One of the two major Well Controls with Lift Mechanism trying to maintain the  actual flowrate  manually specified value of the flowrate :

 q_L(t) = q_{LL} = \rm const

Liquid control is most common for producing wells with SRP and ESP.

The mechanical pump is trying to maintain the target flowrate  but it only succeeds when the wellbore fluid level is above pump location.

If dynamic fluid level lowers all the way down to the pumping chamber, then the pump efficiency deteriorates and the flowware reduces:

while the fluid level and corresponding BHP are getting stabilized:

 p_{wf}(t) = p_c = \rm const

This value of BHP is called critical BHP  and the fluid can not be lifted at the wellbore pressures below critical BHP.

This does not actually qualifies the well operation as Pressure Control and the well is still under Liquid Control conditions and once bottomhole pressure raises above critical value the pump returns to producing the target liquid rate