System Identification (SI) is the process of developing or improving a mathematical representation of a physical system using experimental data. Accurate SI is often a precursor to sophisticated control algorithms which assume that the 'plant' to be controlled is known. To achieve accurate models, many of the best current SI methods require that the size of the identified state space model be significantly larger than the expected system size, a process called overspecification. Large models are impractical for model-based controller design and create numerical difficulties during the SI process. Low order and high accuracy are two conflicting requirements for SI.

Appropriate SI methods for on-orbit modeling of lightly-damped flexible spacecraft are established, including methods such as OKID with ERA, Q-Markov CovER, ORSE and Subspace. Tests on Daisy, a flexible spacecraft emulator, demonstrate that these methods exhibit the overspecification problem.

To investigate SI of low-order models, model reduction techniques are employed. Balanced model reduction offers promising results for stable models. Since model stability is not guaranteed by many SI methods, three new approaches to balanced model reduction are derived and tested when identified models are unstable.

A new identification approach using OKID and cubic smoothing splines is presented, allowing low-order highly-accurate models to be directly identified. Avoiding impractically large models reduces computational requirements and potential for numerical problems.

Augmented SI is an approach that allows existing linear system identification techniques to better model non-idealities such as nonlinear friction. Augmented and standard SI experiments demonstrate that the linear system assumption made throughout this thesis is appropriate for Daisy.