Island microgrid is a typical cyber physical system(CPS)under the background of smart grid. To deal with the new issues such as the threat of communication security

the participation of demand side for system control

and the plug and play mode of distributed generators(DGs)

the traditional thinking on cyber-physical integration should be stretched

and the no-control-center collaborative techniques should be developed. An active power control model is proposed for island microgrid

which contains frequency-trigger demand response units

renewal generation units

diesel generation units

and battery energy storage system units. A fully distributed collaborative method is proposed

which is capable of recovering system frequency in a best economic way. The proposed algorithm can be decomposed into three parts of consensus term

frequency feedback and feedback coefficients. The consensus term regulates generation units obeying the equal increment criteria

the frequency feedback is responsible for quickly recovering system frequency

and the coefficients with information of both global perception and error proofreading are used to enhance the control performance. The effectiveness and reliability of the proposed model and method are verified by simulations. This work is supported by National Natural Science Foundation of China(No. 51577049).