Date of Award

Spring 1995

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Jen-Kuang Huang

Committee Member

Colin Britcher

Committee Member

Sebastian Bawab

Committee Member

Gene Hou


This dissertation presents closed-loop identification algorithms of an unstable system in the time and frequency domains. In the time domain, the projection filter, which is a linear transformation which projects (transforms) a finite number of input-output data of a system into its current space, is used to relate the state-space model with a finite difference model. The method developed can take into account the effects of process noise as well as measurement noise and identify open-loop systems with unknown feedback dynamics in the closed-loop operation. Then the recursive relations between Markov parameters and the ARX model are derived to identify recursively the system, controller and Kalman filter Markov parameters, which are finally used to identify the system, controller and Kalman filter gains. The closed-loop test data demonstrate that the open-loop state-space model identified by using projection filters is fairly accurate in predicting the step responses while the analytical model has several deficiencies. In the frequency domain, the relation between the closed-loop system matrices and the frequency response function is derived to identify system parameters. Also a simulation model of uncertainty to design a robust controller is proposed by using the maximum singular value of unstructured uncertainties caused by underestimated modes and noise. The uncertainty model developed here can be tested and used for the design of a high-performance robust controller in the future. The NASA Large-Angle Magnetic Suspension Test Facility (LAMSTF) is used to validate the algorithms developed.