510666170509124254]


Rights & PermissionsPrintExport Cite as

Article Details

VOLUME: 13
ISSUE: 3
Year: 2020
Published on: 26 December, 2018
Page: [396 - 404]
Pages: 9
DOI: 10.2174/2213111607666181226151059
Price: $25

Article Metrics

PDF: 8
HTML: 1