This paper is concerned with controllability of Timed Continuous Petri nets, under infinite server semantics, with uncontrollable transitions, which are a class of hybrid systems (piecewise-linear). This class of hybrid systems is suitable for representing biological systems, high traffic information networks, heavily loaded supply chains, etc. By adopting a Control Theory approach, the contribution of this paper is the characterisation of controllability over sets of equilibrium markings (potential equilibrium points), first inside a single marking region (or linear mode) and later extended to several regions.