Local control strategies that operate without relying on communication systems enhance flexibility and reliability of AC industrial microgrids. Based on a previous work in which a secondary switched control was proposed, this paper presents a complementary strategy to improve the frequency regulation by reducing the maximum error. To this end, a dynamic-gain droop method driven by a time protocol is used. With this proposal, the maximum frequency error is effectively reduced without relying on complex techniques and maintaining the simplicity of the basis strategy and the non-use of communications. Experimental results obtained on a laboratory microgrid are presented to validate the performance of the proposed complementary control strategy.