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

Abstract

Modeling a flexible rotating spacecraft as a distributed parameters system of a rigid hub attached to a flexible appendage is very common. When considering large angle maneuvers the same model applies to flexible robotic manipulators by adding a tip mass at the end of the flexible appendage to account for the payload. Following Euler-Bernoulli beam theory the dynamics for both no tip mass and 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 then used in a classical control problem where a Lyapunov stable 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.

Analytic Transfer Functions for the Dynamics & Control of Flexible Rotating Spacecraft Performing Large Angle Maneuvers

“…(7), and the boundary conditions, Eq. (8) and Eq. (9), the following expression is obtained, [14,15] dU dt…”

“…Generally, both the aerospace and the control communities have been content with the numerical approximations following finite elements or assumed modes techniques for the past decade. Building on previous developments, this work presents a new approach for the dynamics and control of distributed parameters models by deriving the analytic transfer functions to obtain the system truncation-error-free frequency response, [6,8,26,27]. The existence of the exact transfer functions is then utilized in frequency domain control for gains selection of a Lyapunov stable controller designed to drive the system from its initial state to a target state while suppressing the vibrations of the flexible appendages.…”