Composition and Relative Volatility Estimation in Ethanol-Water Distillation Process through Quadratic Program Based Constrained Kalman Estimation Paradigm

Document Type : Research Article

Authors

1 Department of Electronics and Instrumentation Engineering, VNR VJIET, Hyderabad, INDIA

2 Department of Instrumentation Engineering, MIT, Anna University, Chennai, INDIA

Abstract

Kalman filter is a classic iterative estimation technique widely used to estimate states and parameters of linear dynamic systems with white Gaussian measurement and process noises. However, if the measurement noises are predominant, resulting in a poor signal-to-noise ratio, the estimator fails to provide allowable error covariance and optimal state estimation. In such circumstances, to enhance the estimation accuracy, measurement constraints need to be incorporated into the estimation routine. Through this work, a Quadratic Program-based Constrained Kalman Estimation (QP-CKE) estimation sequence is proposed and developed to handle the additive measurement noise constraints. This is implemented by incorporating a deconvoluted quadratic program with a modified Kalman estimation paradigm to handle the constraint cost function. Composition estimation in a laboratory binary distillation process for ethanol-water mixture separation under steady-state operating conditions is used as a case study. Noise augmented Two Input Two Output (TITO) linearized dynamic model of the process is established by inferring Gaussian distributed tray temperature measurements and mixture vapor-liquid equilibrium data. The performance of this new estimator is tested for top and bottom composition estimation for step input excitation for reflux rate and reboiler power inputs under feed flow disturbances and the results are compared with that of conventional Kalman and Q adaptive Kalman estimators. The performance of the proposed estimator proves to be competent with reasonable computational speed and improved estimation accuracy. Also, relative volatility and vapor-liquid equilibrium trends are derived from estimated tray composition data, and results are found in good relevance with that of the experimental data.

Keywords

Main Subjects

References

[1] Simon D., Chia T., Kalman Filtering with State Equality Constraints, IEEE Trans. Aerosp. Electron. Syst., 39: 128–136 (2003).
[2] Simon D., Simon D.L., Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering, Journal of Engineering for Gas Turbines and Power, 127(2): 323 (2005).
[3] Sarkar A., Mallick B.K., Staudenmayer J., Pati D., Carroll R.J., Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors, Journal of Computational and Graphical Statistics, 23: 1101–1125 (2014).
[4] Prakash J., Patwardhan S.C., Shah S.L., Constrained State Estimation Using Particle Filters, IFAC Proceedings Volumes, 41(2): 6472–6477 (2008).
[5] Li R., Magbool Jan,N., Huang B., Prasad V., Constrained Multimodal Ensemble Kalman Filter Based on Kullback–Leibler (KL) Divergence, Journal of Process Control, 79: 16–28 (2019).
[6] Simon D., Simon D.L., Constrained Kalman Filtering via Density Function Truncation for Turbofan Engine Health Estimation, International Journal of Systems Science, 41(2): 159–171 (2010).
[7] Mehra R.K., “On the Identification of Variances and Adoptive Kalman Filtering”, IEEE Trans. Automatic Control, AC-15(2): 175- 184 (1970).
[8] Mohamed A., Schwarz K., Adaptive Kalman Filtering for INS/GPS, Journal of Geodesy, 73: 193–203 (1999).
[9] Teixeira B., Chandrasekar J., Palanthandalam-Madapusi H.J., Torres L., Aguirre L.A., Bernstein D.S., Gain-Constrained Kalman Filtering for Linear and Nonlinear Systems, IEEE Transactions on Signal Processing, 56(9): 4113–4123 (2008).
[10] Wen C., Cai Y., Liu Y., Wen C., A Reduced-Order Approach to Filtering for Systems with Linear Equality Constraints, Neurocomputing, 193: 219–226 (2016).
[11] Rouhani A., Abur A., Constrained Iterated Unscented Kalman Filter for Dynamic State and Parameter Estimation, IEEE Transactions on Power Systems, 33(3): 2404–2414 (2018).
[12] Mohammadnia V., Salahshoor K., A New Comprehensive Sensor Network Design Methodology for Complex Nonlinear Process Plants, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 31(3): 145-156 (2012).
        doi: 10.30492/ijcce.2012.5961
[13] Zhao J., Mili L., Gomez-Exposito A., Constrained Robust Unscented Kalman Filter for Generalized Dynamic State Estimation, IEEE Transactions on Power Systems, 1–1 (2019).
[14] Sagi B., Thangavelu T., “Data Driven Modelling for Dual Composition Estimation in Binary Distillation Process”, 4th International Conference on Computer, Communication and Signal Processing (ICCCSP),
1-6 (2020).
doi: 10.1109/ICCCSP49186.2020.9315278.
[15] Yang R., Apley D.W., Staum J., Ruppert D., Density Deconvolution with Additive Measurement Errors using Quadratic Programming, Journal of Computational and Graphical Statistics, 1–20 (2019).
[16] Wolters M.A., Braun W.J., Enforcing Shape Constraints on a Probability Density Estimate Using an Additive Adjustment Curve, Communications in Statistics - Simulation and Computation, 47(3): 672–691 (2017).
Iranian Journal of Chemistry and Chemical Engineering
Volume 42, Issue 1 - Serial Number 123
January 2023
Pages 310-320

Files

Share

How to cite

Statistics