Estimation of Liquid Level in a Harsh Environment Using Chaotic Observer
Abstract
The increased demand for liquid level measurement has been a key factor in designing accurate and reliable control systems. Here, a study was carried out to calculate the liquid level in a tank using a pressure sensor for changes in inlet liquid parameters like temperature, density and velocity. Prediction of their variables for the long term is essential due to the randomness present in the input and measurement. Hence, observer design for state estimation of a non-linear dynamic system with uncertainties in the measurement and process becomes important. This work provides a feedback observer solution for a system with multiple inputs and single measurable output. A full state observer model is developed to estimate a system’s states with a sensor placed at a definite position from the pipe’s input point through which the liquid flows at different densities and temperatures. Using the observability properties, Luenberger full state observer is designed by various methods, verified using MATLAB and SIMULINK for the system state estimation. To incorporate process noise and measurement noise, the Kalman estimator is integrated with the system. Chaotic systems are susceptible to initial conditions, variations in parameters and are complex dynamic systems. However, providing consistently precise measurements through particular meters necessitates time-consuming computations that can be reduced by employing machine learning approaches that make use of optimizers. The results obtained are compared with the prediction models obtained using Artificial Neural Networks and are validated through the readings obtained from the experimental setup.
Keywords
Full Text:
PDFReferences
M. S. Shah, J. B. Joshi, A. S. Kalsi, C. S. R. Prasad, and D. S. Shukla, “Analysis of flow through an orifice meter: CFD simulation,” Chemical Engineering Science, vol. 71, pp. 300–309, Mar. 2012.
A. Rocchi, E. Santecchia, F. Ciciulla, P. Mengucci, and G. Barucca, “Characterization and optimization of level measurement by an ultrasonic sensor system,” IEEE Sens. J., vol. 19, no. 8, pp. 3077–3084, 2019.
T. Islam, O. P. Maurya, and A. U. Khan, “Design and fabrication of fringing field capacitive sensor for non-contact liquid level measurement,” IEEE Sens. J., vol. 21, no. 21, pp. 24812–24819, 2021.
R. He, C. Teng, S. Kumar, C. Marques, and R. Min, “Polymer Optical Fiber Liquid Level Sensor: A Review,” IEEE Sens. J., vol. 22, no. 2, pp. 1081–1091, 2022.
G. Dou, R. Chen, C. Han, Z. Liu, and J. Liu, “Research on water-level recognition method based on image processing and convolutional neural networks,” Water (Basel), vol. 14, no. 12, p. 1890, 2022.
G. Chen, T. Sun, P. Wang, and B. Sun, “Design of temperature compensation system of pressure sensors,” 2006 IEEE International Conference on Information Acquisition, 2006.
P. Esmaili, F. Cavedo, and M. Norgia, “Differential Pressure-Based Densitometer in Dynamic Condition,” IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1–7, 2021.
C. F. Lui, Y. Liu, and M. Xie, “A supervised bidirectional long shortterm memory network for data-driven dynamic soft sensor modeling,” IEEE Trans. Instrum. Meas., vol. 71, pp. 1–13, 2022.
M. S. Zarnik and D. Belavic, “Study of LTCC-based pressure sensors in water,” Sens. Actuators A Phys., vol. 220, pp. 45–52, 2014.
M. S. Zarnik, D. Belavic, and S. Macek, “The warm-up and offset stability of a low-pressure piezoresistive ceramic pressure sensor,” Sens. Actuators A Phys., vol. 158, no. 2, pp. 198–206, 2010.
P. Esmaili, F. Cavedo, and M. Norgia, “Characterization of pressure sensor for liquid-level measurement in sloshing condition,” IEEE Trans. Instrum. Meas., vol. 69, no. 7, pp. 4379–4386, 2020.
P. Esmaili, F. Cavedo, A. Pesatori, and M. Norgia, “Liquid level measurement through capacitive pressure sensor,” in 2020 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2020, pp. 1–5.
P. C. Joshi, N. B. Chopade, and B. Chhibber, “Liquid level sensing and control using inductive pressure sensor,” in 2017 International Conference on Computing, Communication, Control and Automation (ICCUBEA), 2017, pp. 1–5.
P. Esmaili, P. Esmaili, F. Cavedo, and M. Norgia, “PSO-based autocalibration for differential pressure level sensor,” in 2021 International Conference on Artificial Intelligence of Things (ICAIoT), 2021, pp. 30–35.
R. Perez et al., “Leak localization in water networks: A model-based methodology using pressure sensors applied to a real network in Barcelona [applications of control],” IEEE control syst., vol. 34, no. 4, pp. 24–36, 2014.
M. A. Boillat, A. J. van der Wiel, A. C. Hoogerwerf, and N. F. de Rooij, “A differential pressure liquid flow sensor for flow regulation and dosing systems,” Proceedings IEEE Micro Electro Mechanical Systems, 1995.
Y. Hongfeng, L. Xingang, S. Hong, and L. Hong, “CFD simulation of orifice flow of orifice-type liquid distributor,” China Pet. Process. Petrochem. Technol., vol. 15, no. 3, p. 70, 2013.
J. F. Wendt, Ed., Computational fluid dynamics: An introduction, 3rd ed. Berlin, Germany: Springer, 2008.
P. Esmaili, F. Cavedo, and M. Norgia, “Characterization of pressure sensor for liquid-level measurement in sloshing condition,” IEEE Trans. Instrum. Meas., vol. 69, no. 7, pp. 4379–4386, 2020.
Z. A. Dayev and A. K. Kairakbaev, “Modeling of coefficient of contraction of differential pressure flowmeters,” Flow Meas. Instrum., vol. 66, pp. 128–131, 2019.
Y. Guan and M. Saif, “A novel approach to the design of unknown input observers,” IEEE Trans. Automat. Contr., vol. 36, no. 5, pp. 632–635, 1991.
M. Hou and P. C. Muller, “Design of observers for linear systems with unknown inputs,” IEEE Trans. Automat. Contr., vol. 37, no. 6, pp. 871–875, 1992.
D. Luenberger, “Observers for multivariable systems,” IEEE Transactions on Automatic Control, vol. 11(2), pp.190-197, 1966
R. Szabolcsi, “Pole Placement Technique Applied in Unmanned Aerial Vehicles Automatic Flight Control Systems Design,” Land Forces Academy Review, vol. 23, no. 1, pp. 88–98, Mar. 2018.
C.-C. Tsui, “Observer design — A survey,” International Journal of Automation and Computing, vol. 12, no. 1, pp. 50–61, Feb. 2015, doi: 10.1007/s11633-014-0865-7.
W. Zheng, C. Wang, and D. Liu, “Data-driven based multi-objective combustion optimization covering static and dynamic states,” Expert Syst. Appl., vol. 210, no. 118531, p. 118531, 2022.
F. Jafarizadeh et al., “Data driven models to predict pore pressure using drilling and petrophysical data,” Energy rep., vol. 8, pp. 6551–6562, 2022.
T. M. Santhi and S. S., “Performance Enhanced Liquid Level Sensing System For Dynamic Environments,” 2019 IEEE 5th International Conference for Convergence in Technology (I2CT), pp. 1-5, Mar. 2019.
M. P. Schoen and J.-C. Lee, “Application of System Identification for Modeling the Dynamic Behavior of Axial Flow Compressor Dynamics,” International Journal of Rotating Machinery, vol. 2017, pp. 1–14, 2017.
M. R. Ananthasayanam, M. S. Mohan, N. Naik, and R. M. O. Gemson, “A heuristic reference recursive recipe for adaptively tuning the Kalman filter statistics part-1: formulation and simulation studies,” Sadhana, vol. 41, no. 12, pp. 1473–1490, Dec. 2016, doi:10.1007/s12046-016-0562-z.
Y. Li and B. Hou, “Observer-based sliding mode synchronization for a class of fractional-order chaotic neural networks,” Advances in Difference Equations, vol. 2018, no. 1, Apr. 2018.
N. Oucief, M. Tadjine, and S. Labiod, “A new methodology for an adaptive state observer design for a class of nonlinear systems with unknown parameters in unmeasured state dynamics,” Trans. Inst. Meas. Control, vol. 40, no. 4, pp. 1297–1308, 2018.
Z. Wang, Y. Shen, and X. Zhang, “Actuator fault estimation for a class of nonlinear descriptor systems,” Int. J. Syst. Sci., vol. 45, no. 3, pp. 487–496, 2014.
M. Liu, L. Zhang, P. Shi, and Y. Zhao, “Fault estimation sliding-mode observer with digital communication constraints,” IEEE Trans. Automat. Contr., vol. 63, no. 10, pp. 3434–3441, 2018.
Y. Wang, V. Puig, and G. Cembrano, “Robust fault estimation based on zonotopic Kalman filter for discrete-time descriptor systems: Robust fault estimation based on zonotopic Kalman filter for discrete-time descriptor systems,” Int. J. Robust Nonlinear Control, vol. 28, no. 16, pp. 5071–5086, 2018.
W. Han, Z. Wang, Y. Shen, and Y. Liu, “Fault detection for linear discretetime descriptor systems,” IET Control Theory Appl., vol. 12, no. 15, pp. 2156–2163, 2018.
A. Zemzemi, M. Kamel, A. Toumi, and M. Farza, “Robust integral-observer-based fault estimation for Lipschitz nonlinear systems with timevarying uncertainties,” Trans. Inst. Meas. Control, vol. 41, no. 7, pp. 1965–1974, 2019.
J. Schmidhuber, “Deep learning in neural networks: An overview,” Neural Networks, vol. 61, pp. 85–117, Jan. 2015.
C. Gershenson, ”Artificial neural networks for beginners,” arXiv preprint cs/0308031, 2003.
K. Prudviraj, S. Deshmukh, R. K. Tripathy, K. Supradeepan, P. Tandon, and P. K. Jha, “Machine learning-based approach for the prediction of an orifice size of aerospace vehicle RCS thrusters during cold flow calibration,” in 2021 IEEE 6th International Conference on Computing, Communication and Automation (ICCCA), 2021, pp. 455–459.
M. Farsi et al., “Prediction of oil flow rate through orifice flow meters: Optimized machine-learning techniques,” Measurement, vol. 174, no. 108943, p. 108943, 2021.
A. R. Behesht Abad et al., “Predicting oil flow rate through orifice plate with robust machine learning algorithms,” Flow Meas. Instrum., vol. 81, no. 102047, p. 102047, 2021.
C. Choi, J. Kim, H. Han, D. Han, and H. S. Kim, “Development of water level prediction models using machine learning in wetlands: A case study of Upo wetland in South Korea,” Water, vol. 12, no. 1, p. 93, 2019.
J. L. Mata-Machuca, R. Mart´ınez-Guerra, and R. Aguilar-Lopez, “An exponential polynomial observer for synchronization of chaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 4114–4130, Dec. 2010.
L. Torres, G. Besanc¸on, D. Georges, and C. Verde, “Exponential nonlinear observer for parametric identification and synchronization of chaotic systems,” Mathematics and Computers in Simulation, vol. 82, no. 5, pp. 836–846, Jan. 2012.
C. C. Nwobi-Okoye, S. Okiy, and A. C. Igboanugo, “Performance evaluation of multi-input–single-output (MISO) production process using transfer function and fuzzy logic: Case study of a brewery,” Ain Shams Engineering Journal, vol. 7, no. 3, pp. 1001–1010, Sep. 2016.
M. L. Lineros, A. M. Luna, P. M. Ferreira, and A. E. Ruano, “Optimized design of neural networks for a river water level prediction system,” Sensors, vol. 21, no. 19, p. 6504, 2021.
S. Beyhan, “Runge–Kutta model-based nonlinear observer for synchronization and control of chaotic systems,” ISA Transactions, vol. 52, no. 4, pp. 501–509, Jul. 2013.
V. Shenoy and K. V. Santhosh, “Design Of Estimator For Level Monitoring Using Data Driven Model,” 2021 2nd International Conference on Computation, Automation and Knowledge Management (ICCAKM), Jan. 2021.
X. Wang and E. E. Yaz, “Second-order fault tolerant extended Kalman filter for discrete time nonlinear systems,” IEEE Trans. Automat. Contr., vol. 64, no. 12, pp. 5086–5093, 2019.
K. van Heusden, M. Yousefi, J. M. Ansermino, and G. A. Dumont, “Closed-loop MISO identification of propofol effect on blood pressure and depth of hypnosis,” IEEE Trans. Control Syst. Technol., vol. 28, no. 1, pp. 254–263, 2020.
S. Rua, R. E. Vasquez, N. Crasta, and C. A. Zuluaga, “Observability analysis and observer design for a nonlinear three-tank system: Theory and experiments,” Sensors (Basel), vol. 20, no. 23, p. 6738, 2020.
S. M. N. Arshad, Y. Ayaz, S. Ali, A. R. Ansari, and R. Nawaz, “Experimental study on slosh dynamics estimation in a partially filled liquid container using a low-cost measurement system,” IEEE Sens. J., vol. 22, no. 16, pp. 16212–16222, 2022.
T. J. Chung, Computational Fluid Dynamics, Cambridge University Press, 2002.
V. Shenoy and K. V. Santhosh, “Characterization of orifice performance using Computational Fluid Dynamics,” 2021 IEEE Mysore Sub Section International Conference (MysuruCon), Oct. 2021.
L. K. Bohra, L. M. Mincks, and S. Garimella, “Experimental Investigation of Pressure Drop Characteristics of Viscous Fluid Flow Through Small Diameter Orifices,” Journal of Fluids Engineering, vol. 143, no. 2, Oct. 2020.
R. D. Grose, “Orifice flow at low Reynolds number,” J. Pipelines; (Netherlands), vol. 3, no. 3, 1983.
R. D. Grose, “Orifice contraction coefficient for inviscid incompressible flow,” J. Fluids Eng., vol. 107, no. 1, pp. 36–43, 1985.
K. Ramamurthi and K. Nandakumar, “Characteristics of flow through small sharp-edged cylindrical orifices,” Flow Meas. Instrum., vol. 10, no. 3, pp. 133–143, 1999.
Y. Ding and L. Jiao, “Research on influnence of orifice parameteers on fluid resistance variations,” CSAA/IET International Conference on Aircraft Utility Systems (AUS 2020), 2021, vol. 2020, pp. 227–231.
J. S. Bay, Fundamentals of linear state space systems. Maidenhead, England: Irwin Professional Publishing, 1998.
S. M. Shinners, Modern control system theory and design, John Wiley & Sons, 1998.
H. Sun, R. Madonski, S. Li, Y. Zhang, and W. Xue, “Composite control design for systems with uncertainties and noise using combined extended state observer and Kalman filter,” IEEE Trans. Ind. Electron., vol. 69, no. 4, pp. 4119–4128, 2022.
M. S. Mahmoud, “Observer-based control design: Basics, progress, and outlook,” in New Trends in Observer-Based Control, Academic Press, pp. 143–208, 2019.
G. Welch and G. Bishop, An introduction to the Kalman filter, 2006.
Y. Zahraoui, M. Akherraz, and A. Ma’arif, “A comparative study of nonlinear control schemes for induction motor operation improvement,” International Journal of Robotics and Control Systems, vol. 2, no. 1, pp. 1–17, 2021.
K. Tan, Q. Ji, L. Feng, and M. Torngren, “Shape estimation of a 3D printed soft sensor using multi-hypothesis extended Kalman filter,” IEEE Robot. Autom. Lett., vol. 7, no. 3, pp. 8383–8390, 2022.
R. J. Meinhold and N. D. Singpurwalla, “Understanding the Kalman Filter,” Am. Stat., vol. 37, no. 2, pp. 123–127, 1983.
P. S. Maybeck, “The Kalman filter: An introduction to concepts,” in Autonomous Robot Vehicles, New York, NY: Springer New York, 1990, pp. 194–204.
A. K. Sahoo and S. K. Udgata, “A novel ANN-based adaptive ultrasonic measurement system for accurate water level monitoring,” IEEE Trans. Instrum. Meas., vol. 69, no. 6, pp. 3359–3369, 2020.
J. M. M. Castillo, J. M. S. Cspedes, and H. E. Cuchango, “Water Level Prediction Using Artificial Neural Network Model,” J. Appl. Eng. Res, vol. 13, pp. 14378–14381, 2018.
A. J. Abougarair, M. K. I. Aburakhis, and M. M. Edardar, “Adaptive neural networks based robust output feedback controllers for nonlinear systems,” International Journal of Robotics and Control Systems, vol. 2, no. 1, pp. 37–56, 2022.
S. Blume, T. Benedens, and D. Schramm, “Hyperparameter optimization techniques for designing software sensors based on artificial neural networks,” Sensors (Basel), vol. 21, no. 24, p. 8435, 2021.
G. I. Parisi, R. Kemker, J. L. Part, C. Kanan, and S. Wermter, “Continual lifelong learning with neural networks: A review,” Neural Netw., vol. 113, pp. 54–71, 2019.
S. Ruder, “An overview of gradient descent optimization algorithms,” arXiv [cs.LG], 2016.
G. Ellis, Control System Design Guide: using your computer to understand and diagnose feedback controllers, Butterworth-Heinemann, 2012.
I. Hosseini, A. Khayatian, P. Karimaghaee, M. Fiacchini, and M. A. Davo Navarro, “LMI-based reset unknown input observer for state estimation of linear uncertain systems,” IET Control Theory Appl., vol. 13, no. 12, pp. 1872–1881, 2019.
DOI: https://doi.org/10.18196/jrc.v3i5.16183
Refbacks
- There are currently no refbacks.
Copyright (c) 2022 Vighnesh Shenoy, Santhosh krishnan vekata
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Journal of Robotics and Control (JRC)
P-ISSN: 2715-5056 || E-ISSN: 2715-5072
Organized by Peneliti Teknologi Teknik Indonesia
Published by Universitas Muhammadiyah Yogyakarta in collaboration with Peneliti Teknologi Teknik Indonesia, Indonesia and the Department of Electrical Engineering
Website: http://journal.umy.ac.id/index.php/jrc
Email: jrcofumy@gmail.com