Date of Award

Winter 1993

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Mechanical Engineering

Committee Director

Thomas E. Alberts

Committee Member

Chuh Mei

Committee Member

G. McRee

Committee Member

Jen-Kuang Huang


One challenge of modern control technology is how to control a flexible structure with accuracy, speed, and economy of effort. Controlling a structure with many degrees of freedom by purely active means implies the implementation of inordinate sensors and actuators and creates the need for numerous calculations that must be done instantly. Experiments have shown that practical structures under active control alone can suffer instabilities due to modal vibrations beyond the bandwidth of the active controller. Furthermore, if there is a high degree of model uncertainty, instabilities can be produced by inputs of modal vibrations not occurring in the system model. The use of passive damping to stabilize those vibrations beyond the domain of the active controller and to help reduce the effects of model uncertainty has been shown to be critical to enabling control of flexible structures.

The question remains as to how passive damping should best be implemented to aid active control. The same amount of damping (by weight) can be applied in different ways--some ways may satisfy performance constraints, while others may not. Part I of this thesis deals with the effects of damping on control. The system to be controlled is defined by its linear matrix differential equation. The system is under the influence of a disturbance and a set of control forces. A performance index is defined, after which are derived closed-form expressions for the optimal feedback gains and the optimal value of the performance index. A modern passive damping technique is applied to a beam, and the cost function is optimized subject to the appropriate constraints. The benefits of the damping are demonstrated in the performance, the displacement output, and in the economic savings.

Part II of this thesis pursues the effects of passive damping on plant model reduction in modal coordinates. Prevailing closed-form expressions in this field assume light damping and widespread natural frequencies. A formula is derived based upon general constant-ratio damping and general spectrum of natural frequencies. Conclusions are drawn, and numerical examples demonstrate the effects of this new formula on model reduction as the modal damping ratio is varied.


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