The hydrodynamics of thin floating plates

Abstract The radiation and diffraction problems are considered in the frequency domain for a thin elastic plate of rectangular planform floating in an irrotational, incompressible ocean of infinite depth. The inner potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion which suits the geometry and zero-draft nature of the plate. Problems associated with distributing sources in the free surface are avoided. The Chen and Mei variational principle is used to weakly match this inner solution and its normal derivative to an outer field described by distributing sources on the exterior of the hemisphere. The validity of the procedure is first illustrated by considering a heaving circular disk. Numerous hydrodynamic coefficients are presented as benchmark data for floating flexible structures. The transient motion of the plate is simulated using rational approximations (in the frequency domain) to the radiation impedance and diffraction mapping which are implemented as ODE's in the time domain

Auto-tuned thermal control on stratospheric balloon experiments

Balloon-borne experiments present unique thermal design challenges, which are a combination of those present for both space and ground experiments. Radiation and conduction are the predominant heat transfer mechanisms with convection effects being minimal and difficult to characterize at 35-40 km. This greatly constrains the thermal design options and makes predicting flight thermal behaviour very difficult. Due to the limited power available on long duration balloon flights, efficient heater control is an important factor in minimizing power consumption. SuperBIT, or the Super-Pressure Balloon-borne Imaging Telescope, aims to study weak gravitational lensing using a 0.5m modified Dall-Kirkham telescope capable of achieving 0.02" stability and capturing deep exposures from visible to near UV wavelengths. To achieve the theoretical stratospheric diffraction-limited resolution of 0.25", mirror deformation gradients must be kept to within 20 nm. The thermal environment must be stable on time scales of an hour and the thermal gradients on the telescope must be minimized. During its 2018 test-flight, SuperBIT will implement two types of thermal parameter solvers: one for post-flight characterization and one for in-flight control. The payload has 85 thermistors as well as pyranometers and far-infrared sensors which will be used post-flight to further understand heat transfer in the stratosphere. This document describes the in-flight thermal control method, which predicts the thermal circuit of components and then auto-tunes the heater PID gains. Preliminary ground testing shows the ability to control the components to within 0.01 K

Satellite Attitude Control Using Analytical Solutions to Approximations of the Hamilton-Jacobi Equation

The solution to the Hamilton-Jacobi equation associated with the nonlinear control problem is approximated using a Taylor series expansion. A recently developed analytical solution method is used for the second-, third-, and fourth-order terms. The proposed controller synthesis method is applied to the problem of satellite attitude control with attitude parameterization accomplished using the modified Rodrigues parameters and their associated shadow set. This leads to kinematical relations that are polynomial in the modified Rodrigues parameters and the angular velocity components. The proposed control method is compared with existing methods from the literature through numerical simulations. Disturbance rejection properties are compared by including the gravity-gradient and geomagnetic disturbance torques. Controller robustness is also compared by including unmodeled first- and second-order actuator dynamics, as well as actuation time delays in the simulation model. Moreover, the gap metric distance induced by the unmodeled actuator dynamics is calculated for the linearized system. The results indicated that a linear controller performs almost as well as those obtained using higher-order solutions for the Hamilton-Jacobi equation and the controller dynamics.Peer Reviewe