MSAW ACTIVATED WHEN REPORTER CROSSED THE FAF FIX 1000' BELOW DESIGNATED CROSSING ALTITUDE.

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I FILED FOR IFR CLRNC PRIOR TO TKOF AT XA20 HRS. I RECEIVED MY CLRNC ENROUTE TO HOUSTON. CLRED DIRECT HOBBY HDG 040' CLIMB AND MAINTAIN 4000'. AS I NEARED HOBBY; I WAS CLRED DESCEND AND MAINTAIN 2000'. THE ATIS INFO WAS DECLARING RWY 12R ILS IN USE. I WAS BEING GIVEN VECTORS TO INTERCEPT THE GLIDESLOPE FOR RWY 12R. PRIOR TO INTERCEPT; THE ILS WAS DECLARED INOPERABLE AND I WAS GIVEN INSTRUCTIONS THAT THE VOR APPROACH WOULD BE USED. DURING THE APPROACH; I WAS HIGH AND TO THE LEFT OF THE LOC. THE TWR ASKED IF I WERE TURNING TO THE RIGHT TO INTERCEPT? I SAID THAT I WAS. THE TWR THEN GAVE INSTRUCTIONS TO CLIMB TO 2000' FOR RE-SEQUENCING. ON THE SECOND APPROACH; I DID NOT CORRECTLY IDENTIFY THE FINAL APPROACH FIX. (POSTY INTXN). THIS INTXN IS AT THE INTERCEPT OF THE HUMBLE 175 DEG RADIAL. AND HOBBY 300 DEG RADIAL MINIMUM DESCENT ALTITUDE AT POSTY IS 1600'. THE TWR ASKS FOR ALTITUDE VERIFICATION? I SAY 800'. TWR SAYS I SHOW YOU AT 600'. TWR THEN ADVISES TO CLIMB TO 1000'; I COMPLY! TWR ADVISES: LOW LEVEL ALARM! I CLIMB TO 1000' AND CONTINUE THE APPROACH. TWR ASKS DO YOU HAVE THE ARPT IN SIGHT? I SAY NEGATIVE LATER I SAY SMA HAS THE ARPT IN SIGHT. TWR SAYS ROGER; CLRED TO LAND; CONTACT GND ON 121.9. NO FURTHER COMMUNICATION WAS MAINTAINED WITH THE TWR. I WAS NOT ASKED TO REPORT TO; OR TO CALL THE TWR. CONCLUSIONS AND OBSERVATIONS: ALTHOUGH THE RESPONSIBILITY OF IDENTIFYING THE FINAL APPROACH FIX LIES WITH THE PLT; A COUPLE OF THINGS PERHAPS WOULD HAVE MADE THIS SITUATION AVOIDABLE. FIRST; MORE ADVANCED WARNING THAT THE ILS WAS INOPERABLE WOULD HAVE GIVEN MORE TIME TO THE PLT TO PREPARE FOR THE ALTERNATE APPROACH. SECONDLY; THE CTLR WAITING UNTIL THE ACFT IS CONSIDERABLY BELOW THE APPROACH MINIMUMS BEFORE ASKING FOR ALTITUDE VERIFICATION RESULTED IN CALLING FOR A MAJOR CORRECTION RATHER THAN A MINOR ADJUSTMENT.