Stability and control of some parametrically excited rotating systems

In this dissertation the stability and control of some parametrically excited rotating mechanical systems is investigated. Modeling of these systems lead to a set of differential equations with periodic coefficients where the stiffness matrices depend on the periodic term as well as the rotation parameter. As an example of a lumped parameter model, a rotating double pendulum subjected to periodic parametric excitation is considered. The linear stability analysis was performed via a numerical implementation of Floquet theory and by the Hill's determinant method. It is observed that additional combination resonance instabilities arise due to the rotation of the system. A full-state feedback and on observer based controllers are designed for the system via Lyapunov-Floquet transformation technique. In this technique the governing equations are transformed to a time invariant form which is suitable for the application of classical time-invariant control methods. It is shown that the unstable system could be controlled effectively by the suggested approach.; The flap motion of a parametrically excited rotating beam is considered as an example of a flexible system. The linear stability and control for this problem is studied in a similar manner as described above and similar conclusions are drawn. However, in this case, control of the nonlinear problem is also investigated. A discretized nonlinear model using one-mode approximation is constructed and a control system is designed via fuzzy logic strategy. The controller performance is found to be satisfactory over a wide range of parameters.; In order to generalize the performed proposed ideas to systems with periodic discontinuities in the states, the control of an elastic rotating beam undergoing periodic impacts is considered. A controller is successfully designed to suppress the elastic vibrations of the beam resulting after an impact with a rigid body.; It is concluded that the Lyapunov Floquet transformation technique is a powerful tool and it can be successfully employed to design active linear controllers for rotating systems. The approach is simple and it can be implemented in real time since it does not require intensive computations. For the nonlinear problems, it is demonstrated that a fuzzy logic controller can be designed to achieve the desired performance. This technique appeals to be a viable tool for the future since it does not require a complete knowledge of the system model.