Efficient and Robust Approaches to the Stability Analysis and Optimal Control of Large-Scale Multibody Systems

Abstract

Linearized stability analysis methodologies, system identification algorithms and optimal control approaches that are applicable to large scale, flexible multibody dynamic systems are presented in this thesis.

For stability analysis, two classes of closely related algorithms based on a partial Floquet approach and on an autoregressive approach, respectively, are presented in a common framework that underlines their similarity and their relationship to other methods. The robustness of the proposed approach is improved by using optimized signals that are derived from the proper orthogonal modes of the system. Finally, a signal synthesis procedure based on the identified frequencies and damping rates is shown to be an important tool for assessing the accuracy of the identified parameters; furthermore, it provides a means of resolving the frequency indeterminacy associated with the eigenvalues of the transition matrix for periodic systems.

For system identification, a robust algorithm is developed to construct subspace plant models. This algorithm uniquely combines the methods of minimum realization and subspace identification. It bypasses the computation of Markov parameters because the free impulse response of the system can be directly computed in the present computational environment. Minimum realization concepts were applied to identify the stability and output matrices. On the other hand, subspace identification algorithms construct a state space plant model of linear system by using computationally expensive oblique matrix projection operations. The proposed algorithm avoids this burden by computing the Kalman filter gain matrix and model dependency on external inputs in a small sized subspace. Balanced model truncation and similarity transformation form the theoretical foundation of proposed algorithm. Finally, a forward innovation model is constructed and estimates the input-output behavior of the system within a specified level of accuracy. The proposed system identification algorithms are computationally inexpensive and consist of purely post processing steps that can be used with any multi-physics computational tool or with experimental data.

Optimal control methodologies that are applicable to comprehensive large-scale flexible multibody systems are presented. A classical linear quadratic Gaussian controller is designed, including subspace plant identification, the evaluation of linear quadratic regulator feedback gain and Kalman filter gain matrices and online control implementation.