International Journal of Dynamics and Control

, Volume 7, Issue 4, pp 1501–1520 | Cite as

Optimized methods for the pre-eminent performance of LQR control applied in a MIMO system

  • Piyali DasEmail author
  • R. K. Mehta
  • O. P. Roy


This paper illustrates various techniques to achieve the best optimization method under the Linear quadratic control strategy that is used for a multiple input multiple output system. The objective of the paper is to find the control criteria using the principle of extended state observer. An advanced optimized iteration method was introduced to select the weighted matrix Q from the control parameters. Another method is simulink response optimization method which also can fulfil the desired output result shown in the paper. Both the variables, the weighted matrix Q and the observer gain La, was modified after applying these optimization methods. The method responses were as per the minimal damping ratio of control logic. Among all these algorithms, the best iterative result was initiated.


MIMO system LQR control ESO Algorithm for advanced optimized iteration method (AOIM) Weighted matrix 



The laboratory model experiments of research work were done in NIT Suratkal, Karnataka, India. Name of the lab is Virtual Lab under Mechanical Engineering Department.


  1. 1.
    Quanser (2006) 2-DOF helicopter user and control manual. Quanser Inc., Canada, pp 1–28Google Scholar
  2. 2.
    Zeghlache S, Kara K, Saigaa D (2014) Type-2 fuzzy logic control of a 2-DOF helicopter (TRMS system). Cent Eur J Eng 4:303–315. CrossRefGoogle Scholar
  3. 3.
    Kumar EV, Raaja GS, Jerome J (2016) Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter. Appl Soft Comput 41:77–90. CrossRefGoogle Scholar
  4. 4.
    Vishnupriyan J, Manoharan PS, Ramalakshmi APS (2014) Uncertainty modeling of nonlinear 2-DOF helicopter model. In: 2014 International conference on computer communication and informatics, Coimbatore, pp 1–6.
  5. 5.
    Phillips A, Sahin F (2014) Optimal control of a twin rotor MIMO system using LQR with integral action. In: World automation congress (WAC), Waikoloa, HI, pp 114–119.
  6. 6.
    AC Aras, O Kaynak (2014) Trajectory tracking of a 2-DOF helicopter system using neuro-fuzzy system with parameterized conjunctors. In: IEEE/ASME international conference on advanced intelligent mechatronicsGoogle Scholar
  7. 7.
    Zhou R, Mehrandezh M, Paranjape R (2014) Model helicopter control using body-mounted vibro-tactile transducers. World J Eng Technol 2(4):322CrossRefGoogle Scholar
  8. 8.
    Beloli ASR, Florêncio JL, Cavalca MSM (2013) A 2 DoF low cost control workstation for control techniques application. In: 22nd International congress of mechanical engineering (COBEM 2013), Brazil, pp 3101–3112Google Scholar
  9. 9.
    Luenberger DG (1966) Observers for multivariable systems. IEEE Trans Autom Control 11:190–197CrossRefGoogle Scholar
  10. 10.
    Zhen Z, Yong Z, Zhigao Z, Shaoping M, Jing W (2011) Semi-active control using mr dampers based on fully decentralized control strategy. In: 2011 International conference on electric information and control engineering. Wuhan, pp 5289–5292.
  11. 11.
    Vilchis JCA, Brogliato B, Dzul A, Lozano R (2003) Nonlinear modeling and control of helicopters. Automatica 39(9):1583–1596MathSciNetCrossRefGoogle Scholar
  12. 12.
    Das P, Meheta RK, Roy OP (2017) Disturbance rejection using Extended State Observer for a MIMO system. In: IEEE International WIE conference on electrical and computer engineering (WIECON-ECE), Dehradun, India, pp 192–198.
  13. 13.
    Shihua L, Yang J, Wen-Hua C, Xisong C (2010) Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Trans Ind Electron 59(12):4792–4802Google Scholar
  14. 14.
    Choudhary MK, Kumar GN (2016) ESO based LQR controller for ball and beam system. IFAC-PapersOnLine 49(1):607–610. MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tao J, Ma L, Zhu Y (2016) Improved control using extended non-minimal state space MPC and modified LQR for a kind of nonlinear systems. ISA Trans 65:319–326. CrossRefGoogle Scholar
  16. 16.
    Mondal S, Mahanta C (2011) Second order sliding mode controller for twin rotor MIMO system. In: 2011 annual IEEE India conference, Hyderabad, pp 1–5.
  17. 17.
    Mishra SK, Purwar S (2014) To design optimally tuned FOPID controller for twin rotor MIMO system. In: 2014 Students conference on engineering and systems, Allahabad, pp 1–6.
  18. 18.
    Goodwin GC, Graebe SF, Salgado ME (2000) Control system design. Pearson, LondonGoogle Scholar
  19. 19.
    Agathoklis P, Grepper PO, Kaiser W, Studer R (1979) Optimal steady-state decoupling of linear systems with prescribed degree of stability. In: IFAC symposium on computer aided design of control systems, 29–31 August 1979, pp 207–216CrossRefGoogle Scholar
  20. 20.
    Franklin GF, Powell JD, Workman ML (1997) Digital control of dynamic systems, 3rd edn. Addison-Wesley Longman Inc. Publication, BostonzbMATHGoogle Scholar
  21. 21.
    Barsaiyan P, Purwar S (2010) Comparison of state feedback controller design methods for MIMO systems. In: 2010 International conference on power, control and embedded systems. Allahabad, pp 1–6.
  22. 22.
    Fang J (2014) The LQR controller design of two-wheeled self-balancing robot based on the particle swarm optimization algorithm. Math Prob Eng 2014:1–6MathSciNetzbMATHGoogle Scholar
  23. 23.
    Tao CW, Taur JS, Chen YC (2010) Design of a parallel distributed fuzzy LQR controller for the twin rotor multi-input multi-output system. Fuzzy Set Syst 161(15):2081–2103MathSciNetCrossRefGoogle Scholar
  24. 24.
    Ogata K (2010) Modern control engineering, 5th edn. Prentice Hall, Upper Saddle RiverzbMATHGoogle Scholar
  25. 25.
    Medanic J, Tharp HS, Perkins WR (1988) Pole placement by performance criterion modification. IEEE Trans Autom Control 33(5):469–472. MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Zheng B, Zhong Y (2011) Robust attitude regulation of a 3-DOF helicopter benchmark: theory and experiments. IEEE Trans Ind Electron 58(2):660–670CrossRefGoogle Scholar
  27. 27.
    Matsuba I, Ushida S, Oku H (2012) MIMO closed-loop subspace model identification and hovering control of a coaxial mini helicopter with 3 DOFs. IFAC Proceedings 45(16):1665–1670. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringNERISTNirjuliIndia

Personalised recommendations