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.