Design a Controller for Bidirectional Converter

Sounds like what you want is a charge controller to charge the battery from the PV and a DC-DC converter from the battery to the load. No need for two way anything. When the PV is sufficient it will supply power to the load, when not, the battery will supply power. If the load draws less than the PV is supplying, it will go to the battery. A well designed charge controller will not overcharge the battery.

I have never heard of a bidirectional DC-DC converter. I think you mis-read the label.

In fact, diodes are frequently employed to avoid DC current flow in the wrong direction, else things burn up.

Typically a DC-DC converter has a forgiving input and a fixed output. The term "bidirectional" implies that there is no distinction between input and output.

The reason the input needs to be forgiven is because it can not provide the desired voltage. If the input voltage drops, the device sucks up more current to make up for the sag.

Lastly, when your output voltage drops to zero, that is an indication that you are in short circuit mode and the device has gone into short circuit protection mode. So you are asking too much or it has failed. I can't tell which, from here.