Date of Award

Fall 1990

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Jen-Kuang Huang

Committee Member

Robert L. Ash

Committee Member

Marion C. Bailey

Committee Member

L. Bernard Garrett

Committee Member

Chuh Mei


Studies on controlling the thermal distortion of large space antennae have generally investigated a single orbital position and have optimized actuator locations based on minimizing the RMS surface deviation from the original parabolic shape. One study showed the benefits of directly using far zone electric field characteristics as the performance measure; but, this approach resulted in a nonlinear programming problem. The objective of the current study is to develop an approach to designing a control system that (1) recognizes the time dependence of the distortion and (2) controls variables that are directly related to far field performance in a quadratic cost sense. The first objective, to explicitly include the time dependence, is accomplished using a principal component analysis to expand an "aperture phase function" into components that are orthogonal in space and time. The aperture phase function is readily calculable from surface distortion and accommodates tapered feeds and arbitrary polarizations. Actuator strokes are shown to be linear combinations of the time dependent components. The spatial components provide a natural space in which to determine the optimal actuator locations and as basis vectors for extrapolating sensor measurements to the entire antenna surface. The approach for the second objective is to expand the far zone electric field in a Zernike-Bessel series. For surface distortions of less than a quarter wavelength, it is shown that the coefficients of this series provide a reliable measure of far field performance. Simulations are performed for a geosynchronous radiometer to determine the robustness of both the open and closed loop systems to variations in solar geometry, structure materials and thermal properties.