Hierarchical schemes are widely used for the designing of the inverter-based AC microgrids control strategies. To ensure reliable operation, hierarchical control must consider together all the functionalities that allow the regulation of key variables and guarantee a safe transition between operation modes. Conventionally, in the literature are proposed three-layer schemes which present relevant drawbacks: they include limited functionalities and they use droop method for the primary layer which, despite its decentralised nature, suffers from issues that have motivated the development of alternative strategies. Considering this, the contribution of this study is two-fold. First, a droop-free hierarchical control strategy that satisfies a proper operation of AC microgrids is proposed. Control objectives such as power-sharing, frequency regulation, optimal power dispatch and voltage regulation are considered. Second, a closed-loop small-signal model, which facilitates the control parameters design and fills a gap in the literature is presented. Differences between the proposal and previous controls are discussed. Selected tests are carried out in a laboratory microgrid under different conditions, including normal operation and the response to failures in the central controller and to communication impairments. The experimental results show a good performance of the proposal even in adverse conditions.