Hi,
first off all, thank you for your replies!
O.K., got some questions here. First, is there some sort of LVDT Linear Variable Delta Transformer or perhaps a linear position indicating potentiometer that closes a feedback loop so that +1 volt exactly equals +1mm (or what ever the scale is)? Next question, do you have a load cell in line with the hydraulic actuator to give a readback of how much force is being applied (pushing or pulling) with a safety limit set on force in case your device being tested hits a hard physical limit? All of these SHOULD be included in your setup. I have an extensive background in this area having worked for Lord Corp and testing every kind of rubber compound and damper your could imagine. We used servo controls from Moog-FCS and our available hydraulic line pressure was 3000psi. The Moog unit could generate the test signals with automatic ramps applied if needed. It could generate sines, sine sweeps, noise (white, pink,brown, etc.), and any combination of triangle or ramp. The Moog-FCS units were expensive but if you are working at university level this is the very least caliber of equipment you should be conducting your tests with. I probably wouldn't even accept the results of your testing as valid with lesser equipment. Cheers mate!!
The testing machine for which we want to implement the system at first is an Instron VHF series machine, equipped with an Instron 8800 classic controller. The piston stroke is actually measured by an LVDT, the force by a differential pressure transducer and a piezoelectric force transducer - all periodically calibrated by an accredited laboratory. The external input signal in parsed by the controller and taken as the set point for the pid controller - therefore all security measures like user set or inbuilt limits, specimen break detection, over/underpressure dectection... are still active. The Instron controller on its own is for sure capable to perform the things I am trying to do - but since we do not have the software and the support is discontinued due to the systems age of 21 years, using an external signal generator is propably the easiest solution...
So, you have 8 Mpts to get the job done.
Unfortunately, I need a few times more. If I sample a sine at lets say 250 pts / cycle, I only have memory for 32000 cycles - of about 5...8e7 cycles for a regular test.
If too high of a dV/dt will damage your machine, you either need to implement an analog filter or use some other method.
I actually do not fear a machine damage, but a step change causes a fairly high strain rate and therefore might the test.
How about returning the control signal to 0 between changes?
Since 0 V equals zero force in my case, I would definitely interfere my test (crack closure due to local plastification) and therefore, this is not an option.
@PreDre, bdunham7 and Circlotron
From your replies, I took the message, that a function generator is not an appropriate device for such an application. I think I will look for an PC controlled analog output and generate the signal on my own. Then I have all the flexibility I need.
Once more, thank you all for your replies!

Best wishes,
Josef