A Convex Optimization Framework for Hybrid Simulation

  • Mohit VermaEmail author
  • Aikaterini Stefanaki
  • Mettupalayam V. Sivaselvan
  • J. Rajasankar
  • Nagesh R. Iyer
Conference paper


Hybrid simulation is a dynamic response evaluation technique which involves the partitioning of the structure into parts—physical and numerical subsystems. The interaction between the two subsystems is realized with the help of a transfer system (an actuator or a shake table). The objective of the hybrid simulation is to find control input to the transfer system such that the impedance of the transfer system is close to the numerical subsystem. The physical limitations of the system needs to be accounted while designing controller for hybrid simulation. This paper presents a framework which enables to pose controller synthesis for hybrid simulation as a multi-objective convex optimization problem using linear matrix inequalities (LMIs). Different control system tools based on LMIs which can be used for abstract formulation are described. A mathematical model based on the linear control theory is presented for the hybrid simulation of a three degrees of freedom system using shake table. The controller obtained from the solution of optimization is used to evaluate the frequency response of the closed loop hybrid system. It is observed that the accuracy of the hybrid simulation decreases with the decrease in the control effort.


Actuator Convex optimization Emulated system Hybrid simulation Linear matrix inequalities 



First author acknowledges the support received from Fulbright-Nehru Doctoral and Professional Research Fellowship under IIE Grant No. 15130894.

The paper is being published with the kind permission of Director, CSIR -Structural Engineering Research Centre, Chennai.


  1. 1.
    Neild SA, Stoten DP, Drury D, Wagg DJ (2005) Control issues relating to real-time substructuring experiments using a shaking table. Earthq Eng Struct Dyn 34(9):1171–1192CrossRefGoogle Scholar
  2. 2.
    Carrion JE, Spencer BF Jr, Phillips BM (2009) Real-time hybrid simulation for structural control performance assessment. Earthq Eng Eng Vibr 8(4):481–492CrossRefGoogle Scholar
  3. 3.
    Chen P-C, Tsai K-C (2013) Dual compensation strategy for real-time hybrid testing. Earthq Eng Struct Dyn 42(1):1–23CrossRefGoogle Scholar
  4. 4.
    Gao X, Castaneda N, Dyke SJ (2013) Real time hybrid simulation: from dynamic system motion control to experimental error. Earthq Eng Struct Dyn 42(6):815–832CrossRefGoogle Scholar
  5. 5.
    Boyd SP, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory, vol 15. SIAM, PhiladelphiaGoogle Scholar
  6. 6.
    Van Antwerp JG, Braatz RD (2000) A tutorial on linear and bilinear matrix inequalities. J Process Control 10(4):363–385Google Scholar
  7. 7.
    Scherer C, Weiland S (2000) Linear matrix inequalities in control. Lecture notes, Dutch Institute for Systems and Control, Delft, The NetherlandsGoogle Scholar
  8. 8.
    Grant M, Boyd S, Ye Y (2008) Cvx: Matlab software for disciplined convex programmingGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  • Mohit Verma
    • 1
    • 2
    Email author
  • Aikaterini Stefanaki
    • 3
  • Mettupalayam V. Sivaselvan
    • 3
  • J. Rajasankar
    • 1
    • 2
  • Nagesh R. Iyer
    • 1
    • 2
  1. 1.CSIR-Structural Engineering Research CentreChennaiIndia
  2. 2.Academy of Scientific and Innovative Research (AcSIR)ChennaiIndia
  3. 3.Department of Civil, Structural and Environmental EngineeringUniversity at BuffaloBuffaloUSA

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