Vibrations and disturbances are becoming more of a concern as lightweight, flexible structures in high-tech systems are pushed towards faster speeds and higher precision. Active Vibration Control (AVC) methods have been effectively used to attenuate vibrations and increase the bandwidth of these systems. With the miniaturisation of electronics, an increasing amount of sensor and actuator pairs can be used for AVC applications. Not only does this allow for higher active damping, it also grants more flexibility in terms of control. This trend has led to the study of robotic metamaterials and meta-structures: large-scale engineered materials build out of a repeating pattern of unit cells, where each unit cell contains a sensor, actuator and sometimes even a computing unit. The optimal control architecture to use for these systems is a difficult dilemma, since decentralised and centralised control schemes both have fundamental trade-offs in terms of performance and scalability. In this paper we study distributed control, a promising middle-ground solution that is hardly used in AVC applications. We show with the use of LQR that a distributed control architecture can achieve optimal performance in the low-frequency range for robotic materials with relative measurements. Additionally, the actuators use lower maximum control forces and a distributed control architecture remains scalable for implementation in large-scale systems. In this paper the robotic cantilever beam is studied as a specific example as it represent many typical high-tech applications. Furthermore, implications on periodic robotic meta-structures are made using LQR in the Spatial Fourier Domain.