Membrane-type acoustic metamaterials (MAM) consist of a thin pre-stretched membrane with masses periodically attached to the membrane. MAM can be designed to be very lightweight and exhibit anti-resonances at low frequencies with sound transmission loss values that can be much higher than the mass-law. This makes MAM very appealing for different noise control applications. However, the typically narrow bandwidth of the anti-resonances is a big challenge for applying MAM to noise sources that consist of changing tonal frequencies and/or broadband noise. In this contribution the preliminary results of a concept study for a self-adjusting MAM using active control are presented. In this concept, the added mass is replaced by an inertial electrodynamic shaker which enables the actuation of the MAM. The performance of different control strategies is evaluated using analytical and numerical models of the MAM. In particular, this evaluation will focus on methods to enable the MAM to adjust its anti-resonances to changing tonal frequencies and to improve the broadband noise reduction of the MAM. Additionally, it is investigated how the performance of the active MAM is affected when not every unit cell of the MAM contains an actuator in order to reduce the complexity of the system.