Design of a Kalman Filter and Three Observers in a CSTR for the Estimation of Concentration and Temperature in Jacket.

Santiago Cortes, Luis E. Cortes, Etty Sierra Vanegas

Abstract


The control implementation loops for the chemical process require measurements and variable estimations that are hard, difficult, and expensive; this is due to the lack of reliable devices, delays, wrong measurements, and expensive devices. The state estimation and non-linear systems parameters let restores state variables that the process requires to identify using the input and output known variables. This paper presents four-state estimators, Luenberger observer, Unknown Inputs, Sliding modes, and Kalman Filter, applied to a chemical process in a Continuous Stirred-Tank Reactor (CSTR) at three dynamics: concentration (CA), temperature (T), and temperature of the jacket (Tj). The estimation of the dynamics is carried out from the measurement of the values of the inputs and outputs of the process. Each estimator was tuned to have values close to the real ones. The three dynamics of the CSTR were assessed with perturbations and parametric changes based on the chemical process's phenomenological model. The estimators' results were close to those of the real process, with estimated deviations of the state variables between 5% and 10% of the real value. The SMO algorithm accepts a greater range of variation at nominal flow input F until 30%, while KF, UIO, and OL reach 5% maximum; this makes possible better estimation of chemical process variables in a CSTR using SMO.


Keywords


Observer; sliding surface; Kalman filter; continuous stirred-tank reactor; Luenberger.

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References


B Wayne Bequette. Behavior of a cstr with a recirculating jacket heat transfer system. In Proceedings of American Control Conference, volume 4, pages 3275–3280, 2002.

Giraldo Bertulfo. “Observador de estado mediante modos deslizantes de alto para procesos no lineales,” M. Eng. Thesis, Universidad Nacional de Colombia, Manizales, 2012.

Botero Héctor. “Formalismo para la síntesis de sensores virtuales basados en un modelo maestro de base fenomenológica”. D. Eng., Universidad Nacional de Colombia sede Medellín, Ingeniería Sistemas Energéticos, 2008.

Na, J., Chen, A. S., Herrmann, G., Burke, R., & Brace, C. Vehicle engine torque estimation via unknown input observer and adaptive parameter estimation. IEEE Transactions on Vehicular Technology, 67(1), 409-422, 2018.

Warrad, S. B., & Boubaker, O. Full order unknown inputs observer for multiple time-delay systems. International Journal on Smart Sensing and Intelligent Systems, 9(4), 1750-1775. doi:10.21307/ijssis-2017-938, 2016.

Bindlish, R. Non-linear model predictive control of an industrial polymerization process. Computers & Chemical Engineering, 73, 43-48, 2015.

Zhao D., Spurgeon S.K., Yan X. An Adaptive Finite Time Sliding Mode Observer. In: Clempner J., Yu W. (eds) New Perspectives and Applications of Modern Control Theory. Springer, Cham, 2018.

Leonid Fridman and et. al. Higher order sliding mode observer for state esti-mation and input reconstruction in non-linear systems. International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal, 18(4-5):399–412, 2008.

Graham C Goodwin, Stefan F Graebe, Mario E Salgado, et al. Control system design. Prentice Hall, 2001.

Yuanwei Zhang, Zhongxi Chao, Hugo A. Jakobsen, Modelling and simulation of chemical looping combustion process in a double loop circulating fluidized bed reactor, Chemical Engineering Journal,Volume 320, pp 271-282, 2017.

Kalman, R. E. A New Approach to Linear Filtering and Prediction Problems. ASME. J. Basic Eng, 82(1): 35–45, 1960.

Nouri A.S., Bouazi F.A., Derbel N. On the Sliding Control. In: Derbel N., Ghommam J., Zhu Q. Applications of Sliding Mode Control. Studies in Systems, Decision and Control, vol 79. Springer, Singapore, 2017.

D. G. Luenberger, Observing the State of a Linear System, in IEEE Transactions on Military Electronics, vol. 8, no. 2, pp. 74-80, 1964.

A. Uppal, W.H. Ray, A.B. Poore, On the dynamic behavior of continuous stirred tank reactors, Chemical Engineering Science, Volume 29, Issue 4, pp 967-985, 1974.

R Oliveira, E. C. Ferreira, and S. Feyo De Azevedo. Stability, dynamics of convergence and tuning of observer based kinetics estimators. Journal of Process Control, 12(2):311–323, 2002.

Fahad Wallam, Attaullah Y. Memon, A robust control scheme for non-linear non-isothermal uncertain jacketed continuous stirred tank reactor, Journal of Process Control, Volume 51, Pages 55-67, 2017.

Paul, P., Bhattacharyya, D., Turton, R., & Zitney, S. E. Non-linear dynamic model-based multiobjective sensor network design algorithm for a plant with an estimator-based control system. Industrial and Engineering Chemistry Research, 56(26), 7478-7490, 2017.

Abhinav Sinha, Rajiv Kumar Mishra, Temperature regulation in a Continuous Stirred Tank Reactor using event triggered sliding mode control, IFAC-PapersOnLine, Volume 51, Issue 1, pp 401-406, 2018.

Yan Yan, Shuanghe Yu, Xinghuo Yu, Quantized super-twisting algorithm based sliding mode control, Automatica, Volume 105, pp 43-48, 2019.

Eric A. and et al.The unscented Kalman filter for non-linear estimation. In Proceedings IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium, 153–158, 2000.

Adrian E. Onyeka, Xing-Gang Yan, Jianqiu Mu, Sliding Mode Control of Time-Delay Systems with Delayed Nonlinear Uncertainties, IFAC-PapersOnLine, Volume 50, Issue 1, pp 2696-2701, 2017.

Kalaga Mbukani, M. W., & Gule, N. Comparison of high-order and second order sliding mode observer based estimators for speed sensorless control of rotor-tied DFIG systems. IET Power Electronics, 12(12), 2019.




DOI: http://dx.doi.org/10.18517/ijaseit.11.4.13722

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