hi Bill,
Posting a working circuit of your proposed design would be a lot more helpful to the TS, rather than just generalized suggestions.

E

Certainly EG is right, however, it seems that the TS is rather technically competent, having created a linear ramp generator circuit to provide a moving position setpoint for the RC servo package. Besides that, my computer with the cad software has been dead ever since the lightning hit a while ago. So producing a completed design to share would be quite a big deal for me. I suggested a much more simplified scheme in post #34, also.
Besides all of that, usually I get paid for delivering working circuit designs. A working circuit design is a lot more effort than offering valid advice.
And on top of all that, the TS has not made any comment or shown one bit of interest in that alternative scheme.

 

Can't you just leave the power on all the time?

Hi Carl,

The problem is that when the power is on all the time ... The servomotor will move anyway on the first on.

Another idea :
A friend suggested me to connect the RESET pin 4 of both NE 555 (astable+monostable) to a resistor+capa network.
Unfortunately it doesn't work : the servomotor rotates about 30 ° and gets back.

I have checked on the NE555 datasheet : the minimum RESET voltage starts at 0,4/0,7 V and the voltage of the R+C network ramps up too fast !

 

The problem is that when the power is on all the time ... The servomotor will move anyway on the first on.

Don't understand.
First on of what?

I have checked on the NE555 datasheet : the minimum RESET voltage starts at 0,4/0,7 V and the voltage of the R+C network ramps up too fast !

You could use a small MOSFET to increase the off time (below):

 

Don't understand.
First on of what?
You could use a small MOSFET to increase the off time (below):

View attachment 284998

Good evening !
I had found a solution just before your post.
The idea is similar to yours.
I used a CD4093 to generate a signal connected to RESET which forces it to low during 2 seconds.
Now everything works fine
Your circuit with the integrator was instrumental.
Thank you very much again for your time and simulations !
Thanks too to @ericgibbs
Best regards

Philippe