Robust control of flexible structures

The control of flexible mechanical systems has application to control of space systems, aircraft, robotics and active optics, to name a few. Structural mechanical systems are typically lightweight and highly flexible. These systems have distributed-parameter dynamics; their natural damping is very small; they have many densely packed low-frequency modes; and their model parameters are uncertain. Moreover, performance requirements such as pointing accuracy, shape control, and bandwidth are very stringent and make the problem of structural vibration more acute. Examples of flexible mechanical systems include a variety of space structures ranging from large antennas to very complex space stations. Another important application of flexible structural control is in robotics. The goal is to develop lighter and faster robots capable of moving larger payloads with low energy requirements.; In this dissertation, we first examined the single-input, single-output control of flexible structures. We established important time and frequency-domain properties that characterize elastic systems. Particularly, we demonstrated an interesting pattern of movement of the plant zeros as a function of the sensor location. This zero motion has a considerable implication on control design. We then presented a compensation method based on a frequency minimax technique, and uses a search procedure which always converges to the optimal controller.; We also proposed the concept of "generalized lead-lag compensation". This method is intended for the noncollocated control of flexible structures. A theorem giving necessary and sufficient conditions for the existence of such a stabilizing controller is proved, and a systematic design procedure is given.; We also investigated the multi-output control of flexible structures. An optimal sensor placement procedure, based on eigenstructure assignment, is developed for the robust control of elastic systems.