Adjustment of Optimal Parameters to Control the Temperature in Different Conductors | ||
| مدل سازی در مهندسی | ||
| Volume 22, Issue 77, August 2024, Pages 107-116 PDF (1.01 M) | ||
| Document Type: Research Paper | ||
| DOI: 10.22075/jme.2023.28427.2336 | ||
| Authors | ||
| Amirhossein Oudi1; Samaneh Faramarzi2; Maryam Hosseini3; Yegane Davoodbeygi* 4 | ||
| 1Ph.D. Candidate, Department of Chemical Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran | ||
| 2MSc. Student, Department of Chemical Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran | ||
| 3MSc, Department of Chemical Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran | ||
| 4Assistant Professor, Department of Chemical Engineering, University of Hormozgan, Bandar Abbas, Iran | ||
| Receive Date: 16 September 2022, Revise Date: 18 December 2023, Accept Date: 23 December 2023 | ||
| Abstract | ||
| PID controller is a closed-loop control algorithm and method using the concept of feedback that is used in many industrial processes to control the speed of DC motors, pressure control, temperature control, and so on. For this purpose, a horizontal object with different conductivities was chosen to control its temperature by changing the heat flux. Then, the studied system was written in the state space. In this method, partial differential equations were converted into ordinary differential equations with the help of finite difference, then a suitable controller was designed for temperature control. In this method, the differential equations expressing the process were written as simultaneous first order differential equations. The results show that for the stability of systems with poor thermal conductivity (small α value), should be K_p/K_i =10. For systems with medium thermal conductivity should be K_p/K_i =0.1. For systems with strong thermal conductivity (large α value) should be K_p/K_i =1. According to the optimization done, Kd was a small value in all three cases, so the PI controller can be used in such systems. | ||
| Keywords | ||
| PID controller; Temperature control; Conductive heat transfer; Conductive horizontal object | ||
| References | ||
|
[1] H. Aschemann, G.V. Kostin, A. Rauh, and V.V. Saurin. "Approaches to control design and optimization in heat transfer problems." Journal of Computer and Systems Sciences International 49 (2010): 380-391. [2] F.P Incropera. "Principles of Heat and Mass Transfer." (2013). [3] G.V. Grenkin, A.Y. Chebotarev, A.E. Kovtanyuk, N.D. Botkin, and K.H. Hoffmann. "Boundary optimal control problem of complex heat transfer model." Journal of Mathematical Analysis and Applications 433, no. 2 (2016): 1243-1260. [4] D.W. Hahn, and M. Necati Özisik. Heat conduction. John Wiley & Sons, 2012. [5] J.P. Holman. "Free convection from vertical planes and cylinders." Heat Transfer (2002): 321-328. [6] R.A. Meric. "Finite element analysis of optimal heating of a slab with temperature dependent thermal conductivity." International Journal of Heat and Mass Transfer 22.10 (1979): 1347-1353. [7] R.A. Meric. "Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem." International Journal for Numerical Methods in Engineering 14.12 (1979): 1851-1863. [8] A. Maidi, and J.P. Corriou. "Distributed control of nonlinear diffusion systems by input–output linearization." International Journal of Robust and Nonlinear Control 24.3 (2014): 389-405. [9] N. Boonkumkrong, and S. Kuntanapreeda. "Backstepping boundary control: An application to rod temperature control with Neumann boundary condition." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 228.5 (2014): 295-302. [10] N. Özdemir, , Y. Povstenko, D. Avcı, and B. Billur İskender. "Optimal boundary control of thermal stresses in a plate based on time-fractional heat conduction equation." Journal of Thermal Stresses 37, no. 8 (2014): 969-980. [11] Y. Yang , and S. Dubljevic. "Linear matrix inequalities (LMIs) observer and controller design synthesis for parabolic PDE." European Journal of Control 20.5 (2014): 227-236. [12] T.A.h Luong, K.H. Cho, M.G. Song, J.C. Koo, H.R. Choi, and H. Moon. "Nonlinear tracking control of a conductive supercoiled polymer actuator." Soft robotics 5, no. 2 (2018): 190-203. [13] S. Wan, P. Xu, K. Wang, J. Yang, and S. Li. "Real-time estimation of thermal boundary of unsteady heat conduction system using PID algorithm." International Journal of Thermal Sciences 153 (2020): 106395. [14] T.G. Alexandru, and C. Pupaza. "The development of PID temperature controllers based on FEM thermal analysis." MATEC Web of Conferences. Vol. 342. EDP Sciences, 2021. [15] S. Bennett. A history of control engineering, 1930-1955. No. 47. IET, 1993. [16] K.J. Astrom. "PID controllers: theory, design, and tuning." The international society of measurement and control (1995). [17] J.G. Ziegler, and N.B. Nichols. "Optimum settings for automatic controllers." Transactions of the American society of mechanical engineers 64.8 (1942): 759-765. [18] G. Cohen, and G.A. Coon. "Theoretical consideration of retarded control." Transactions of the American Society of Mechanical Engineers 75.5 (1953): 827-834. [19] D.W. Pessen. "A new look at PID-controller tuning." (1994): 553-557. [20] D.R. Coughanowr, and L.B. Koppel. Process systems analysis and control. Vol. 2. New York: McGraw-Hill, 1965. [21] M. Morari, "Robust process control." Prentice-Hall google schola 2 (1989): 654-658. [22] W.K. Ho, C.C. Hang, and L.S. Cao. "Tuning of PID controllers based on gain and phase margin specifications." Automatica 31.3 (1995): 497-502. [23] S.K. Godunov, and I. Bohachevsky. "Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics." Matematičeskij sbornik 47.3 (1959): 271-306. | ||
|
Statistics Article View: 520 PDF Download: 638 |
||