그림 1. 전향보상 PID 제어기 Fig. 1 Forward PID controller
그림 2. 이항계수차수 3 에서 6의 유리차수 미분기 Fig. 2 The Fractional Derivative controller when binomial coefficient order is 3 to 6
그림 3. α에 대한 유리차수 미분기 Fig. 3 The Fractional Derivative controller when α is 0.31 to 0.91
그림 4. 유리차수미분기의 이득
그림 5. 유리차수미분기를 포함하는 PID 제어기 Fig. 5 The PID controller with fractional derivative
그림 6. 솔레노이드 밸브의 위치제어 Fig. 6 The position control of the Solenoid valve
References
- L. Debnath, "A brief historical introduction to fractional calculus," Int. J. of Mathematical Education in Science and Technology, vol. 35, no. 4, 2004, pp. 487-501. https://doi.org/10.1080/00207390410001686571
- P. Torvik and R. Bagley, "On the appearance of the fractional derivative in the behavior of real material," J. of Applied Mechanics, Transaction of the ASMF, vol. 51, no. 2, 1984, pp. 294-298. https://doi.org/10.1115/1.3167615
- C. Ma and Y. Hori, "Fractional-Order Control: Theory and Applications in Motion Control," IEEE Industrial Electronics Mag., vol. 1, no. 4, 2007, pp. 6-16. https://doi.org/10.1109/MIE.2007.909703
- B. Dumitru, Z. Guvenc, and J. Tenreiro Machado, "New Trends in Nanotechnology and Fractional Calculus Applications." Dordrecht, Springer, 2010.
- J. Sabatier, O. Pgrawal, and J. Tenreiro Machado, "Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering," Dordrecht, Springer, 2007.
- Y. Bae, "Comparison Analysis of Behavior between Differential Equation and Fractional Differential Equation in the Van der Pol Equation," J. of the Korea Institute of Electronic Communication Sciences, vol. 11, no. 1, 2016, pp. 81-86. https://doi.org/10.13067/JKIECS.2016.11.1.81
- J. Kang and Y. Jeon, "Position Control for Solenoid Valve using the Fractional Order Controller," J. of the Korea Institute of Electronic Communication Sciences, vol. 13, no. 1, 2018, pp. 101-106. https://doi.org/10.13067/JKIECS.2018.13.1.101
- T. Kajima and Y. Kawamura, "Development of a high-speed solenoid valve : investigation of solenoids," IEEE Trans. Industrial Electronics, vol. 42, no. 1, 1995, pp 1-8. https://doi.org/10.1109/41.345838
- M. Rahman, N. Cheung, and K. Lim, "Position estimation in solenoid actuators," IEEE Trans. Ind. Applications, vol. 32, no. 3, 1996, pp. 552-559. https://doi.org/10.1109/28.502166