What does 'not controllable' mean in power electronics?
simulate this circuit &ndash; Schematic created using CircuitLab
Figure 1.

(a) A diode will conduct if it is forward biased. There is no control pin on it. It is not controllable.


Figure 2. The upper waveform shows the result of the diode or the thyristor when triggered at the start of the half-cycle. The third waveform shows the result of triggering half-way through the half-cycle. Image source: Electronics Tutorials.

(b) A thyristor has a control pin and can be turned on part way through the AC cycle. Once triggered it remains on until the current through it falls to zero. In that regard it is semi-controllable - you can turn it on but will require special circuitry to force it off if you don't want to wait for the next AC zero-cross.
(c) A MOSFET's conductivity can be controlled by its gate voltage and can be increased or decreased on command. It is fully controllable.

Feedback is used to adjust the actual output to bring it closer to the desired setpoint. It's irrelevant in (a), it might be useful in (b) to control the resultant output voltage or power and it would be most often found in (c) to control the current or voltage in the load.