A flexible wing system of bending and twisting deformations is described by a fourth-order partial differential equation(PDE) and a second-order partial differential equation(ODE), where the disturbances in all channels and references are supposed to be from an unknown exosystem. In this sense, all the disturbances and references are composed of uncertain coefficients and time-varying states due to unknown initial values. Firstly, the robust output regulation is firstly transformed into a stabilization problem of the tracking error system, where the unknown time-varying terms from disturbances and references are rewritten into unknown coefficients but known time-varying terms. Then, adaptive nonlinear controls are proposed where adaption laws are used to estimate the unknown coefficients and nonlinear terms are used to guarantee the output constraint. Based on a Barrier Lyapunov function, the tracking errors of the closed-loop system are proved to converge toward zero, and are further restrained by time-varying constraints. Two numerical simulations are provided to show the effectiveness of the adaptive controls.