Journal of Central South University

, Volume 26, Issue 1, pp 98–105 | Cite as

Application of composite nonlinear feedback control approach to linear and nonlinear systems

  • H Ebrahimi Mollabashi
  • A H MazinanEmail author
  • H Hamidi


The objective of this research is to realize a composite nonlinear feedback control approach for a class of linear and nonlinear systems with parallel-distributed compensation along with sliding mode control technique. The proposed composite nonlinear feedback control approach consists of two parts. In a word, the first part provides the stability of the closed-loop system and the fast convergence response, as long as the second one improves transient response. In this research, the genetic algorithm in line with the fuzzy logic is designed to calculate constant controller coefficients and optimize the control effort. The effectiveness of the proposed design is demonstrated by servo position control system and inverted pendulum system with DC motor simulation results.

Key words

composite nonlinear feedback parallel-distributed compensation sliding mode controller optimization 



针对一类具有平行分布补偿的线性和非线性系统,采用滑模控制技术,实现了一种复合非线性 反馈控制方法。所提出的复合非线性反馈控制方法由两部分组成。第一部分给出了闭环系统的稳定性 和快速收敛响应,而第二部分改进了瞬态响应。本研究设计了符合模糊逻辑的遗传算法来计算常系数 和优化控制效果。通过伺服位置控制系统和倒立摆系统的仿真,验证了所提设计的有效性。


复合非线性反馈 并行分布补偿 滑模控制器 优化 


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  1. [1]
    LI Y, TONG SH, LI T I. Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation [J]. IEEE Transactions on Cybernetics, 2015, 45(10): 2299–2308. DOI: 10.1109/TCYB.2014.2370645.MathSciNetCrossRefGoogle Scholar
  2. [2]
    TONG S H, LI Y, SUI S H. Adaptive fuzzy tracking control design for SISO uncertain non-strict feedback nonlinear systems [J]. IEEE Transactions on Fuzzy Systems, 2016, 24(6): 1441–1454. DOI: 10.1109/TFUZZ.2016.2540058CrossRefGoogle Scholar
  3. [3]
    ZHANG B, LAN W. Improving transient performance for output regulation problem of linear systems with input saturation [J]. Int J Control, 2014, 23(10): 1087–1098. DOI: 10.1002/rnc.2941.MathSciNetzbMATHGoogle Scholar
  4. [4]
    WANG R, HU C, YAN F, CHADLI M. Composite nonlinear feedback control for path following of four-wheel independently actuated autonomous ground vehicles [J]. IEEE Trans Intell Transp Syst, 2016, 17(7): 2063–2074. DOI: 10.1109/TITS.2015.2498172.CrossRefGoogle Scholar
  5. [5]
    WANG C H, CHU X I, LAN W E. Composite nonlinear feedback control for output regulation problem of linear discrete-time systems with input saturation [J]. Journal of Systems Engineering and Electronics, 2014, 25(6): 258–263. DOI: 10.1109/JSEE.2014.00120.Google Scholar
  6. [6]
    THUM C K, DU C L, CHEN B M, ONG E H, TAN K P. A unified control scheme for track seeking and following of a hard disk drive servo system [J]. IEEE Trans Control Syst Technol, 2010, 18(2): 294–306. DOI: 10.1109/TCST.2009. 2017513.CrossRefGoogle Scholar
  7. [7]
    FENG Y, HO D W C. Transient performance for discrete-time singular systems with actuators saturation via composite nonlinear feedback control [J]. Int J Robust Nonlinear Control, 2014, 24(5): 955–967. DOI: 10.1002/ rnc.2930MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    HU C, WANG R, YAN F, CHEN N. Robust composite nonlinear feedback path-following control for underactuated surface vessels with desired-heading amendment [J]. IEEE Trans Ind Electron, 2016, 63(10): 6386–6394. DOI: 10.1109/TIE.2016.2573240.CrossRefGoogle Scholar
  9. [9]
    HE Y, CHEN B M, WU C. Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation [J]. Syst Control Lett, 2005 54(5): 455–469. DOI: 10.1016/j.sysconle.2004.09.010.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    CHENG G, PENG K, CHEN B M, LEE T H. Improving transient performance in tracking general references using composite nonlinear feedback control and its application to high-speed XY-Table positioning mechanis [J]. IEEE Transactions on Industrial Electronics, 2007, 54(2): 1039–1051. DOI: 10.1109/TIE. 2007.892635CrossRefGoogle Scholar
  11. [11]
    EREN S, PAHLEVANINEZHAD M, BAKHSHAI A, JAIN P. Composite nonlinear feedback control and stability analysis of a grid-connected voltage source inverter with LCL filter [J]. IEEE Transactions on Industrial Electronics, 2012, 60(11): 5059–5074. DOI: 10.1109/TIE.2012.2225399.CrossRefGoogle Scholar
  12. [12]
    PENG K, CHEN B M, CHENG G, LEE T H. Modeling and compensation of nonlinearities and friction in a micro hard disk drive servo system with nonlinear feedback control [J]. IEEE Transactions on Control Systems Technology, 2005, 13: 708–721. DOI: 10.1109/TCST.2005.854321.CrossRefGoogle Scholar
  13. [13]
    LAN W, THUM C K, CHEN B M. A hard-disk-drive servo system design using composite nonlinear feedback control with optimal nonlinear gain tuning methods [J]. IEEE Transactions on Industrial Elecronics, 2010, 57: 1735–1745. DOI: 10.1109/TIE.2009.2032205.CrossRefGoogle Scholar
  14. [14]
    NIKDEL P, HOSSEINPOUR M, BADAMCHIZADEH M A, AKBARI M A. Improved Takagi–Sugeno fuzzy model-based control of flexible joint robot via Hybrid-Taguchi genetic algorithm [J]. Engineering Applications of Artificial Intelligence, 2014, 33: 12–20. DOI: 10.1016/j.engappai. 2014.03.009.CrossRefGoogle Scholar
  15. [15]
    YAHAYA M D, SHAHDAN S, LIYANA R, KHAIRI M, GHAZALI R. A reduce chattering problem using composite nonlinear feedback and proportional integral sliding mode control [C]// IEEE International Control Conference Asian. 2015: 1–6. DOI: 10.1109/ASCC.2015.7244566.Google Scholar
  16. [16]
    FANG F, SHI Y. Adaptive back-stepping-based composite nonlinear feedback water level control for the nuclear U-Tube steam generator [J]. IEEE Transactions on Control Systems Technology, 2014, 22: 369–377. DOI: 10.1109/ TCST.2013.2250504.CrossRefGoogle Scholar
  17. [17]
    HE Y, CHEN B M, LAN W. On improving transient performance in tracking control for a class of nonlinear discrete-time systems with input saturation [J]. IEEE Trans on Autom Control, 2007, 52(7): 1307–1313. DOI: 10.1109/ TAC.2007.900836.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    WANG T, ZHANG Y F, QIU J B, GAO H J. Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements [J]. IEEE Transactions on Fuzzy Systems, 2015, 23(2): 302–312. DOI: 10.1109/ TFUZZ.2014.2312026.CrossRefGoogle Scholar
  19. [19]
    KHOOBAN M H, VAFAMAND N, DRAGICEVIC T, BLAABJERG F, NIKNAM T. Model predictive control based on T-S fuzzy model for electrical vehicles delayed model [J]. IET Electr Power Appl, 2016, 64: 231–240. DOI: 10.1016/j.isatra.2016.04.019.Google Scholar
  20. [20]
    LILLY H J. Fuzzy control and identification [M]. New York: Wiley, 2010.CrossRefzbMATHGoogle Scholar
  21. [21]
    MÁRQUEZ R, GUERRA T M, BERNAL M, KRUSZEWSKI A. A non-quadratic Lyapunov functional for H8 control of nonlinear systems via Takagi–Sugeno models [J]. J Frankl Inst, 2016, 353(4): 781–796. DOI: 10.1016/ j.jfranklin.2016.01.004.CrossRefzbMATHGoogle Scholar
  22. [22]
    GUERRA T M, ESTRADA-MANZO V, LENDEK Z. Observer design for Takagi–Sugeno descriptor models: An LMI approach [J]. Automatica, 2015, 52: 154–159. DOI: 10.1016/j.automatica.2014.11.008.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    VAFAMAND N, ASEMANI M H, KHAYATIYAN A. A robust L1 controller design for continuous-time TS systems with persistent bounded disturbance and actuator saturation [J]. Eng Appl Artif Intell, 2016, 56: 212–221. DOI: 10.1016/j.engappai.2016.09.002.CrossRefGoogle Scholar
  24. [24]
    CHIANG T, LIU P. Robust output tracking control for discrete-time nonlinear systems with timevarying delay: Virtual fuzzy model LMI-based approach [J]. Expert Systems with Applications, 2012, 39: 8239–8247. DOI: 10.1016/ j.eswa.2012.01.163.CrossRefGoogle Scholar
  25. [25]
    VAFAMAND N, SHASADEGHI M. More relaxed non-quadratic stabilization conditions for TS fuzzy control systems using LMI and GEVP [J]. Int J Control Autom Syst, 2015, 13(4): 995–1002. DOI: 10.1007/s12555-013-0497-7.CrossRefGoogle Scholar
  26. [26]
    TANAKA K. Fuzzy control systems design and analysis: A linear matrix inequality approach [M]. New York: Wiley, 2001.CrossRefGoogle Scholar
  27. [27]
    NAMAZOV M, TEKGUN B, CELIKKALE E. Design of a stable takagi-sugeno fuzzy control system via LMIs with disturbance rejection [C]// IEEE International Symposium on Innovations in Intelligent Systems and Application (INISTA). IEEE, 2012: 950–956. DOI: 10.1109/INISTA.2012.6246945.Google Scholar

Copyright information

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Control Engineering, Faculty of Electrical EngineeringSouth Tehran Branch, Islamic Azad UniversityTehranIran
  2. 2.Department of Information Technology EngineeringK. N. Toosi University of TechnologyTehranIran

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