Sliding mode observer design for decentralized multi-phase flow estimation

Robust flow measurement in multi-phase systems has extensive applications in understanding, design, and operation of complex environmental, energy and industrial processes. The nonlinearity and spatiotemporal variability of the interactions between different flow phases makes the multi-phase flow measurement a challenging task. Two Sliding Mode Observer (SMO) schemes are proposed in this study for the state estimation of a decentralized multi-phase flow measurement system. The developed observers are shown to be theoretically valid and numerically applicable for a real-life case study data. The multi-phase flow system considered in this paper can be described as two interconnected sub-systems including fluid and gas sub-systems, and two scenarios are considered in the design of the observers. The first scenario considers the interconnections as bounded disturbance (SMOD), while the second scenario considers the interconnections as an uncertainty (SMOU). Hence, the Sliding Mode Observers are adopted to mitigate the effects of disturbance in the system and uncertainties in the parameters. Numerical simulations are conducted using MATLAB and dynamic HYSYS simultaneously, using the data obtained from field-based multi-phase flow measurements. The results demonstrate the appropriateness and robustness of the proposed Sliding Mode Observer (SMO) for estimation of the multi-phase fluid specifications including the density, velocity, and the volume phases fraction in each subsystem. The analysis of the results highlights that the proposed model is computationally efficient with fast transient response, accurate tracking capability of the real process data, and very low steady-state error. This study shows that choosing an appropriate Lyapunov-Krasovsky function results in the asymptotic stability of the decentralized system and improves the performance of the proposed observers. Uncertainty analysis is conducted on the velocity estimation results obtained from the Sliding Observers. Overall, SMOU method shown better performance with RMSE of 0.24%, while RMSE of 0.46% was achieved for the SMOD. Comparison of the numerical results with the field-based flow measurement, as a benchmark, shows that although uncertainty in SMOU is approximately half of the uncertainty in SMOD, state estimation for both schemes was achieved in a finite time with high order of precision. It was shown that both observers developed in this study are well capable of estimating the multi-phase flow variables and states