In this paper we consider two separate approaches to the development of finite dimensional control systems for approximating distributed parameter models. One method uses the “standard finite element” approximations to construct the basic system matrices. The resulting system can then be balanced by any of several balancing algorithms. The second method is based on truncating infinite dimensional balanced realizations of the input-output map. Both approaches are applied to a control problem governed by the heat equation. We present a comparison of the resulting finite dimensional models. / Ph. D.

An indirect adaptive quenching algorithm for a nonlinear single-degree-of-freedom system with unknown constant system parameters is presented. The system is subject to external or parametric sinusoidal disturbances and the resulting control signal is also sinusoidal. The quenching algorithm provides a reduction in the control effort required compared to direct disturbance cancellation. The disturbance sinusoid and the unknown parameters are incorporated into the system model and an extended Kalman filter (EKF) with modified update equations is used to estimate the system state and parameters. The estimates are then used to form the quenching signal. The adaptive quenching algorithm is found to work well inside a quenching region defined by the separatrices and suggests the use of a hybrid control law. The algorithm was verified by implementing it on an analog computer. / Master of Science