how to restore from backup from ios 11 beta to public version

The following is from Apple Beta Software Program

How do I restore a prior shipping release of iOS, macOS, or tvOS?

Always back up your iOS device or Mac before installing the public beta. Since Apple TV purchases and data are stored in the cloud, there's no need to back up your Apple TV. To use a previously-released version of macOS or iOS, you can restore your device from the backup that you created before installing the public beta.

Learn more about restoring your iOS and macOS devices

For the detailed instructions, click iOS in the MacOS - iOS button near the top of Restore Shipping Software

You can only restore a Beta made backup to a public iOS version that is higher than the Beta. i.e the public reelase version of the Beta you were using or a subsequent version.

You cannot restore a Beta made backup to an older iOS version. Which is why it is always important to have a backup made before installing the Beta as mentioned in Apple's Beta Faq presented to you when enrolling in the Beta program officially.