I want to make a power DC supply with voltage rating 0-200V.
I want it to be a variable power supply with voltage from 1V to 200v.
What should be my approach?
My approach, but I've got not experience in building measurement-grade supplies, would be the following. Please, do take this slightly "and the details are left for the reader to implement" approach with a grain of salt.
You can buy voltage references (do not go too cheap on this, a few cents more here will help you not worry about that source of error later on). Say, you get one with 2.048V +- 0.1% over the temperature range you care about.
Then, you'd take the voltage output by that, and pass it through a multiplying DAC, or voltage DAC with external reference input. That DAC has more effective bits than your intended resolution needs. Using more bits than strictly necessary allows for later software calibration.
Then, you'll need a > 200V DC source, ideally filtered against noise, but I don't know what you need in spectral hygiene.
You'll want a high-side pass bijunction transistor, with a load resistors stronger than your maximum load. (Which means you want different load resistances, swapped based on your output voltage range, effectively. You can also do that with e.g. a single n-channel mosfet controlled by a relatively rough DAC to give the desired output current "minimum load".)
That pass transistor's base voltage is controlled by a control loop that compares the voltage on its output, divided by a different resistive voltage divider (0.1% resistors are relatively cheap) for each range, to the voltage generated by your precision DAC above.
Use a low-offset, low-bias-current opamp, or instrumentation amplifier circuit, to implement that feedback loop.
Sprinkle in a series R and a parallel C filtering on the opamp's output to dampen the oscillations you'd get on voltage adjustments/load changes. Put analog switch IC's on the output of that – another few ohms of resistance doesn't hurt the control loop, and neither will the parasitic capacitance; now, replicate for each voltage range, and you'll have selectable controllers for all of your output.
What I described above is basically an opamp-controlled linear regulator, one for each double-octave of output voltage. The redundancy comes from the fact that getting the same resolution over such a large voltage range using a single resistive divider ist hard, and I don't see an elegant way to get a high-accuracy multiplying DAC to work at 200V.
Now comes the annoying part: everything done, this thing will probably not be 1% accurate. You'll need to have a microcontroller that translates the desired voltage to both a selection for the active controller and a non-linearity-compensated DAC value. Depending on your resolution (1% accuracy sadly doesn't tell us what the resolution is) and thermal and time-stability needs, this might imply hacks like keeping all your hybrid/analog circuity in a temperature-controlled heated enclosure, or a temperature-compensation calibration, or bright "do not operate when temperature is outside 18°-22°C" stickers or something.