## 1 Introduction
In addition to DMs, some studies [22] also introduce a tip-tilt mirror into the system to compensate for tilt aberration. For double wavefront correctors' AO architecture, the distribution scheme of the workload determines the performance of an algorithm. Additionally, the modeling strategy affects the implementation of modeling and the computation of controlling voltages. [PERSON]. [23, 24] used a Lagrange-multiplier (LM)-based damped least-squares (DLS) control method based on a function of wavefront slopes for controlling voltages. It solved controlling voltages by multiplying the inverse of the influence matrix to the left of the sensed wavefront slopes. The method receives effective results, though, it cannot thoroughly remove the coupling between wavefront correctors. Therefore, the damping factor should be designed carefully. Otherwise, either a conservative iteration step is selected or the stability of the algorithm may suffer a loss. In [25, 26], the authors decouple low-order aberrations from high-order aberrations by separating Zernike coefficients and distributing a reasonable workload to wavefront correctors. However, the modeling strategy for FSM considers angle value as a variable of Zernike coefficients. Similarly, the model for DM depicts the influence of controlling voltages towards Zernike coefficients. Firstly, the Zernike coefficients cannot be directly observed from SHWS which may introduce a fitting error into the model by using a wavefront restoration matrix fitting Zernike coefficients from wavefront slopes. Secondly, controlling voltages are the direct signal when using an embedded development board which means that another mapping relationship can be built when controlling FSM. To make the dependent and independent variables in a modeling strategy more intuitive, ref. [27, 28] built a linear mapping relationship between controlling voltages and wavefront slopes and used a digital PI controller when solving controlling voltages. The latter arranges the Zernike polynomials into a matrix and makes a linear transformation to make the algorithm adapt to irregular pupil regions. Nevertheless, according to our previous work [29], the spots offsets (which are proportional to the wavefront slopes) are a linear function of the square of the controlling voltages. Consequently, we separate the Zernike coefficients to distribute the workload considering the balance of complexity and performance and use a complete second-order modeling strategy to depict the mapping relationship between spots offsets and controlling voltages. Furthermore, due to the nonlinearity of the model structure, we use an iterative method to solve controlling voltages. The main contribution of this paper is that we use Zernike mode decomposition to decompose the wavefront into 2 nd, 3 rd and 4 th\(\sim\)15 th orders, and use FSM to compensate for low-order aberrations with DM compensating for high-order aberrations, which improves the compensation range and response rate to tilts aberrations of the AO architecture allowing the AO architecture to high-dynamically compensate aberrations. Then, the DM is modeled with the complete second-order model and the FSM is modeled with the coupled second-order model to ensure compensation accuracy. Finally, we use the iterative compensation algorithm to solve the controlling voltages. The remainder of this paper is structured as follows: Section 2 introduces the proposed FSM-DM cascaded architecture. Section 3 introduces our proposed high-dynamic atmospheric turbulence compensation algorithm which is our main contribution. Section 4 illustrates experimental simulative results collected from our testbed which is our third contribution. Finally, conclusions are drawn in Section 5.