The Richards equation plays an important role in the study of agro-hydrological systems. It models the water movement in soil in the vadose zone, which is driven by capillary and gravitational forces. Its states (capillary potential) and parameters (hydraulic conductivity, saturated and residual soil moistures and van Genuchten-Mualem parameters) are essential for the accuracy of mathematical modeling, yet difficult to obtain experimentally. In this work, an estimation approach is developed to estimate the parameters and states of Richards equation simultaneously. In the proposed approach, parameter identifiability and sensitivity analysis are used to determine the most important parameters for estimation purpose. Three common estimation schemes (extended Kalman filter, ensemble Kalman filter and moving horizon estimation) are investigated. The estimation performance is compared and analyzed based on extensive simulations.

The estimation of soil moisture is essential for developing advanced closed‐loop irrigation schemes. One associated problem is how to place the sensors appropriately in the soil to provide good measurements for state estimation. In this work, we address the problem of optimal sensor placement for state estimation of agro‐hydrological systems. A systematic approach is proposed to find the minimum number of sensors that ensures the observability of the entire system and then to find the best locations of the sensors in terms of degree of observability. The Richards equation that is used to describe the dynamics of the agro‐hydrological system is discretized into a large‐scale nonlinear state‐space model. In the proposed procedure, the key steps include order reduction of the large‐scale system model, exploration of the minimum number of sensors needed for state estimation and optimal placement of the sensors in the soil. Three different scenarios are considered and optimal sensor placement is addressed for all the scenarios using the proposed procedure. Simulation results show the effectiveness of the proposed procedure and methods.

To achieve proportional power sharing among similar sources in DC microgrid, droop controllers are used. However, due to interconnecting cable impedances, power shared by the sources deviate from their desired values. To alleviate this problem, techniques utilising shift in droop characteristics and/or modification in droop gain are suggested in literature. Methods which use both of them offer better performance due to higher degree of freedom in control. However, these methods utilise distributed proportional-integral control, which leads to winding-up phenomenon. To address this problem, a distributed secondary controller using full communication is proposed. The current of each source is shared with other sources using lowbandwidth communication. Using this information, each source calculates the ideal value of current to be supplied, which is then used to update its droop gain. To improve the average system voltage, shifting of droop characteristics is incorporated. Detailed small signal model of the proposed controller is developed. Effect of communication delay on the performance of the proposed controller is analysed using the characteristic equation of the system. To evaluate the performance of the proposed scheme, detailed simulation studies are carried out. A scaled down laboratory prototype is developed to determine the viability of the proposed controller.

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