## 1 Introduction  
The parafoil unmanned aerial vehicle (UAV) is a type of flexible aircraft. A conventional parafoil comprises a canopy, parachute, and payload, enabling it to carry out tasks such as airdrops and aircraft recovery. With the development of autonomous aircraft technology, powered parafoils appeared, incorporating thrust devices into the traditional parafoil design, thus enhancing their endurance capabilities [1]. Hence, powered parafoils possess the capability to execute precise tasks, such as stationary airdrops, and effective trajectory tracking control is paramount for mission success. Nevertheless, the challenges of trajectory tracking control encompass wind disturbances, underactuation, coupling, and unexpected dynamics. A mathematical model is necessary for analyzing the motion characteristics of a parafoil system given the limitations imposed by actual flight tests, which involve substantial preparation work, time, and expenses. Currently, there are numerous ways to express models of powered parafoils. From a dynamics standpoint, this includes three-degree-of-freedom (DOF) modeling [2], four-DOF modeling [3], six-DOF modeling [4], eight-DOF modeling [5], and nine-DOF modeling [6]. Among them, the eight-DOF model takes into account the slew, sway, have, pitch, and roll motions, as well as the relative pitch and relative yaw motion between the parafoil canopy and the payload, which effectively describe the motion state of the actual parafoil [7]. Trajectory tracking control of powered parafoils is a challenging task. The main difficulties arise from three aspects. Firstly, the actual model is more intricate than the constructed model, and there are unmodeled dynamics. Secondly, parafoil trajectory control is achieved by controlling the steering gear during flight, while altitude control is achieved through thrust, resulting in coupling and underactuation between these two control processes. Thirdly, during flight, the system is susceptible to wind disturbances, potentially leading to severe loss of control. Taking into account the issues mentioned above, research has been conducted. However, most of the literature only addresses the problem of path following [8; 9]. In our opinion, the main difference between implementing trajectory tracking and path following lies in the design of the guidance law. The guidance law plays a crucial role in expressing the tracking error in alternative forms and effectively addressing the challenges of underactuation. However, in path following control, the guidance law typically overlooks the consideration of forward tracking errors [10]. For example, [PERSON] et al. [11] formulated the guidance law as a sliding mode surface and employed linear extended state observer (LESO) to decouple horizontal path following and height tracking. Subsequently, they accomplished a three-dimensional path following control by utilizing sliding mode controllers (SMCs). Similarly, [PERSON] et al. [12] also utilized an SMC for path following control. [PERSON] et al. [13] utilized the barrier Lyapunov function and backstepping method, and developed an adaptive path-following controller. [PERSON] et al. [14] introduced a horizontal path following guidance law that utilized the lateral tracking error and yaw angle, enabling control of lateral tracking and the yaw angle through flap deflection. However, the study overlooked the parafoil's sideslip angle. There are very few research results on parafoil trajectory tracking control. [PERSON] et al. [15] transformed tracking errors into guidance commands for the yaw angle and glide slope angle and employed PID controllers to achieve trajectory tracking control. For a powered parafoil without forward thrust, we proposed a new guidance law and initially realized trajectory tracking control [16]. When selecting a controller, apart from the aforementioned SMCs and PID controllers, other control methods are available, such as LADRC. LADRC is a control method that has been developed based on PID.