###### Abstract
In the control design, the neural network and the adaptive method were used to design a quantization controller, achieving asymptotic convergence of tracking errors. Because of the existence of Coulomb friction, an actuator mechanical system could not order the input command signal, and this phenomenon can be seen as dead-zone non-linearity and can be regarded as the characteristic between the whole input (the applied voltage of the direct current (DC) motor) and the whole output (the load angular velocity) of the system [13], thus a voltage dead-zone exists widely in the electric actuator systems. Active disturbance rejection control (ADRC) is an excellent controller for systems with uncertainties and disturbances. [PERSON] [14] first proposed ADRC, then [PERSON] [15] et al. developed the controller and simplified the parameter tuning method [16]. The modeling error and a variety of unknown uncertainties of the object are regarded as total disturbance, an expand state observer (ESO) estimates the disturbance in real-time, and then compensates the system to be a series integer type, finally a normal error feedback controller can be constructed to control the nominal model, so that ideal dynamic performance and closed-loop stability can be obtained. Literature [17; 18; 19] suggests that this approach can significantly reduce the dependency on the system model and have a remarkable control effect. [PERSON] [20] aimed a high-performance attitude control of the aircraft, and adopted ESO to estimate the uncertainty factors of the model, unknown non-linear dynamics factors, and the non-smooth feedback law was adopted to improve the control performance, notable control performance is achieved. [PERSON] [21] proposed an improved ADRC controller according to the non-linear disturbances such as friction torque existing in the actuator system and attained substantial results. Aiming at the non-linear problem of an actuator, [PERSON] used a model-free control method to analyze four non-linear compensations. Experimental results accredited the excellent ease of implementation and pivotal performance [22]. Although ADRC has been applied in the non-linear control of actuators and the attitude control of aircraft, no research was reported that a system combining the wind disturbance in the ascent phase with dead-zone non-linearity dynamics of an actuator. The major difficulties are highly precise non-linear actuator control and formulating an appropriate mathematical model of the missile considering wind disturbance. Therefore, it is hard to obtain notable control performances for the traditional control method, which relies on the accurate model. Aiming at compensating and suppressing the adverse effects of non-linear dynamics of the actuator, un-modeled dynamics and wind disturbance on pitch control of the guidance rocket during the boost phase, in this paper a cascade control strategy based on ADRC is proposed; mathematical models of the actuator loop and the pitch loop of the guidance rocket are constructed; and the controllers are designed and simulated respectively. The block diagram of the missile attitude control system studied in this paper is shown in Figure 1.  
The paper is divided into four sections. The first section is an introduction. In the second section, the actuator close loop is modeled and simplified considering dead-zone non-linearity. Simulation analysis of the system under ADRC and proportion integral differential (PID) control is carried out for different voltage dead-zones, different loads, and different command angles. In the third section, the simulation of traditional gain scheduling control and ADRC control is carried out and compared considering wind disturbance and actuator dynamics. The fourth section summarizes the full content.