Solenoids partially on? That's a new one on me.

Automatic transmissions use a PWM'ed solenoid valve to maintain a certain hydraulic pressure to engage the clutches, depending upon the power required.

In case you didn't know, it takes a large initial current to charge a coil (they act like a short at t=0)

This is not correct.
At T=0, there is no current flow through the coil, so it is essentially an open circuit. Of course, this changes shortly thereafter. The current builds in a linear fashion as the magnetic field expands. If the coil reaches saturation, the current increases at a much faster rate.

Having the initial voltage higher than the coil rating will result in establishing the current flow more quickly, thus actuating the solenoid more quickly.

 

Automatic transmissions use a PWM'ed solenoid valve to maintain a certain hydraulic pressure to engage the clutches, depending upon the power required.

And this solenoid holds a valve partially open? I've been in plenty of auto transmissions, and haven't seen any like that. I'd be happy to learn about them if you can provide a reference.

This is not correct.
At T=0, there is no current flow through the coil,

Fine, granted at T=0 there is no current flow. At the next moment, there is plenty of current.

 

And this solenoid holds a valve partially open? I've been in plenty of auto transmissions, and haven't seen any like that. I'd be happy to learn about them if you can provide a reference.

There are actually lots of applications of proportional valves controlled by solenoids, both hydraulic and pneumatic, including applications in closed-loop systems. "Partially on" is a full-time experience for these solenoids, but my original point was that this question was not about one of those applications.

Fine, granted at T=0 there is no current flow. At the next moment, there is plenty of current.

No, it goes through a standard exponential rise (proportional to V*(1-e^(-t)). Peak current doesn't exceed steady-state current. There is some slight variation to this, caused by the physical motion of the slug, but there is no huge inrush of current, only an attempt by some controllers to shorten the time to reach peak current.

Some solenoids switch out some parallel, high-current windings once engaged, e.g. a car starter solenoid. But still, the current in each of the windings rise only to their own steady-state value.

 

There are actually lots of applications of proportional valves controlled by solenoids, both hydraulic and pneumatic, including applications in closed-loop systems. "Partially on" is a full-time experience for these solenoids, but my original point was that this question was not about one of those applications.

No, it goes through a standard exponential rise (proportional to V*(1-e^(-t)). Peak current doesn't exceed steady-state current. There is some slight variation to this, caused by the physical motion of the slug, but there is no huge inrush of current, only an attempt by some controllers to shorten the time to reach peak current.

Some solenoids switch out some parallel, high-current windings once engaged, e.g. a car starter solenoid. But still, the current in each of the windings rise only to their own steady-state value.

Well, you're right about proportional solenoids, I just hadn't seen one, like I said, that's a new one on me.
http://www.fas.ch/info_tech_actions.asp?sectionID=t&Langue=english

As far as the rest goes, if you have a huge coil, and not much work to do, you can be a lazy engineer, and nobody will notice. On the other hand, if you don't have room for a huge coil, or time to wait on it you can no longer ignore the work done by the coil. That means that you cannot simply turn them on with a switch. A coil by itself isn't a solenoid. Take a valve such as this one, it won't last a minute under those conditions.
http://www.matrix.to.it/matrix_2005/business3.asp?id=14&id2=2&id_barea2=41