I'm working with a LM358 op-amp as a non-inverting amplifier to get a 0-24 V output from a 0-5 V input. When the input is 1.5 to 5 V, the gain is 4.8 which is OK (set by resistors), but below 1.5 V this gain decreases more and more until 0 V.
How can I make this 4.8 gain stable along the range 0-5 V?
Picture of the circuit I'm using, R1 = 1 kΩ, R2 = 3.8 kΩ.
but below 1.5 V this gain decreases more and more until 0 V.
This sounds very much like the input offset voltage not being factored into your calculations. For the LM358 it is 2 mV typically but, can be as high as 3 mV. Some op-amps are even worse. Some op-amps boast an input offset error of only 5 μV. However, your circuit gain is 4.8 hence, it manifests as a DC error on the output of 9.6 mV. This can be a positive or negative error voltage.
As you can see, the closer you get towards zero, the error magnifies.
Then there are your measurement errors to consider. All-in-all what you say doesn't surprise me but, it's not that the gain is reducing it's just that it appears to reduce because of DC offset errors.
If you want to measure gain, use an AC signal and decent meters to take readings of the AC voltages.
... but below 1.5 V this gain decreases more and more until 0 V.
As pointed out by @Andy aka ...
I think you talk about voltage output, because, in fact, it is something like 0.1 V at input.
Here is a simulation also in the case of the opamp being supplied with -5 V (in place of the ground).
DC Dynamic Analysis
TRANsient Analysis: see the variable "gain", curves in "red" ...
