Hello everyone. I have problem to solve. I need to control a coil of pneumatic distributor, which looks like this(24V, 2W) 
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I need to use PWM control and I don't know how to handle it. I've never done something with arduino so i want to ask you which components I have to buy to solve my problem. Sorry for my bad english. Cheers.
Taking that 0820... number as an identifier, I found this, where I don't see anything about PWM. Do you have a better document?
Agree - it looks like an on/off valve or one that sends flow to either of two ports - it’s not a modulating valve so sending a PWM signal to it will do nothing
I did some photos of mine distributor. The fun fact that the professor of the university told me that I have to use PWM to control this. I wanted to use this coil (black one on the screen) as a pneumatic resistance, which i want to control. Now i am confused a little bit since I've made some steps already and wasted time seems like.
You need to get a decent datasheet or operator manual or similar before you can proceed. That's a basic rule of electronics, else you don't know what you're dealing with. In the real world before you accepted such an undertaking you would make it clear to your client that access to such data was a requirement.
That said, have a look at a circuit like this, where your solenoid coil would be in the place of the motor. You would pwm the gate of the mosfet, and your 24V would be at the top where it says 12V.
edit: If the device has some control electronics built in, and simply needs a pwm'ed 24V control signal (in a way analogous to how a servo has a control signal separate from the power) then you could consider this discussion. Note that OP's initial circuit with no pullup is wrong; look at the circuit in #3 there, reproduced below. You would have 24V at the top, and perhaps could / should use a larger pullup to reduce the current (I'm not sure about that).
But you really need some documentation, or you're working in the dark.
@havingFunSoFar, @hammy : in hydraulics and pneumatics, PWM Solenoid Theory | TLX Technologies to drive solenoid valves with PWM for flow control and / or limiting the current in the coil to avoid overheating.
There are ICs for that (like the DRV102 from TI)
MichaelBagieta:
I did some photos of mine distributor. The fun fact that the professor of the university told me that I have to use PWM to control this. I wanted to use this coil (black one on the screen) as a pneumatic resistance, which i want to control. Now i am confused a little bit since I've made some steps already and wasted time seems like.
The pneumatic equivalent to a variable resistance is a "needle valve".
Paul
What about ULN2003?
Yes, essentially obsolete IC, drops a couple of volts. What about it? 
Hi,
You need to contact the Rexroth dealer and check that the valve has a PWM/throttle type spindle.
If not then you will be very disappointed with the results.
Also the valve that you are aiming to use may have a specific PWM frequency that it operates at.
- To high a frequency and the inductance of the coil will cause current limiting and you will not get full operation.
- To low a frequency and you will not have smooth operation/response to your control signal.
The fact that you are in a University should provide you with many sources of information about such devices.
There are specific specialized MOSFETs for operating PWM solenoid systems.
Tom... 
TomGeorge:
- To high a frequency and the inductance of the coil will cause current limiting and you will not get full operation.
No amount of inductance limits the DC component of the current, the issue with high frequencies is
the excess losses due to eddy-currents, ie a failure to limit AC component of current causing high power
requirements and heating of the magnetic core.