How to fix the error in v-model rendering

I have the following fragments in my index.blade.php:

The content section:

.
.
.
<div class="col-12 col-md-12 mb-3">
    <label for="attachment" text-muted">Attachment</label>
    <div class="col-md-12">
        <div>
            <b-form-file
                ref="attachment"
                id="attachment"
                v-model.trim="$v.feedback.upload.attachment.$model"
                placeholder="Click to upload..."
            ></b-form-file>
        </div>
    </div>
</div>
.
.
.

The script section:

.
.
.
var app = new Vue({
    el: '#app',
    data() {
        return {
            'feedback': { 'upload': {'attachment': null} }
        }
   }
})
.
.
.

Everytime I try to load the page, it caused this error as below:

[Vue warn]: Error in render: “TypeError: $v.feedback.upload is undefined”
(found in Root)

I would like to ask what caused the above error because when I commented the v-model.trim="$v.feedback.upload.attachment.$model" line, everything loads fine.
Thank you in advance for any response.