# Fractional-Order Sliding Mode with Active Disturbance Rejection Control for UAVs
## 1 Introduction  
In today's rapidly developing field of aviation technology, unmanned aerial vehicles (UAVs) have become a hot spot for research and application because of their unique design and operational flexibility. These vehicles have shown great potential for surveillance, reconnaissance, cargo transportation, and aerial photography [1]. Many controllers have been applied to the attitude stabilization of UAVs, such as the proportional-integral-derivative (PID) control strategy [2, 3], optimal linear quadratic regulator (LQR) control algorithm [4], and \(H_{\infty}\) control algorithm [5]. However, when performing some specific tasks, such as agricultural spraying pesticides and forest area inspections, UAVs need to hover accurately and have certain anti-interference capabilities, so their control problems are still full of challenges, especially their nonlinear dynamic characteristics, parameter uncertainty, and external environmental disturbance, which put forward higher requirements for its flight stability and control accuracy. Researchers have proposed a variety of control strategies to address these uncertainties and external disturbances problems. Among them, the sliding mode controller (SMC) is favored for its excellent robustness to unknown system dynamics and relatively fast response time. Robustness in control systems refers to the ability of the system to maintain its performance stability in the face of external disturbances or internal parameter changes. Specifically, robustness means that the control system has the characteristic of maintaining certain performance under certain (structural, size) parameter perturbations. If the switching gain of the SMC is chosen to be large enough to exceed the upper bound of the uncertainty or unmodeled term, robust stabilization can theoretically be achieved. The'switching gain' here refers to the strength of the control signal switching near the sliding mode surface. However, in practice, the upper bound of the uncertainty term is usually unknown. Therefore, in order to cope with the wide range of uncertainties, the switching gain is chosen to be sufficiently large, which results in strong robustness but may also cause jittering of the system, limiting its performance in practical applications [6]. [PERSON] et al. [7] used a backstepping SMC combined with adaptive control theory to attenuate the effects of uncertainty. [PERSON] et al. [8] used an adaptive law to predict the upper bound of uncertainty, used fast terminal SMC to control the attitude system, and achieved better control than the traditional SMC. [PERSON] et al. [9] designed a fractional-order sliding mode controller by introducing fractional-order calculus to provide robustness, high-performance control, and finite-time convergence under uncertainty and external disturbances. In addition, the active disturbance rejection controller (ADRC) technique has a simple structure and strong control performance, and it does not require an accurate mathematical model for nonlinear, strongly coupled quadrotor systems [10,11], which improves the system by estimating and compensating for disturbances in the system [12]. In [13], an ADRC is applied to the control of an airship model, where they used an extended state observer (ESO) to estimate model uncertainties and external perturbations, compensated for dynamic feedback in real time, and demonstrated its immunity to perturbations using simulation experiments. [PERSON] et al. [14] used a backstepping sliding mode controller with ab ADRC to achieve better immunity, and [PERSON] et al. [15] added an observer to the control system structure of the SMC to achieve certain immunity. Existing controllers have been improved on the basis of the SMC with certain anti-interference capabilities, but the controller output still has the disadvantage of high-frequency oscillation, which puts high demands on the motor.