I am working on a problem for a flight controls class. I have an equation related to pure yaw. My goal is to get the transfer function associated with it, and then obtain the system static gain.
The original equation is as follows: $\ddot{\beta}-N_r\dot{\beta}+N_\beta\beta=-N_{\delta}\delta_r $
where
$ N_r = -0.76 $ $ N_\beta = 4.55 $ $ N_\delta =-4.6 $
I think I understand how to go about finding the transfer function, but please correct me if I'm wrong. I believe it is the following:
$ s^2 Β(s)-N_r sB(s)+N_β B(s)=-N_δΔδ_r (s) $
$ s^2 Β(s)+0.76sB(s)+4.55B(s)=4.6Δδ_r (s) $
$ G(s)=\frac{B(s)}{Δ\delta_r(s)}=\frac{4.6}{s^2+0.76s+4.55} $
I think G(s) is my transfer function. Now to go about finding the static gain, I think I need to compute the laplace transform of this function, which I am having trouble doing because it doesn't fit the form of anything in the table I am to use. Any help would be much appreciated!
Thanks