A BEECH F90 AT 11000 FT DIVERTED DUE TO LOSS OF L ENG PROP CTL. DIFFICULTY ENCOUNTERED WITH L PROP CAUSED ALT UNDERSHOOT.

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ACFT JUST COMPLETED PHASE 2 INSPECTION. ON GND; AFTER START-UP; FUEL FLOW INDICATOR WAS INOP. SHUT DOWN FOR REPAIR. DEPARTED ZZZ 20 MINS LATER WITH ALL SYS APPEARING OP. ON CLBOUT TO 11000 FT PROPS WOULD NOT SYNC AND L PROP LEVER WAS STUCK. PROP LEVER FINALLY MOVED REDUCING RPM FROM 1900 TO 1850 BUT IMMEDIATELY REALIZED IT WOULD NOT MOVE BACK TO 1900. CONTACTED ZZZ1 APCH AND ASKED FOR A RETURN TO ZZZ. WAS GIVEN VECTORS FOR LOC BACK-COURSE RWY 27L AT ZZZ AND CLRED TO DSND TO 4000 FT MSL. DURING DSCNT PROP CTL SEEMED TO FUNCTION AGAIN BUT THEN RPM ON L PROP WOULD NOT COME UP FROM 1800. CLRED FOR APCH TO MAINTAIN 3000 FT TILL ESTABLISHED. WAS ESTABLISHED AND OUTSIDE ZZZ2 (MUST MAINTAIN 2300 FT MSL UNTIL ZZZ2) DSNDING THROUGH 3000 FT MSL. WHILE ATTEMPTING TO RETURN L PROP RPM TO 1900 FOR LNDG; I DSNDED BELOW 2300 FT WHILE STILL OUTSIDE ZZZ2. AT 1900 FT MSL; ATC ISSUED A LOW ALT WARNING AND I IMMEDIATELY CLBED BACK TO 2300 FT MSL. 1 MI LATER AND INSIDE ZZZ2 I HAD ZZZ IN SIGHT AND MADE A NORMAL APCH AND UNEVENTFUL LNDG. THE DISTR OF THE MALFUNCTIONING PROP CTL CAUSED ME TO TEMPORARILY LOSE TRACK OF MY POS AND THUS I INITIATED A PREMATURE DSCNT; BUSTING THE ALT MINIMUMS OUTSIDE ZZZ2 ON THE APCH.