Assume that we have this ODE which describes a hydraulic cylinder.
$$M\ddot{x} = AP - B\dot{x} - F_L$$
Where $M$ is mass and and $A$ is the piston area and $P$ is the pressure and $B$ is the damping and $F_L$ is the force load on the mass.
One problem with this is that this ODE is for a hydraulic cylinder. We cannot choose a pressure $P$ because the load $F_L$ is determining the pressure $P$.
To make the cylinder move up/down, the pressure $P$ need to be larger that $F_L$. The pressure only need to be a little bit lager, not so much. The speed of the hydraulic cylinder is determined by the flow $Q$.
The formula for the flow is:
$$Q = Dn$$
Where $D$ is the deplacement of the pump and $n$ is the revolution of the pump shaft.
The flow $Q$ is also equal to
$$A\dot{x} = Q = Dn$$
Where $\dot{x}$ is the velocity of the piston and $A$ is the piston area. So my idea is to rewrite the ODE like this:
$$M\ddot{x} = \frac{D}{A}n - B\dot{x} - F_L$$
Because
$$\dot{x} = \frac{D}{A}n$$
And now you may wonder "Is not $\dot{x}$ a state?. Yes it is, and that's why I asking you if this ODE is correct done?
I replace the $AP$ with $\frac{D}{A}n$ and let the revolution $n$ be the input signal. Because when $\dot{x} = F_L$, then the cylinder stop.