PA-34-200 Seneca I
Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Commercial; Flight Crew Multiengine
Flight Crew Last 90 Days 24; Flight Crew Total 1210; Flight Crew Type 100
Situational Awareness
Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew FLC Overrode Automation
Aircraft; Human Factors
I was instructing an instrument student and was cleared to intercept the ILS.  I armed the approach on the autopilot and when the autopilot commanded a turn to final we started to descend.  I was expecting the autopilot to descend and did not check immediately that we were on glideslope.  When I saw we did not have the glideslope and our position; I instructed the student to climb and at that time ATC reported an altitude alert and directed a climb.
The pilot and instructor of a PA34 experienced a premature descent when the autopilot had not yet captured the glideslope. The instructor advised a climb just prior to ATC reporting an altitude alert.