One of the two major Well Controls with Lift Mechanism maintaining the manually specified bottom-hole pressure (for producers) or THP (for Injectors). 

The Pressure Control is a usual condition for water injectors and gas injectors and specified by the THP maintained by the ground booster pump with discount fo the pressure losses along the pipelines and the wellhead choke.

In this case a reservoir takes as much fluid as it can depending on formation pressure  quality of well-reservoir contact,  reservoir capacity,  reservoir transmissibility around a given injector.

Sometimes producing wells produce at nearly constant bottomhole pressure, when it is being reduced by the downhole pump to its minimal value $//<![CDATA[ \begin{array}{l}p_{wf} = p_c = \rm const\end{array} //]]>$, specified by the pump location inside the wellbore.

In this case the liquid rate starts declining  $//<![CDATA[ \begin{array}{l}q^{\uparrow}_L(t) < q^{\uparrow}_{LL}\end{array} //]]>$

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 minimal the pump returns to producing the target liquid rate  $//<![CDATA[ \begin{array}{l}q^{\uparrow}_L(t) = q^{\uparrow}_{LL} = \rm const\end{array} //]]>$. 

See Also

Petroleum Industry / Upstream /  Production / Subsurface Production Operations / Well Control

[ Liquid Control ]

[ Pressure Control (Dynamic Modelling) ]