Design of Level Control in A 10 L Pure Capacitive Tank: Stability Analysis and Dynamic Simulation

Yulius Deddy Hermawan, Renung Reningtyas, Siti Diyar Kholisoh, Tutik Muji Setyoningrum



The open loop experiment of a 10 L pure capacitive tank has been successfully done in laboratory. The square tank connected with a pump was designed for investigation in laboratory, and the water was chosen as a fluid with its input volumetric rate of fi(t) [cm3/min]. The output volumetric rate of fo(t) can be adjusted by changing the pump voltage of vpu(t) [volt]. The open loop experiment has given the steady state parameters, and it could then be used for calculating the dynamic parameters. This study has proposed the level control configuration of a 10 L pure capacitive tank system; liquid level in the tank h(t) was kept constant by manipulating the pump voltage of vpu(t); and the input water volumetric rate of fi(t) was considered as a disturbance. The P-only-control was implemented to control the level. Purposes of this study are to analyze the stability of the closed loop responses and to do the closed loop dynamic simulation. The closed loop mathematical model was solved analytically with Laplace Transform, and Routh-Hurwitz criterion was chosen to analyze the stability. Since the closed loop model was found in the 2nd order system, the response depended on the value of the damping coefficient (ζ), in which it was really affected by the controller gain (Kc). In order to examine the control configuration, the input water volumetric rate disturbance (with amount of ±14%) was made based on step function. Based on the stability analysis, a stable response would be achieved if the controller gain is negative (Kc<0) and the damping coefficient is positive (ζ>0). Based on the dynamic simulation, the controller gain was recommended in between -117.36 [volt/cm] and -1.17 [volt/cm] and the damping coefficient in between 0 and 1. This study also revealed that by tuning an appropriate controller gain, the fastest and the stable response would be achieved.


Closed loop, Dynamic simulation, Level control, Pure capacitive, Routh-Hurwitz, Stable response

Full Text:



Dias, M.M., Rodrigues, A.E., and Castro, J.A. 2003. Frequency response of linear systems containing pure capacitance elements, Chemical Engineering and Processing 42: 939–942. doi:10.1016/S0255-2701(02)00186-1.

Hermawan, Y.D. 2014. Dynamic Simulation and Liquid Level Control in A Pure Capacity System (2 Tanks in Series). Proceedings of 2nd International Seminar on Fundamental and Application of Chemical Engineering (ISFAChE) 2014, Department of Chemical Engineering, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember, Bali, November 12-13, 2014, ISBN: 978-979-8897-72-6, p. G02-131 – G02-137.

Hermawan, Y.D., Kholisoh, S.D., Hamdani, A.F. and Puspita, D.D. 2014. Process Dynamic of Pure Capacity System of 2 Tanks in Series. Proceedings of Seminar Rekayasa Kimia dan Proses (SRKP) 2014, Department of Chemical Engineering, Faculty of Engineering, University of Diponegoro, Semarang, August 20-21, 2014, ISSN: 1411-4216, p. F-2-1 – F-2-6. (in Indonesian).

Hermawan, Y.D., and Haryono, G. 2012. Dynamic Simulation and Composition Control in A 10 L Mixing Tank. Jurnal Reaktor 14 (2): 95–100, Oktober 2012. Department of Chemical Engineering, Faculty of Engineering, University of Diponegoro.

Hermawan, Y.D., Haryono, G., Agustin, M., and Abiad, H. 2012. Composition Dynamic in A 10 L Mixing Tank. Proceedings of Seminar Nasional Teknik Kimia “Kejuangan” 2012. Department of Chemical Engineering, Faculty of Industrial Technology, UPN “Veteran” Yogyakarta, March 6, 2012, ISSN: 1693-4393, p. C15-1 – C15-6. (in Indonesian).

Hermawan, Y.D. 2011. Implementation of Process Reaction Curve for Tuning of Temperature Control Parameters in A 10 L Stirred Tank Heater. Journal of Materials Science and Engineering A1 1(4): 572–577, Sept. 2011.

Hussien , S.Y.S., Jaafar, H.I., Selamat N.A., Shair, E.F., and Abidin, A.F.Z. 2015. Development of Mathematical Model for Coupled Tank System using System Identification (SI). International Journal of Innovative Technology and Exploring Engineering (IJITEE) 4(12): 73–77.

Kala, H., Deepakraj, D., Gopalakrishnan, P., Vengadesan, P., and Iyyar, M.K. 2014. Performance Evaluation of Fuzzy Logoc and PID Controller for Liquid Level Process. International Journal of Innovative Research in Electrical, Electronics, Instrumentation and Control Engineering (IJIREEICE) 2(3): 1311–1314.

Luyben, W.L. 1996. Process Modeling, Simulation and Control for Chemical Engineers, 2nd ed. McGraw Hill International Editions, Chemical Engineering Series, ISBN: 0-13-128629-3: 167-192.

Marlin, T.E. 2000. Process Control: Designing Processes and Control Systems for Dynamic Performance. 2nd Ed. McGraw-Hill Higher Education ISBN: 0-07-039362-1, Singapore: 136 – 141 and 564 – 577.

Pena, J.M. 2004. Characterizations and Stable Tests for the Routh–Hurwitz Conditions and for Total Positivity. Linear Algebra and its Applications 393: 319–332. doi:10.1016/j.laa.2003.11.013

Rao, C.V.N., Rao, A.S., and Sree, R.P. 2011. Design of PID Controllers for Pure Integrator Systems with Time Delay. International Journal of Applied Science and Engineering 2011 9(4): 241–260.

Roopamala, T.D., and Katti, S.K. 2010. Comments on “Routh Stability Criterion”. International Journal of Computer Science and Information Security (IJCSIS) 7(2): 77–78.

Sigal, R. 1990. Algorithms for the Routh-Hurwitz Stability Test. Mathematical and Computer Modelling 13(8): 69–77.


Singh, M., and Saksena, D. 2012. Parametric Estimation of Inverse Response Process Compressing of First Order System and Pure Capacitive System. International Journal of Information Technology and Knowledge Management 5(2): 397–400.

Singh, M., and Sharma, A. 2012. Inverse Response Compentation by Estimating Parameters of A Process Compresing of Two First Order Systems. International Journal of Information Technology and Knowledge Management 5(2): 433–480.

Singh, M., Pant, B., and Lamba, R. 2012. Compensator Design for Taming Inverse Response. International Journal of Information Technology and Knowledge Management 6(1): 15–17.

Smith, C.A. and Corripio, A.B. 1997. Principles and Practice of Automatic Process Control, John Wiley & Sons, Inc., USA, ISBN: 0-471-57588-7: 168–172.

Stephanopoulos, G. 1984. Chemical Process Control: An Introduction to Theory and Practice, PTR. Prentice-Hall, Inc., A Simon and Shuster Company, New Jersey, 1984, ISBN: 0-13-128629-3: 287–290 & 302–306.

Zahreddine, Z. 2003. On The Interlacing Property and The Routh-Hurwitz Criterion. International Journal of Mathematics and Mathematical Sciences 2003 (12): 727–737.


  • There are currently no refbacks.

Published by Department of Chemical Engineering University of Diponegoro Semarang
Google Scholar

IJSE  by is licensed under Creative Commons Attribution 3.0 License.