State Variable Estimation of Nonisothermal Continuous Stirred Tank Reactor Using Fuzzy Kalman Filter

Risa Fitria, Didik Khusnul Arif

Abstract


Increasing safety and product quality, reducing manufacturing cost, minimizing the impact of environment in fault detection system for Nonisothermal Continuous Stirred Tank Reactor (CSTR) are the reason why accurate state estimation is needed. Kalman filter is an estimation algorithm of the stochastic linear dynamical system. Through this work, a modification of Kalman Filter that combines with fuzzy theory, namely Fuzzy Kalman Filter (FKF) is presented to estimate the state variable of Non-Isothermal CSTR. First, we approximate the nonlinear system of CSTR as piecewise linear functions and then change the crisp variable into the fuzzy form. The estimation results are simulated using Matlab. The simulation shows the comparison results, i.e computational time and accuracy, between FKF and Ensemble Kalman Filter (EnKF). The final result of these case shows that FKF is better than EnKF to estimate the state variable of Nonisothermal CSTR. The error estimation of FKF is 72.9% smaller for estimation of reactans concentration, 39.9% smaller for tank temperature, 76.47% smaller for cooling jacket temperature and the computational time of FKF is 76.47% faster than the computational time of EnKF.

Keywords


Continuous stirred tank reactor; estimation; fuzzy Kalman filter

Full Text:

PDF

References


J. M. Lewis, S. Lakshmivarahan, and S. Dhall, Dynamic data assimilation: a least squares approach. Cambridge University Press, 2006, vol. 13.

R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of basic Engineering, vol. 82, no. 1, pp. 35–45, 1960.

G. Burgers, P. Jan van Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly weather review, vol. 126, no. 6, pp. 1719–1724, 1998.

M. Verlaan and A. W. Heemink, “Convergence of the RRSQRT algorithm for large scale Kalman filtering problems,” Delft University of Technology, pp. 97–19, 1997.

G. Evensen, “The ensemble Kalman filter: Theoretical formulation and practical implementation,” Ocean dynamics, vol. 53, no. 4, pp. 343–367, 2003.

E. Apriliani, D. Adzkiya, and A. Baihaqi, “The reduced rank of ensemble Kalman filter to estimate the temperature of non isothermal continue stirred tank reactor,” Jurnal Teknik Industri, vol. 13, no. 2, pp. 107–112, 2012.

G. Chen, Q. Xie, and L. S. Shieh, “Fuzzy Kalman filtering,” Information Sciences, vol. 109, no. 1-4, pp. 197–209, 1998.

R. A. Sani, “Estimasi variabel keadaan gerak longitudinal pesawat terbang menggunakan metode fuzzy Kalman filter,” Jurnal Sains dan Seni ITS, vol. 5, no. 2, 2016.

Z. Ermayanti, H. Apriliani, E. Nurhadi, and T. Herlambang, “Estimate and control position autonomous underwater vehicle based on determined trajectory using fuzzy Kalman filter method,” in International Conference on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation (ICAMIMIA), 2015, pp. 156–161.

S. Rajaraman, J. Hahn, and M. S. Mannan, “A methodology for fault detection, isolation, and identification for nonlinear processes with parametric uncertainties,” Industrial & engineering chemistry research, vol. 43, no. 21, pp. 6774–6786, 2004.

N. Yazdanparast, M. Shahbazian, M. Aghajani, and S. P. Abed, “Design of nonlinear CSTR control system using active disturbance rejection control optimized by asexual reproduction optimization,” Journal of Automation and Control, vol. 3, no. 2, pp. 36–42, 2015.

J. Curn, “Estimate and control position autonomous underwater vehicle based on determined trajectory using fuzzy Kalman filter method,” Ph.D. dissertation, University of Dublin, 2014.

J. A. Rodger, “Toward reducing failure risk in an integrated vehicle health maintenance system: A fuzzy multi-sensor data fusion Kalman filter approach for IVHMS,” Expert Systems with Applications, vol. 39, no. 10, pp. 9821–9836, 2012.




DOI: http://dx.doi.org/10.12962/j24775401.v3i1.2116

Refbacks

  • There are currently no refbacks.



View My Stats


Creative Commons License
International Journal of Computing Science and Applied Mathematics by Department Mathematics ITS is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at http://iptek.its.ac.id/index.php/ijcsam.