Calc Bode

calc_bode

This skill builds a state-space model from a mechanical system defined by mass (M), stiffness (K), and damping (C) matrices, and generates a frequency response (Bode Plot) using the python-control library.

Workflow

1. System Matrix Acquisition:

   • Extract the $M$ and $K$ matrices from a physical model or linearization tool.
   • Define the damping matrix $C$ as needed (typically proportional to stiffness or using modal damping).

2. State-Space Construction:

   • Define the state vector as $x = [q, v]^T$, where $q$ is displacement and $v$ is velocity.
   • Transform the system's equation of motion $M \ddot{q} + C \dot{q} + K q = F u$ into the standard state-space form $\dot{x} = Ax + Bu$:
   • $A = \begin{bmatrix} 0 & I \ -M^{-1}K & -M^{-1}C \end{bmatrix}$
   • $B = \begin{bmatrix} 0 \ M^{-1}F \end{bmatrix}$

3. Application of python-control: