## 1 Introduction  
Nowadays, quadrotor UAVs have become an important tool and a technology carrier in various fields. Because of its advantages such as good mobility and easy operation, it is gradually becoming an indispensable technological tool in various fields of modern society, bringing new possibilities and opportunities for the development and progress of human beings [1, 2, 3]. However, the control problem of quadrotor UAV has been a popular research direction in the control discipline because of its strong nonlinearity, strong coupling, underactuation, and multiple inputs and multiple outputs. The ultimate control goal of a quadrotor UAV is to achieve precise position control, while good attitude control is a prerequisite for precise position control. In the past decades, many studies have studied the attitude control problem. The control methods can be divided into linear control methods and nonlinear control methods. The common linear control methods are PID and LQR. As early as 2005, [PERSON] et al. [4] used a PID algorithm to implement attitude control on a small quadrotor aircraft and achieved good control results. However, the PID algorithm also has some problems, such as parameter tuning relying on the designer's experience, sensitivity to noise, limitation to linear systems, and lack of stability proof. To address these problems, [PERSON] et al. [5] combined the PID and the backstepping method to give a tuning range of PID parameters. For the problems of slow tuning process and large overshoot, [PERSON] et al. [6] proposed an adaptive control method based on single neuron PID, which can enhance the robustness of the controller by adaptively adjusting parameters. [PERSON] et al. [7] use a particle swarm algorithm to optimize the proportional and differential parameters in the position controller. They also designed a robust adaptive integral backstepping-based attitude controller to achieve the stable control of the UAV under external wind disturbances. [PERSON] et al. [8] proposed an LQR control method based on gain scheduling, and this control method can select different feedback gain matrices according to the error of the system. Although the above linear control methods can achieve good attitude control, they are often designed based on a linearized model with small angle assumptions, and when the attitude of the quadrotor UAV changes significantly, the linear control methods often fail to obtain good control results. Therefore, many researchers began to turn their attention to the study of nonlinear control methods [9; 10; 11; 12; 13]. Nonlinear dynamic inversion (NDI) [14] is one of the commonly used control algorithms for aircrafts. It is a nonlinear control method based on feedback linearization, which cancels out the nonlinear terms in the original system through the form of state feedback to achieve the linearization of the nonlinear system. [PERSON] et al. [15] used an approach based on feedback linearization and that utilized extended state observers for the online estimation of unknown disturbances. However, this method requires a high-accuracy system model. Studies [16; 17; 18] incorporate an adaptive approach to improve the robustness of NDI. [PERSON] et al. [19] improved the detrimental effect of the dynamic inversion nonlinear term on error elimination by adding additional feedback to the state feedback link of the dynamic inversion. Due to the existence of disturbance and modeling errors, methods based on disturbance estimation have received extensive attention from scholars. In the studies [20; 21; 22; 23], all of them use the extended state observer (ESO) to estimate the total disturbance in the UAV's attitude system to achieve active disturbance rejection control (ADRC). Based on a dual closed-loop active disturbance suppression generalized predictive control, [PERSON] et al. [24] proposed a robust controller for quadrature trajectory tracking control.