I have a one question about convert state equation to state-space model.

I can not create a state-space model because of $g$ term from given this state equations...

$\dot{x_{1}} = \dot{z} = x_{2};$

$\dot{x_{2}} = \ddot{z} = g - \frac{U_{1}}{m};$

Where, $U_{1} = C_{T}(w_{1}^{2} + w_{2}^{2} + w_{3}^{2} + w_{4}^{2});$

I have considered next form also, but If I do this, new $U_{1}$ give perturbation to another input $U_{2,3,4}$.

$\dot{x_{1}} = \dot{z} = x_{2};$

$\dot{x_{2}} = \ddot{z} = U1;$

$U_{1} = g - \frac{1}{m}C_{T}(w_{1}^{2} + w_{2}^{2} + w_{3}^{2} + w_{4}^{2});$

How I can make state-space model with $g$ term ?


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