The maximum magnitude of a steady-state maneuver is entirely dependent on the plant. It is independent of the control system. The steady-state transfer function matrix is derived as follows
$$\begin{matrix}
\dot{x}=Ax+Bu \
y=Cx
\end{matrix}$$
By solving for Y in the complex plane we get
$$y(s)=(C[sI-A]^{-1})U(s)$$
The steady-state transfer function matrix is the matrix before U
$$G=C[sI-A]^{-1}$$
We can also solve for the input transfer function U
$$U(s)=G(s)^{-1}y(s)$$
Where \(y(s)=k/s\). You can use this matrix (\(G^{-1}\)) to see how much a commanded control surface or actuator will move for a given desired output. This matrix should also match the steady state of the time series data after any transients have occurred. If the rates and accelerations are output values, then the matrix will be singular, caused by an additional derivative “s” in the numerator.
[[Measurement Matrix]]
[[Steady-State Error]]
- courtheynMultivariableControlLaw
[[Singular Value of a Matrix]]
[[State-Space Model]]
[[Transfer Functions]]