I have the dynamics of an aircraft described in terms of three nonlinear differential equations that are largely dependent on external variables. That is, variables that are NOT one of the three state variables. I can describe this thusly:
$V' = f(a, Cd, F, V, \theta)$;
$\psi$' = $f(a, Cl, F, V, b)$;
$\theta ' = f(a, Cl, F, V, \theta, b)$;
The state variables are $V, Psi$, and $\theta$. The relationships between the other variables $a, F, Cd, Cl, b$ are very complicated: $Cl$ is a function of a and $b$,$ F$ is a function of Theta, $V, Cl, a,$ etc. Suffice it to say the block diagram of this system is very complex.
I need to linearize this system so that I can tune a two PID controllers. In order to do that I need to first linearize the system (right?). My question is, how do you linearize a system like this when putting it into state space form doesn't seem to capture much of the actual dynamics? Do you just put in constant values for the other external variables that represent a certain mode of flight?