Linearization of a Nonlinear Geometric System Model for Robust Controller Design

A large order flexible space structure, such as a segmented reflector space telescope, requires a high degree of precision and accuracy in order to maintain its nominal shape in order to form clear images. The tracking control for the pointing of such a large complex multiple-input multiple-output (MIMO) system requires a robust controller to maintain the telescope pointing accurately and reliably at it's target. The segmented space telescope testbed at the Structures, Propulsion, And Controls Engineering (SPACE) NASA University Research Center (URC) of Excellence at California State University, Los Angeles, utilizes a segmented primary mirror and a novel motorized laser platform for simulating the testbed's intended target and demonstrating the testbed's pointing accuracy. The motorized platform along with two sets of accessory mirrors comprises a Peripheral Pointing Architecture (PPA). In order to design a suitable controller, the highly nonlinear geometric model describing the laser paths from source to optical detector plane was linearized to produce an LTI state-space model for controller design.