Recursive multibody dynamics and discrete-time optimal control

A recursive algorithm is developed for the solution of the simulation dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal control problem. For each relevant quantity in the multibody dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies

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