This thesis investigates linear control theory as applied to smart structures. Specifically, the problem of active vibration damping in a flexible cantilever beam using piezo-electric ceramic crystals (PZT) as sensors and actuators is addressed.

The problem of controlling linear time invariant systems subject to hard input constraints is considered. Some existing methods are reviewed and some new methods are presented.

The subject of rapid prototyping and automatic system identification is addressed. Automatic system identification techniques are developed and combined with a commercially available rapid prototyping system to create a test bed which can be used to rapidly model and control existing plants.

Closed loop control laws designed to actively damp vibrations in a flexible cantilever beam were tested in various laboratory experiments. The experiments are described, the design of the control laws is discussed, and the results of the experiments are presented.

Finally, impact between a flexible robotic arm and a fixed sphere is addressed. A model for the impact forces is developed and compared with experimentally determined impact data. An open loop control law using a neural network is implemented to control the magnitude of the impact force.