You may be missing some things from your theory,
Do you mean an offline PS, mains input, 1.2-20V output?
Or just a DC-DC, where the source is handled somehow (perhaps an iron core transformer and rectifier)?
There are options for both, but the first is considerably more difficult -- it covers a
lot more domains of electrical theory, to build a successful design.
You do have a greater chance of success, with less theory, with the DC-DC converter.
As for "controller" chips, understand: a
regulator contains integrated switches, and is only good up to so much voltage and current, at its switch. There are integrated regulators for converters and isolated supplies, but they are limited in power. Usually up to 100W (mains powered) or ~5A (converter).
In contrast, a
controller has gate-drive outputs: you add your own switch, and support components. It can be scaled up to any voltage or current you desire, though there are some practicalities, such as: control and protection methods, that become desirable at higher power levels; where to source auxiliary power from; how much adjustable range is desired; and how feedback, isolation and regulation is handled.
For example, at a <100W power level, for an offline converter, you could choose the venerable UC3842 peak current mode controller. It's a controller, so you have to supply it with auxiliary power, and add your own switch, current sense (shunt) resistor, timing and feedback components, etc. The usual approach is: switching into an isolation transformer (actually a tightly coupled inductor, as it stores energy), with a TL431 performing load-side regulation (the controller is simply wired as a follower, so it follows the TL431's command proportionally). This works great for fixed supplies, but if you want more than about a 40% adjustable range (i.e., 12-20V say), the aux supply to the UC3842 disappears (it's self powered from an extra winding on the transformer), and it browns out and goes into a clicking auto-restart mode. You can solve this by adding a dedicated supply (which can be built from a regulator chip and parts, or a drop-in module), but then you can only adjust down to a few volts before the TL431 itself runs out of headroom to operate in. The flyback topology is also a poor choice to use for wide output voltage ranges: the lower the voltage, the longer the discharge time is, which changes the controller's response. It's not designed for that regime (continuous current mode, CCM), so it's better to avoid going too far that way.
There are plenty of other options. If flyback isn't suitable, then you might consider forward topology. The classic controller here is the TL494, but it has a number of quirks that makes it tedious and slow, and operate poorly. (To make it work optimally, you need more external parts.) The traditional design would have an auxiliary supply (separate chip or module), which puts a steady, say, +12V on the secondary (load) side. This supplies the TL494, which is on the load side. Two transformers are used: one couples the TL494 outputs (via gate drive IC) to the switching MOSFETs, the other is the main power transformer. Because the gate drive signal has to pass through a transformer, it's limited on how big the transistors can be, and how fast they can switch. This is suitable up to about a kilowatt or so, before you want something more elaborate (like isolated driver circuitry). Since the TL494 is powered separately, it can regulate the output voltage over any range, and the forward converter topology is suitable for wide range outputs like this.
Tim
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