(17h) State Estimation and Controller Design Using Dynamic Model Reduction for Agro-Hydrological System

The fast-growing population of the world is estimated to increase to 9 billion by 2050 with the requirement of double the amount of food demand [1]. The agriculture sector requires a huge amount of fresh water to ensure future food security. The freshwater crisis is ranked as one of the top global risks [2]. The increase in irrigation requirement not only put the freshwater in risk but also account for the increase in greenhouse gas (GHG) emission. The agriculture sector itself causes 10-12% of the world global GHG emission [3] and the irrigation activities account for a large fraction of the emission in agriculture. Thus the improvement in irrigation efficiency will be a win-win situation to manage water crisis and the reduction of GHG emission. The closed-loop irrigation is one of the promising techniques to increase irrigation efficiency. In the current scenario, the irrigation decision is not based on real-time feedback information from the field which is manly in an open-loop manner. The closed-loop irrigation which makes the irrigation decision based on the real-time feedback from the field while considering the weather condition. The important segments in the closed-loop irrigation are field model, soil moisture estimation (state estimation) and controller design. The agro-hydrological system model comprises huge number of states due to the discretization of the large field. The large scale system makes it very challenging in state estimation and controller design. An effective model reduction technique is one of the efficient ways to deal with a large scale system.

For the agro-hydrological system, there are many results on state estimation using extended Kalman filter, ensemble Kalman filter (ENKF) and particle filter methods [4]. One of the limitations of the above-discussed methods is that it is not efficient to handle the constraints. The constraints make a huge impact on the performance of state estimation. In [5], we used the moving horizon estimation algorithm to estimate the parameter and state estimation. But this work has also certain limitations to apply directly on large-scale real field. There are also many works done for the controller design for the agro-hydrological system using model predictive control, PID controller and neural network model [6]. In the above studies, either the simple identified model or the data-based model have been used to perform the controller design but in reality, the agro-hydrological model is highly complex and non-linear.

In this talk, to deal with the challenge, we have proposed a novel dynamic model reduction technique in the presence of heterogeneous soil and non-uniform inputs. The accuracy of the reduced model largely depends upon the magnitude of the input which implies if the input changes, the reduced model may change. The controller changes the input profile at certain period of time so using an offline static model reduction using prescribed input might result in large error in the reduced system or a higher number of states in the reduced order. So in the proposed algorithm, we have used the online dynamic model reduction i.e. we may get the different reduced models at different periods of time if the controller changes the input largely. Firstly, we apply the DBSCAN clustering approach to do system structure-preserving model reduction based on the trajectory of the non-linear system. Then, based on the reduced model, we estimate the states (soil moisture) using the measurement from the sensors by moving horizon estimation (MHE). Then the estimated states are used to design the model predictive controller (MPC). The challenges arise when the model orders are different in the horizon of the MPC or MHE. To handle the changing of model order, we have modified the MPC and MHE algorithm a little bit by considering the information exchange between the reduced models. To test the effectiveness of the proposed approach, we consider a real field in Lethbridge, Alberta with heterogeneous soil types and with the central pivot irrigation system. The central pivot makes the system input periodic and the result shows the effectiveness of online dynamic model reduction with these types of setup.

References

[1] H. Turral, B. Jacob, and F. Jean-Marc, “Climate change, water and food security," FAO

Water Reports Rome, 2011

[2] “Global risks 2015," World Economic Forum, 2015

[3] “IPCC, 2014: Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change” [Core Writing Team, R.K. Pachauri and L.A. Meyer (eds.)]. IPCC, Geneva, Switzerland, 151 pp.

[4]H. Vereecken, A. Schnepf, J.W. Hopmans, M. Javaux, D. Or, T. Roose, J. Vanderborght, M.H.Young, W. Amelung, M. Aitkenhead, et al., “Modeling soil processes: review, key challenges, and new perspectives,” Vadose Zone J., vol. 15, p. 5, 2016

[5] S. Bo, S.R. Sahoo, X. Yin, J. Liu, “Parameter and State Estimation of One-Dimensional Infiltration Processes: A Simultaneous Approach”, Mathematics, vol. 8, p. 134, 2020

[6] O. Adeyemi, I. Grove, S. Peets, and T. Norton, “Advanced Monitoring and Management

Systems for Improving Sustainability in Precision Irrigation," Sustainability, vol. 9, p. 353, 2017