# A Novel Disturbance Rejection Control of Roll Channel for Small Air-to-Surface Missiles
## 1 Introduction  
Modern missiles have the characteristics of high speed, high control accuracy, stronger mobility and larger flight envelope [1]. However, the low cost makes the device performance not high, and there is a problem of insufficient error accuracy in the manufacturing process. Then, disturbance deviations such as large difference of aerodynamic parameters, deterioration of structural mass characteristics, and deterioration of inertial navigation drift performance occur. In addition, during the guidance process, the missile will encounter random wind, turbulence and other external disturbances. These factors bring great difficulties to the design of attitude control system. It is necessary to design an attitude control system with excellent performance to achieve high-precision and high stability attitude control. At present, missile control mostly adopts PID feedback control [2, 3]. In PID control, it takes time to transmit control commands and the actuator responds to control commands. When the actuator responds to the control command, the characteristics of the controlled object change greatly. This leads to poor control quality in trajectory simulation or flight experiments. Therefore, for small missiles with small and complex moments of inertia, it is difficult to meet the requirements of high-performance attitude control using classical control theory PID. Compared with PID control method, active disturbance rejection control technology [4] is represented by active disturbance rejection controller (ADRC), including tracking differentiator, extended state observer (ESO), nonlinear feedback and other technologies. The controller designed by this technique has the characteristics of small overshoot, fast convergence, high precision, strong anti-disturbance ability and simple algorithm [5]. Extended state observer is the core part of ADRC, which expands the disturbance affecting the controlled output into a new state quantity. Using special feedback mechanism to establish the extended state observer, It does not depend on the mathematical model of the controlledobject. It has a good inhibition effect on the changes of the parameters and structure of the controlled object, as well as internal and external disturbances. The algorithm is especially suitable for solving various problems existing in the actual flight of the missile [6]. In view of the above advantages, the extended state observer has been widely concerned since it was proposed. It has been successfully applied in many fields such as aviation, aerospace, weapons and industrial control [7; 8; 9]. Research has been conducted in-depth on the field of the extended state observer. References [10; 11] analyzed the convergence of uncertain nonlinear systems and multiple-input multiple-output systems, respectively. Literatures [12; 13] discussed the relationship between the bandwidth of linear extended state observer and observer error for the controlled object with uncertain model. Reference [14] studied aircraft flight control based on second-order attitude observer and a nonlinear feedback. The active disturbance rejection controller based on extended state observer was designed in the literature [15]. The attitude stability control of a single channel spacecraft with flexible solar panels was analyzed. References [16; 17] studied the control law and attitude stability of satellites based on ADRC technology. In the aspect of aircraft attitude control, extended state observer also played an important role and has achieved a lot of research results. Literature [18] took \"Tihang-2\" small solid rocket as the object, designed the three-channel attitude controller based on the extended state observer, and verified its performance. Literature [19] applied the third-order extended state observer to the design of ADRC, studied the attitude maneuver control problem with three-channel coupling, and completed the parameter setting of ADRC. References [20; 21; 22] proposed robust flight control method based on the extended state observer.