Model order reduction and controller design for segmented primary mirror of a large optical telescope.

摘要

The Very Large Optical Telescope (VLOT) is a concept, proposed by the National Research Council - Herzberg Institute of Astrophysics, to address future demands of the international astrophysics community. To develop and evaluate the VLOT designs, an Integrated Modeling approach is employed. The Integrated Model (IM) is a single simulation tool which accounts for the interactions between different telescope modules to produce the final image quality generated by the telescope. The work in this thesis relates directly to two of the modules of the IM: (1) the structural dynamics and (2) the primary mirror control module.; In order to obtain accurate optical performance predictions from the IM, a high fidelity structural model of the telescope is required. However, the finite-element model of the telescope, which is its nascent structural model, is prohibitively large in size for practical simulation. This problem can be addressed by applying a suitable Model Order Reduction technique. In the first half of this thesis, we compare five Model Order Reduction techniques from the literature for the VLOT application. These methods are evaluated and compared in frequency and time domains. Based on these results, we conclude that the Singular Perturbation Approximation method is suitable for the VLOT application.; The primary mirror, which is the main light-gathering surface of the telescope, must be maintained in a particular profile in order to provide the desired image quality. Currently, this control objective is achieved with an enhanced integral controller based on a SISO control approach. The primary mirror, however, is a MIMO system and hence the second objective of this thesis is to evaluate a MIMO control design approach, in particular, the Linear Quadratic Gaussian (LQG) controller. The LQG design is evaluated in two steps: initially with a single mirror segment model and then with the VLOT structural model. Based on our results, we conclude that even with currently available computational resources, it is not feasible to employ the LQG control approach in a centralized manner to a large scale system such as VLOT.