Topic: Is general sustain pedal compatible with MIDI port on digital piano?

I have Yamaha Clavinova CLP 550 without it's own pedal and I can't find any of it on the internet.The problem is CLP 550 has only 4 pin pedal connector and it doesn't have another sustain port.

If I want to use the general sustain pedal (1/4 audio jack)

connect to the MIDI in or out  port of the piano
by using the "1/4 audio jack female" to "MIDI 5 pin male" adapter
https://m.ebay.com/sch/i.html?_from=R40 … 2F4+female

Compatible or not ?

If not, do you have another way to use sustain pedal with this piano.

Thank you