Attitude Control Considering Variable Input Saturation Limit for a Spacecraft Equipped with Flywheels

A new attitude controller is proposed for spacecraft whose actuator has variable input saturation limit. There are three identical flywheels orthogonally mounted on board. Each rotor is driven by a brushless DC motor （BLDCM）. Models of spacecraft attitude dynamics and flywheel rotor driving motor electromechanics are discussed in detail. The controller design is similar to saturation limit linear assignment. An auxiliary parameter and a boundary coefficient are imported into the controller to guaran- tee system stability and improve control performance. A time-varying and state-dependent flywheel output torque saturation limit model is established. Stability of the closed-loop control system and asymptotic convergence of system states are proved via Lyapunov methods and LaSalle invariance principle. Boundedness of the auxiliary parameter ensures that the control objective can be achieved, while the boundary parameter＇s value makes a balance between system control performance and flywheel utilization efficiency. Compared with existing controllers, the newly developed controller with variable torque saturation limit can bring smoother control and faster system response. Numerical simulations validate the effectiveness of the controller.

An Efficient Multiple-Dimensional Finite Element Solution for Water Flow in Variably Saturated Soils

Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richards＇ equation. Because of the nonlinearity of the Richards＇ equation and the complexity of natural soils, most practical simulations rely on numerical solutions with the nonlinearity solved by iterations. The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate. A recent theoretical analysis by the authors, however, revealed that for solving the diffusive flow, the classical Picard method is actually a chord-Newton method, converging at a rate faster than first order; its linear convergence rate is due to the treatment of the gravity term. To improve computational efficiency, a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term. Testing examples for one-dimensional flow showed significant improvement. The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence. In this paper, we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.

Iterative Method on Well Bore Boundary in Numerical Modeling of Variably Saturated Flow

An iterative method was developed for incorporating the well bore boundary into the finite difference model of water flow in variably saturated porous media. Six cases were presented involving groundwater pumping or injection to demonstrate the advantages of the iterative method over the traditional method. For the iterative method, the total flux gradually approached the well discharge and the flux profile was non-uniform. And the iterative method took into account the variation of well bore water table. Compared to the traditional method, the iterative method can simulate the variably saturated flow caused by pumping or injection more realistically.