This model is then used to develop and test sophisticated algorithms. Because the rocket's properties (like mass and frequency) change constantly as fuel is consumed, these algorithms must be robust and adaptive. Common control solutions include using notch filters to remove control energy at specific bending frequencies, preventing the controller from exciting and amplifying structural vibrations.
: Discretizing the rocket structure into smaller elements to capture its bending and torsional modes. Researchers often select global modes to represent the entire system's vibration with fewer degrees of freedom. dynamics and simulation of flexible rockets pdf
[MrrMrfMfrMff][ν̇η̈]+[Crr00Cff][νη̇]+[000Kff][ξη]=[FextFmode]the 2 by 2 matrix; Row 1: cap M sub r r end-sub, cap M sub r f end-sub; Row 2: cap M sub f r end-sub, cap M sub f f end-sub end-matrix; the 2 by 1 column matrix; Row 1: nu dot, Row 2: eta double dot end-matrix; plus the 2 by 2 matrix; Row 1: cap C sub r r end-sub, 0; Row 2: 0, cap C sub f f end-sub end-matrix; the 2 by 1 column matrix; Row 1: nu, Row 2: eta dot end-matrix; plus the 2 by 2 matrix; Row 1: 0, 0; Row 2: 0, cap K sub f f end-sub end-matrix; the 2 by 1 column matrix; xi, eta end-matrix; equals the 2 by 1 column matrix; cap F sub e x t end-sub, cap F sub m o d e end-sub end-matrix; ν represents rigid-body velocity states. η represents modal bending amplitudes (modal coordinates). M, C, K are the mass, damping, and stiffness matrices. are external forces and generalized modal forces. 2.2 Modal Analysis This model is then used to develop and
The equations of motion for a flexible rocket can be derived using the following steps: : Discretizing the rocket structure into smaller elements
The time-delay and force limitations of the gimbaled engines. B. Linearization and Frequency-Domain Analysis
The resulting thrust oscillations further excite the structural vibrations.