# Single-Parameter-Tuned Attitude Control for Quadrotor with Unknown Disturbance
## 1 Introduction  
Quadrotor unmanned aerial vehicles (UAVs) have shown great potential for both civil and military applications, because of low cost, small volumes, simple structures, flexible operation, and vertical take-off and landing capability [1, 2]. However, quadrotor UAVs present control challenges because of high-dimensional nonlinear dynamics, difficulties in measuring system parameters, and ever-changing noise and disturbances. Various control algorithms have been tested on quadrotor UAVs, among which the classic proportional-integral-derivative (PID) controller is the most widely used. For example, paper [3] presents a quadrotor UAV attitude control method to realize complex acrobatic UAV maneuvers using the double-ring PID algorithm and Smith predictor. In paper [4], quadrotor attitude and position controller using rotation matrix based PID algorithm are designed. The linear quadratic regulator (LQR) algorithm has also being used in quadrotor UAVs with some success [5]. Researchers compared the performance of a Qball-X4 quadrotor with PID controller and LQR controller, and the tracking trajectory with LQR controller is more smooth and it has less disturbance [6]. LQR algorithm can also be applied on a morphing quadrotor and achieve a success [7]. Nonlinear control algorithms, such as back-stepping (BS), sliding mode control, and H-infinity control, have been applied to quadrotors. Researchers propose an approach of the backstepping control running parallel with a sliding mode observer for a quadrotor UAV [8, 9]. Paper [10] presents quadrotor altitude control withsliding mode control and paper [11] designed attitude and position control using sliding mode control. H-infinity control is another optimal control algorithm that provides a robust stable closed-loop system with high performance tracking and disturbance rejection. Paper [12] present H-infinity style quadrotor attitude controller, where the system transfer function is identified based on input and output experimental data. In paper [13], a H-infinity observer is designed to compensate the effect of actuator failures, sensor failures, and external disturbances. However, these algorithms rely heavily on model accuracy, which severely affects application to real quadrotor platforms. The active disturbance rejection controller (ADRC) technique is based on the traditional PID: a tracking differentiator (TD) is set to arrange the transition process and extract the differential signals, and an extended state observer (ESO) is used to estimate the state of the control object and the unknown disturbances. A nonlinear state error feedback (NLSEF) is formed by a nonlinear combination of the results from the TD and the ESO, including the compensation for external disturbances if needed [14]. Both external disturbances and model errors can be estimated while using ESOs. The critical gain parameter (CGP) is the gain in the input channel that characterizes the proportional relation between the input signal and the derivative of the process output of a specific order [15]. In this paper, the CGP is the proportional relation between the control signal and the angular accelerations of three axes. Studies have shown that the ADRC can be used to stably control a quadrotor in the presence of external disturbances [16; 17; 18]. Acceptable control performance have been demonstrated for the control systems proposed by previous researchers. However, model-based control algorithms, such as LQR and BS, heavily rely on model accuracy, which hinders their application to real quadrotor platforms. It is difficult to tune the parameters of model-free algorithms, such as PID and ADRC. When considering the traditional double-ring PID algorithm as an example, typically three or more parameters must be tuned for each axis, and the tuning process can be time consuming and dangerous.