Dynamic Stiffness Transfer Function of an Electromechanical Actuator Using System Identification

  • Sang Hwa Kim
  • Min-Jea Tahk
Original Paper


In the aeroelastic analysis of flight vehicles with electromechanical actuators (EMAs), an accurate prediction of flutter requires dynamic stiffness characteristics of the EMA. The dynamic stiffness transfer function of the EMA with brushless direct current (BLDC) motor can be obtained by conducting complicated mathematical calculations of control algorithms and mechanical/electrical nonlinearities using linearization techniques. Thus, system identification approaches using experimental data, as an alternative, have considerable advantages. However, the test setup for system identification is expensive and complex, and experimental procedures for data collection are time-consuming tasks. To obtain the dynamic stiffness transfer function, this paper proposes a linear system identification method that uses information obtained from a reliable dynamic stiffness model with a control algorithm and nonlinearities. The results of this study show that the system identification procedure is compact, and the transfer function is able to describe the dynamic stiffness characteristics of the EMA. In addition, to verify the validity of the system identification method, the simulation results of the dynamic stiffness transfer function and the dynamic stiffness model were compared with the experimental data for various external loads.


Dynamic stiffness Electromechanical actuator (EMA) System identification Transfer function 

List of symbols

\(B_i , B_\mathrm{m} , B_\mathrm{s} \)

Damping coefficients of spur gears (\(i = 1, 2)\), BLDC motor, and output shaft, \(\hbox {N}~ \hbox {m/(deg/s)}\)

\(\mathrm{Fr}_i , \mathrm{Fr}_\mathrm{m} , \mathrm{Fr}_\mathrm{s}\)

Coulomb friction coefficients of spur gears (\(i = 1, 2\)), BLDC motor, and output shaft, \(\hbox {N}~ \hbox {m}\)

\(i_{ds} , i_{qs}\)

d-axis and q-axis currents of BLDC motor, A

\(J_i , J_\mathrm{m} , J_\mathrm{s}\)

Moments of inertia of gears (\(i=1,{\ldots },5\)), BLDC motor, and output shaft, \(\hbox {kg}~\hbox {m}^{2}\)


Back electromotive force constant of BLDC motor, V/(deg/s)

\(K_i , K_\mathrm{s} \)

Static stiffnesses of components within gear train (\(i = 1, 2\)) and output shaft, \(\hbox {N}~\hbox {m/deg}\)


Torque constant of BLDC motor, \(\hbox {N}~\hbox {m/A}\)

\(L_{d} , L_{q}\)

d-axis and q-axis inductances of BLDC motor, H


Gear ratio within gear train (\(i = 1, 2, 3\))


Number of poles of BLDC motor


Stator resistance of BLDC motor, \(\Omega \)


Load into BLDC motor, \(\hbox {N}~\hbox {m}\)


External load into output shaft of electromechanical actuator, \(\hbox {N}~\hbox {m}\)

\(T_\mathrm{m} \)

Motor output torque, \(\hbox {N}~ \hbox {m}\)

\(\eta _i \)

Efficiencies of spur gears (\(i = 1, 2\)) and worm gear (\(i = 3\))

\(\theta _\mathrm{m} , \theta _{i} , \theta _{\mathrm{gt}} , \theta _\mathrm{s} \)

Deflection angles of BLDC motor, gears (\(i = 1, 2\)) in gear train, gear train, and output shaft of electromechanical actuator, deg

\(\lambda _{ds} , \lambda _{qs} \)

d-axis and q-axis flux linkages of BLDC motor, \(\hbox {V}~\hbox {s}\)

\(\lambda _\mathrm{m} \)

Magnitude of flux linkage established by permanent magnet, \(\hbox {V}~\hbox {s}\)

\(v_{ds} , v_{qs} \)

d-axis and q-axis voltages of BLDC motor, V

\(\omega _\mathrm{r} \)

Electrical angular velocity of BLDC motor, deg/s


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Copyright information

© The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Ph.D., Principal ResearcherAgency for Defense DevelopmentDaejeonRepublic of Korea
  2. 2.Professor of Aerospace Engineering, Department of Aerospace EngineeringKorea Advanced Institute of Science and TechnologyDaejeonRepublic of Korea

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