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

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

Abstract

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.

Keywords

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

List of Symbols

\({\mathbf{a}}\)

System matrix

\({\hat{\mathbf{a}}}\)

Identified system matrix

\({\mathbf{b}}\)

System matrix

\(B_{m}\)

Damping coefficient

\({\hat{\mathbf{b}}}\)

Identified system matrix

\({\mathbf{c}}\)

Constant matrix

\({\mathbf{d}}\)

Force vector

\({\hat{\mathbf{d}}}\)

Identified force vector

\(f_{e}\)

External force

\(f_{f}\)

Friction force

\({\text{FF}}\)

Fitness function

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

Current

\(J_{m}\)

Moment of inertia

\(K_{t}\)

Motor torque constant

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

Armature inductances

\(m_{0}\)

Mass of table

\(R_{s}\)

Stator resistance

\({\mathbf{u}}\)

Control input vector

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

Stator voltages

\({\mathbf{x}}\)

State vector

\({\mathbf{y}}\)

Output state vector

\({\hat{\mathbf{y}}}\)

Identified output state vector

\(\zeta\)

Viscous damping coefficient

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

Stator flux linkages

\(\mu\)

Coefficient of friction

\(\tau_{e}\)

Motor torque

\(\omega_{r}\)

Angular velocity

\(\omega_{s}\)

Inverter frequency

\(\Delta m\)

External uncertain mass

Notes

Acknowledgements

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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