The servo loop is what contains the PID function.
The trapedziodal function, you refer to, is a separate part of motion control systems. It's what's called the profile generator and is fire-and-forget in nature, ie: Open-loop, it's not reactive to feedback. Typically, this is used to produce smooth lines from geometrical descriptions but also is used to achieve simultaneous synchronous moves.
As you have already been thinking, the profile generator can be replaced with a simple "setpoint" that is shifted around in a step like manner. This is how most temperature controllers are configured and it's simple for operators to manage.
If you don't care when the hydraulic rams pass any given intermediate positions then you can indeed construct the servo to handle a large step function instead of smooth profile. If you want speed then Prop+Diff for the servo are what's needed, the derivative in this case is oddly constructed. Intergral, all by itself, is only to be used for slow steady reaction to the step.
However, having said all that, I recommend going the path of following a defined profile and use a normal PID function. This will give reliable smooth control that can be set to alarm-out on tight tolerances hopefully preventing possible damage and safety concerns.
Note: Your description of setpoint is really a cut-to-length function that is generated from the setpoint and, yes, this will be a trapeziodal or S-curve profile.
To answer your first question, I and D often don't make a difference. D in particular can add unwanted wear to the machinery. It depends on how accurate and fast the mechanics are verses their need. Commissioning is usually a time of redevelopment ...
Evan
