A Comparison of the Fitness Functions to Identify the Motor-Table System: Simulations and Experiments

  • Yuan-Chou Jing
  • Kun-Yung ChenEmail author
Regular Paper


The different state-error fitness functions (FFs) are proposed and compared numerically and experimentally to identify a motor-table system by using self-learning particle swarm optimization (SLPSO). Firstly, the completed mathematical model containing both of mechanical and electrical equations is successfully formulated. Secondly, the FFs containing different state-errors are compared by using PSO and SLPSO to identify the unknown parameters. It is found that the identify performance of the SLPSO algorithm by using FF with full-state error of displacement, velocity and current is the best than the other methods. Thus, the FF with full-state errors is adopted in experiments for a real mechatronic motor-table system. Then, the unknown parameters are successfully identified by the SLPSO algorithm. The contributions of this paper are: (1) the more states of the system are measured and used in the FF, the more parameters of system are accurately identified by the proposed identification approach, (2) the FF with full-state errors is performed in a real mechatronic motor-table system, and the unknown parameters are successfully identified by the SLPSO algorithm in experimental results.


Fitness functions Motor-table system System identification Self-learning particle swarm optimization 

List of Symbols


System matrix


Identified system matrix


System matrix


Damping coefficient


Identified system matrix


Constant matrix


Force vector


Identified force vector


External force


Friction force


Fitness function

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



Moment of inertia


Motor torque constant

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

Armature inductances


Mass of table


Stator resistance


Control input vector

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

Stator voltages


State vector


Output state vector


Identified output state vector


Viscous damping coefficient

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

Stator flux linkages


Coefficient of friction


Motor torque


Angular velocity


Inverter frequency

\(\Delta m\)

External uncertain mass



The author is grateful to the Ministry of Science and Technology for the financial support under Contract No. MOST 105-2221-E-344-003. The author is also grateful to Prof. Rong-Fong Fung from National Kaohsiung University Science and Technology (NKUST) Taiwan to provide the experimental equipment.


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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Graduate Institute of China Military Affairs Studies, Fu Hsing Kang CollegeNational Defense UniversityTaipei CityTaiwan, ROC
  2. 2.Department of Mechanical EngineeringAir Force Institute of TechnologyKaohsiung CityTaiwan, ROC

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