Skip to main content
SpringerLink
Log in

Study on LQR control algorithm using superelement model

  • Geological, Civil, Energy and Traffic Engineering
  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

The conventional linear quadratic regulator (LQR) control algorithm is one of the most popular active control algorithms. One important issue for LQR control algorithm is the reduction of structure’s degrees of freedom (DOF). In this work, an LQR control algorithm with superelement model is intended to solve this issue leading to the fact that LQR control algorithm can be used in large finite element (FE) model for structure. In proposed model, the Craig-Bampton (C-B) method, which is one of the component mode syntheses (CMS), is used to establish superelement modeling to reduce structure’s DOF and applied to LQR control algorithm to calculate Kalman gain matrix and obtain control forces. And then, the control forces are applied to original structure to simulate the responses of structure by vibration control. And some examples are given. The results show the computational efficiency of proposed model using synthesized models is higher than that of the classical method of LQR control when the DOF of structure is large. And the accuracy of proposed model is well. Meanwhile, the results show that the proposed control has more effects of vibration absorption on the ground structures than underground structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. LIU X D, WU Y J, ZHANG Y, XIAO S. A control method to make lqr robust: A planes cluster approaching mode [J]. International Journal of Control, Automation, and Systems, 2014, 12(2): 302–308.

    Article  Google Scholar 

  2. HUI Q. Distributed semistable LQR control for discrete-time dynamically coupled systems [J]. Journal of the Franklin Institute, 2012, 349: 74–92.

    Article  MathSciNet  MATH  Google Scholar 

  3. TAO C W, TAUR J S, CHEN Y C. Design of a parallel distributed fuzzy LQR controller for the twin rotor multi-input multi-output system [J]. Fuzzy Sets and Systems, 2010, 161: 2081–2103.

    Article  MathSciNet  MATH  Google Scholar 

  4. TARAPAD A R, DEBABRATA C. Optimal vibration control of smart fiber reinforced composite shell structures using improved genetic algorithm [J]. Journal of Sound and Vibration, 2009, 319(1/2): 15–40.

    Google Scholar 

  5. BASU B, NAGARAJAIAH S. A wavelet-based time-varying adaptive LQR algorithm for structural control [J]. Engineering Structures, 2008, 30(9): 2470–2477.

    Article  Google Scholar 

  6. POODEH M B, ESHTEHARDIHA S, KIYOUMARSI A, ATAEI M. Optimizing LQR and pole placement to control buck converter by genetic algorithm [J]. Control, Automation and Systems, 2007, 17/18/19/20: 2195–2200.

    Google Scholar 

  7. POURZEYNALI S, LAVASANI H H, MODARAYI A H. Active control of high rise building structures using fuzzy logic and genetic algorithms [J]. Engineering Structures, 2007, 29(3): 346–357.

    Article  Google Scholar 

  8. JIANG Z, HAN J D, WANG Y C, SONG Q. Enhanced LQR control for unmanned helicopter in hover [J]. Systems and Control in Aerospace and Astronautics, 2006, 6: 1437–1443.

    Google Scholar 

  9. TODOROV E, SAN D C, LI W W. A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems [J]. American Control Conference, 2005, 1: 300–306.

    Google Scholar 

  10. TAYFUN C, STEPHEN P B. Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria [J]. Systems & Control Letters, 2004, 53(5): 327–346.

    Article  MathSciNet  MATH  Google Scholar 

  11. SAM Y M, OSMAN J H S, GHANI M R. A class of proportional-integral sliding mode control with application to active suspension system [J]. Systems & Control Letters, 2004, 51(3/4): 217–223.

    Article  MathSciNet  MATH  Google Scholar 

  12. ADELI H, KIM H. Wavelet-hybrid feedback-least mean square algorithm for robust control of structures [J]. Journal of Structural Engineering, 2004, 130(1): 128–137.

    Article  Google Scholar 

  13. KIM H J, ADELI H. Hybrid feedback-least mean square algorithm for structural control [J] Journal of Structural Engineering, 2004, 130(1): 120–127.

    Article  Google Scholar 

  14. VADIGEPALLI R. A distributed state estimation and control algorithm for plantwide processes [J]. Control Systems Technology, 2003, 11(1): 119–127.

    Article  Google Scholar 

  15. KIM S, CHU B, HONG D, PARK H K. Synchronizing dual-drive gantry of chip mounter with LQR approach [J]. Advanced Intelligent Mechatronics, 2003, 2: 838–843.

    Google Scholar 

  16. TRINDADE M A, BENJEDDOU A, OHAYON R. Piezoelectric active vibration control of damped sandwich beams [J]. Journal of Sound and Vibration, 2001, 246(4): 653–677.

    Article  MATH  Google Scholar 

  17. LI Q S, LIU D K, FANG J Q, TAM C M. Multi-level optimal design of buildings with active control under winds using genetic algorithms [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2000, 86(1): 65–86.

    Article  Google Scholar 

  18. BOER S E, AARTS R G K M, MEIJAARD J P, BROUWER D M, JONKER J B. A nonlinear two-node superelement with deformable-interface surfaces for use in flexible multibody systems [J]. Multibody System Dynamics, 2014, 31: 405–431.

    Article  MathSciNet  MATH  Google Scholar 

  19. PAUL L C V, DANIEL J R. An impulse based substructuring method for coupling impulse response functions and finite element models [J]. Computer Methods in Applied Mechanics and Engineerging, 2014, 275: 113–137.

    Article  MathSciNet  MATH  Google Scholar 

  20. FEHR J, EBERHARD P. Simulation process of flexible multibody systems with non-modal model order reduction techniques [J]. Multibody System Dynamics, 2011, 25: 313–334.

    Article  MATH  Google Scholar 

  21. MOURELATOS Z P. An efficient crankshaft dynamic analysis using substructuring with ritz vectors [J]. Journal of Sound and Vibration, 2000, 238(3): 495–527.

    Article  Google Scholar 

  22. ALBERTO C. Superelements modelling in flexible multibody dynamics [J]. Multibody System Dynamics, 2000, 4: 245–266.

    Article  MATH  Google Scholar 

  23. NORTIER B P, VOORMEEREN S N, RIXEN D J. Application of residual vectors to superelement modeling of an offshore wind turbine foundation [J]. Topics in Experimental Dynamics Substructuring and Wind Turbine Dynamics, Conference Proceedings of the Society for Experimental Mechanics Series, 2012, 2: 149–163.

    Article  Google Scholar 

  24. GUO J, CHEN J Y, BOBET A. Influence of a subway station on the inter-story drift ratio of adjacent surface structures [J]. Tunnelling and Underground Space Technology, 2013, 35: 8–19.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian, 116023, China

    Qiang Xu  (徐强), Jian-yun Chen  (陈健云), Jing Li  (李静), Chen-yang Yuan  (苑晨阳) & Chun-feng Zhao  (赵春风)

Authors
  1. Qiang Xu  (徐强)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-yun Chen  (陈健云)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jing Li  (李静)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chen-yang Yuan  (苑晨阳)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chun-feng Zhao  (赵春风)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiang Xu  (徐强).

Additional information

Foundation item: Project(LZ2015022) supported by Educational Commission of Liaoning Province of China; Projects(51138001, 51178081) supported by the National Natural Science Foundation of China; Project(2013CB035905) supported by the Basic Research Program of China; Projects(DUT15LK34, DUT14QY10) supported by Fundamental Research Funds for the Central Universities, China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, Q., Chen, Jy., Li, J. et al. Study on LQR control algorithm using superelement model. J. Cent. South Univ. 23, 2429–2442 (2016). https://doi.org/10.1007/s11771-016-3302-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-016-3302-y

Key words

Search

Navigation