An adaptive servo control system estimating the unknown reference signal model for a single-input single-output plant is proposed. In order to follow reference signals as in servo systems, the models of the reference signals should be included in the control laws as internal models. So far, in the cases that the model of the signals is unknow or varies, a servo control law can not be designed. To design a servo system in such cases, in this paper, an adaptive adjusting law is used to identify the unknown parameters of the reference signal model. To simplify the control system, the design is based on coprime factorization of the plant model over the ring of stable proper rational functions. Stability of the closed-loop system including the proposed adaptive servo system is proved.