How to set tags to a TagsInput using $set

Hello i would like some help to set tags using $set i have tried :

$set('tags', 'a,tag');
$set('tags', ['a','tag']);
$set('tags', ['tag'=>'tag']);

$set('tags', 'a,tag');
$set('tags', ['a','tag']);
$set('tags', ['tag'=>'tag']);

as show in the image , it shows as if the input is not empty but not displaying anything,

thank you for the help