How to add CC/CV feature with single LM358 for variable linear power supply?
So yes, the design it's perfectly working, by now I tested on LTSpice and works very well the error that I had in my simulation was the reference Vo3(is the voltage out regulated) that is AGND of the control circuit without that reference the control circuit wouldn't work. Here's the updated circuit
And the schematic:

I understanded the principle of CC/CV mode from this webpages:

How Does a Power Supply regulate It’s Output Voltage and Current?
Error Amplifier with Forced Equilibrium Adaptor