Dynamics and Controls of a Generalized Frequency Domain Model Flexible Rotating Spacecraft

Modeling a exible rotating spacecraft as a distributed parameters system of a rigid hub attacjed to a exible appendage is very common. When considering large angle maneuvers the same model applies to exible robotic manipulators by adding a tip mass at the end of the exible appendage to account for the payload. Following Euler-Bernoulli beam theory the dynamics for both a no tip mass and a tip mass models are derived. A generalized state space (GSS) system is constructed in the frequency domain to completely solve for the input-output transfer functions of the models. The analytical solution of the GSS is obtained and compared against the classical assumed modes method. The frequency response of the system is used in a classical control problem. A Lyapunov function based controller is derived and tested for gain selection. The assumed modes method is used to obtain the time response of the system to verify the gain selections and draw connections between the frequency and the time domains. The GSS approach provides a powerful tool to test various control schemes in the frequency domain and a validation platform for existing numerical methods utilized to solve distributed parameters models.

Dynamics and Controls of a Generalized Frequency Domain Model Flexible Rotating Spacecraft Conference Paper