How to Restore Controlfile from the backup ?

If you loss or if your all copies of control file is corrupted and if you have backup of your control file then it is required to restore your control file from your backup.

Restore control file to default location:
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The default location is defined by CONTROL_FILES parameter of pfile/spfile. If you don't specify any location while restoring your control file then the control file will be restored to the location set by CONTROL_FILES parameter. TO determine DBID check

SQL> Select dbid from v$database

Otherwise we can find the dbid in the name of rman backup piece

RMAN>SET DBID 3386862614
RMAN> RUN {
RESTORE CONTROLFILE FROM AUTOBACKUP;
}
Restore of the Control File from Control File Autobackup
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If you are not using a recovery catalog, you must restore your control file from an autobackup. The database must be in a NOMOUNT state. And you have to set DBID. RMAN uses the autobackup format and DBID to determine where to find for the control file autobackup.

RMAN>SET DBID 3386862614
RMAN> RUN {
SET CONTROLFILE AUTOBACKUP FORMAT
FOR DEVICE TYPE DISK TO 'autobackup_format';
RESTORE CONTROLFILE FROM AUTOBACKUP;
}

Restore of the Control File When Using a Flash Recovery Area
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Suppose you restored a backup of the control file. Now in that control file the backup information may not updated/full. May be it contains only current backup information of that session while taking backup. If you use flash recovery area then RMAN automatically catalog the backups in the flash recovery area. As a result the restored control file has a complete and accurate record of all backups in your flash recovery area and any other backups that were known to the control file at the time of the backup.

Restoring a Control File When Using a Recovery Catalog
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The recovery catalog contains a complete record of your backups, including backups of the control
file. Therefore, you do not have to specify your DBID or control file autobackup format.
Just use,

$rman TARGET / CATALOG catdb/catdb
RMAN> RESTORE CONTROLFILE;

Restore of the Control File From a Known Location
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If you know the backuppiece of controlfile or any copy then simply you can use,

RMAN> RESTORE CONTROLFILE from 'filename';

Restore of the Control File to a New Location
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In prior cases RMAN restore the control file to the location specified by CONTROL_FILES parameter of the spfile or pfile.

If you want to restore the control file to another location use,
RMAN>RESTORE CONTROLFILE TO 'give_here_new_location';

You can also change CONTROL_FILES parameter and then perform RESTORE CONTROLFILE to change location.

Limitations When Using a Backup Control File
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After you restore your database using a backup control file, you must run RECOVER DATABASE and perform an OPEN RESETLOGS on the database.