Cooperative transportation by multiple Unmanned Aerial Vehicles (UAVs) has been a topic of interest amongst robotics researchers since a decade. Researchers have developed different control schemes to address some of the issues related to cooperative transport. However, most of the existing control strategies assume a stationary center of gravity (CG) coinciding with the geometric center of the payload. In real world applications such as package delivery or human transport, position of CG, in general, would not be at geometric center, or would not be even known a – priori. This paper proposes a Proportional, Integral and Derivative (PID) controller to address the issue of control when the CG is offset during transportation of a common payload using multiple UAVs. The proposed PID scheme is centralized in nature in that it provides the same control action to all UAVs. Using extensive numerical simulations, the paper shows that such a scheme is shown to work effectively irrespective of the location of CG on the payload. The control scheme is also independent of the payload geometry and number of UAVs employed for cooperative transport. The work presented in this paper provides the groundwork to develop better control strategies to solve the problem of multi-UAV cooperative transport with a – priori unknown CG.