Current Ramp with constant voltage.
I don't think you´ll ever get a constant voltage applied in a load with linear behavior current flowing through, since $$V(t)=R*I(t)$$ If current is a linear function: $$ I(t) = kt + b$$ then the voltage is going to have the same behavior.

A simple example you can build to apply a varying voltage to yield a ramping current is creating a current source applied to a capacitor and such source driven by a PNP transistor. Then applying the signal to a buffer and finally to the load.







simulate this circuit &ndash; Schematic created using CircuitLab

That´s a simple schematic showing how you could somehow design your circuit.
Calculate R and C in order to yield any desired ramp by using $$I=C\frac{dv}{dt}$$ and assuming the voltage across R3 is going to be constant up to a limit, which is when the voltage across the capacitor causes the Base-Collector junction to be reverse-biased, thus not behaving like a constant current source anymore.