Optimal control of a rotating cylinder partially filled with ideal fluid

Optimal control theory analysis is applied to a rotating cylinder partially filled with an inviscid, incompressible fluid. Two models of the system are investigated: (1) a two discrete mass system with fluid inside one mass and the control force applied to the other, and (2) a continuously distributed cylindrical mass system with control force applied to a discrete lower suspension mass. For (2) the method of assumed modes is used to discretize the system and obtain a set of n linear algebraic equations. In both cases the treatment is two dimensional and axial motion of the fluid is considered negligible.

In both models, the uncontrolled system, shown by earlier researchers to be inherently unstable, is found to be controllable. The appropriate optimal feedback control is derived and system responses investigated.

In addition, both models are shown to be observable. Direct measurement of only a portion of the components of the state vector are sufficient, using a Luenberger Observer, to estimate the entire state vector.