Control of rotor systems with parametric excitation using gain-scheduled H-infinity control

Subject of this paper are systems with periodic, time-variant system matrices, that are called parametrically excited systems. Dependent on the frequency and amplitude of the parameters the systems may become unstable. The dynamics of these systems can be determined by an extended modal approach. To avoid the unstable regions the design of a controlled system is necessary. Gain-scheduled H-infinity control is an appropriate method. On the basis of linear matrix inequations a time-varying controller can be designed, that ensures the stability of the system in a given range of the time-varying parameters. MatLab LMI-control toolbox has been used for the controller design. For an introduction to the method a 1-DOF oscillator with parametric excitation is used (Mathieu-equation). More technical applications are given in rotor dynamics. Rotors (gyros) with three different moments of inertia lead to parametric excitations. The basic behaviour is shown for a cardanic gyro. Finally the method is applied to a laboratory structure, where in the first step the system is identified by an experimental modal analysis. In the second step the controller is derived from the experimental identification.