Controller Synthesis for Steer-by-Wire System Performance in Vehicle

  • Nabil El FezaziEmail author
  • El Houssaine Tissir
  • Fatima El Haoussi
  • Fernando Augusto Bender
  • Abdul Rashid Husain
Research Paper


A controller with anti-windup compensator is proposed in this paper, for coping with the saturating nature where the delays are included in certain parts of the state-space representation and the perturbation must be rejected effectively to achieved the desired performance using a steer-by-wire technology that is a technique to eliminate the mechanical linkage between the steering and the front wheels. Then, a simplified and detailed description of this technology is discussed to establish a linearized mathematical model in order to ensure the robust stability of a vehicle under the complicated condition of work and road. By incorporating the delay-decomposition technique, the generalized sector condition and the Finsler's lemma, sufficient conditions in the form of LMIs are derived to satisfy the \(H_{\infty }\) control based on the Lyapunov–Krasovskii (L–K) functional. The simulation results are presented to show that high performance and robustness are achieved.


Steer-by-wire system Controller Anti-windup compensator Robust stability Delay-decomposition technique 


  1. Ahmida F, Tissir EH (2013) Exponential stability of uncertain T–S fuzzy switched systems with time delay. Int J Autom Comput 10(1):32–38CrossRefGoogle Scholar
  2. Anwar S (2005) Generalized predictive control of yaw dynamics of a hybrid brake-by-wire equipped vehicle. Mechatronics 15(9):1089–1108CrossRefGoogle Scholar
  3. Anwar S, Chen L (2007) An analytical redundancy-based fault detection and isolation algorithm for a road-wheel control subsystem in a steer-by-wire system. IEEE Trans Veh Technol 56(5):2859–2869CrossRefGoogle Scholar
  4. Bender FA (2010) Técnicas de síntese de compensadores antiwindup para sistemas com atraso, Doctoral thesis, Universidade Federal do Rio Grande do Sul, Porto Alegre. Brazil, pp 1–102Google Scholar
  5. Bender FA (2013) Delay dependent antiwindup synthesis for time delay systems. Int J Intell Control Syst 18(1):1–9MathSciNetGoogle Scholar
  6. Bertoluzzo M, Buja G, Menis R (2007) Control schemes for steer-by-wire systems. IEEE Ind Electron Mag 1(1):20–27CrossRefGoogle Scholar
  7. Boyd S, El Ghaoui L, Feron E, Balakrisshnan V (1994) Linear matrix inequalities in system and control theory. Soc Ind Appl Math 15:xii+-193MathSciNetzbMATHGoogle Scholar
  8. Chang S-C (2007) Synchronization in a steer-by-wire vehicle dynamic system. Int J Eng Sci 45(2–8):628–643CrossRefGoogle Scholar
  9. Chen H, Zhu L, Liu X, Yu S, Zhao D (2013) Study on steering by wire controller based on improved H\(_{\infty }\) algorithm. Int J Online Eng 9(S2):35–40Google Scholar
  10. El Fezazi N, Tissir EH, El Haoussi F, Alvarez T, Tadeo F (2017a) Control based on saturated time-delay systems theory of Mach number in wind tunnels. Circuits Syst Signal Process 37(4):1505–1522MathSciNetCrossRefGoogle Scholar
  11. El Fezazi N, El Haoussi F, Tissir EH, Alvarez T (2017b) Design of robust H\(_{\infty }\) controllers for congestion control in data networks. J Frankl Inst 354(17):7828–7845Google Scholar
  12. El Fezazi N, El Haoussi F, Tissir EH, Alvarez T, Tadeo F (2018) Robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations. Int J Appl Math Comput Sci 28(1):111–122MathSciNetCrossRefGoogle Scholar
  13. El Fezazi N, El Haoussi F, Tissir EH, Bender FA, Alvarez T (2019) Multiclass AQM on a TCP/IP router: a control theory approach. Int J Robust Nonlinear Control.
  14. Gu K, Chen J, Kharitonov V (2003) Stability of time-delay systems. Springer, BerlinCrossRefGoogle Scholar
  15. Huang C, Du H, Naghdy F, Li W (2015) Takagi-Sugeno fuzzy H\(_{\infty }\) tracking control for steer-by-wire systems. In: 1st IEEE international conference on control applications, Sydney, Australia, pp 1716–1721Google Scholar
  16. Idrissi S, Tissir EH (2012) Robust stability of T–S fuzzy systems with time-varying delay and polytopic-type uncertainty. Int J Ecol Econ Stat 24(1):17–26zbMATHGoogle Scholar
  17. Idrissi S, Tissir EH, Boumhidi I, Chaibi N (2013) Delay-dependent robust stability of time delay systems with polytopic-type uncertainty. Int J Ecol Dev 26(3):67–77Google Scholar
  18. Lamrabet O, El Fezazi N, El Haoussi F, Tissir EH (2017) Using input delay approach for synthesizing an anti-windup compensator to AQM in TCP/IP networks. In: 3rd IEEE international conference on advanced technologies for signal and image processing, Fez, Morocco, pp 1–6Google Scholar
  19. Lamrabet O, Tissir EH, El Haoussi F (2018) Anti-windup compensator synthesis for sampled-data delay systems. Circuits Syst Signal Process.
  20. Mohamed ES, Albatlan SA (2014) Modeling and experimental design approach for integration of conventional power steering and a steer-by-wire system based on active steering angle control. Am J Veh Des 2(1):32–42Google Scholar
  21. Oh S-W, Chae H-C, Yun S-C, Han C-S (2004) The design of a controller for the steer-by-wire system. Int J Ser C Mech Syst Mach Elem Manuf 47(3):896–907Google Scholar
  22. Park T-J, Oh S-W, Jang J-H, Han C-S (2002) The design of a controller for the steer-by-wire system using the hardware-in-the-loop-simulation system. SAE technical paper 2002-01-1596.
  23. Shah MBN, Husain AR, Dahalan ASA (2013) An analysis of CAN-based steer-by-wire system performance in vehicle. In: 3rd IEEE international conference on control system, computing and engineering, Penang, Malaysia, pp 350–355Google Scholar
  24. Tarbouriech S, Garcia G, Da Silva JMG, Queinnec I (2011) Stability and stabilization of linear systems with saturating actuators, control engineering. Springer, Berlin, pp 1–453CrossRefGoogle Scholar
  25. Tissir EH (2012) Robust exponential stability of switched linear systems with mixed time delays. Int J Ecol Dev 22(2):1–11MathSciNetzbMATHGoogle Scholar
  26. Virgala I, Frankovský P, Kenderová M (2013) Friction effect analysis of a DC motor. Am J Mech Eng 1(1):1–5CrossRefGoogle Scholar
  27. Yih P, Ryu J, Gerdes JC (2005) Modification of vehicle handling characteristics via steer-by-wire. IEEE Trans Control Syst Technol 13(6):965–976CrossRefGoogle Scholar
  28. Zakaria MI, Husain AR, Mohamed Z, El Fezazi N, Shah MBN (2015) Lyapunov–Krasovskii stability condition for system with bounded delay-an application to steer-by-wire system. In: 5th IEEE international conference on control system, computing and engineering, Penang, Malaysia, pp 543–547Google Scholar
  29. Zheng B, Altemare C, Anwar S (2005) Fault tolerant steer-by-wire road wheel control system. In: IEEE American control conference, Portland, USA, pp 1619–1624Google Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.LESSI, Department of Physics, Faculty of Sciences Dhar El MehrazUniversity Sidi Mohammed Ben AbdellahFes-AtlasMorocco
  2. 2.IASCM, Department of Mathematic and Informatics, Polydisciplinary FacultySelouaneMorocco
  3. 3.Center of Exact Sciences and TechnologyUniversidade de Caxias do SulCaxias do Sul-RSBrazil
  4. 4.Department of Control and Mechatronic EngineeringTeknologi UniversitySkudaiMalaysia

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