# Finite-Time Height Control of Quadrotor UAVs
## 1 Introduction  
Quadrotor UAVs have many advantages, including vertical takeoff and landing, low cost and flexibility [1; 2; 3]. Nowadays, there are many specific applications of quadrotor UAVs, such as rescue, surveillance, inspection, aerial photography, mapping and logistics [4; 5; 6]. Therefore, stable hovering, rapid maneuvering and safe operations are very important requirements for quadrotor UAVs in order to realize these functions [7]. However, the quadrotor UAV belongs to an open-loop unstable nonlinear system, which is underactuated and has strong coupling and vulnerability to external disturbances [8; 9]. Especially in the height control of the quadrotor UAV, there are not only disturbances, such as gust and aerodynamic drag, but also control challenges caused by load change and body vibration [10; 11]. Based on the terminal sliding mode, a novel control strategy is proposed to solve the position and attitude tracking problem of quadrotor UAVs under external disturbances and system uncertainties [10]. In [11], a cascade control method with an Active Disturbance Rejection Control (ADRC) algorithm [12] is designed to control the out-of-water motion of amphibious multirotor UAVs under complex external disturbances. Therefore, a robust height control strategy with anti-disturbance ability is of great significance for maintaining flight safety of quadrotor UAVs. For the height control problem of quadrotor UAVs, experts and scholars have developed SMC, PID control, optimal control and back-stepping control methods [13]. However, these methods are mainly based on the idea of passive anti-disturbance, and some methods even require accurate disturbance models, which creates difficulties in compensating for disturbances in practice [14]. The extended state observer (ESO) can estimate disturbanceswithout prior knowledge to actively compensate in the controller [15]. Therefore, the ESO has been increasingly used and developed in various fields of control [16; 17; 18]. Note that traditional SMC methods slow down the convergence speed of the system, and peak effects may occur in the large gain of traditional ESOs [19]. Compared to asymptotically stable control methods, finite-time control methods ensure that the system error tends to zero within a finite time [20; 21; 22]. Although the convergence time is related to the initial state, the finite-time method not only accelerates the convergence speed of the system but also alleviates the peak effect of the ESO, thereby achieving a real-time estimation ability for rapidly changing disturbances [23]. Recently, many other novel height controllers have been designed for multirotor UAVs, considering disturbances in different scenarios. A combined model reference adaptive control law is given for height control loop of a multirotor [24]. An adaptive nonsingular fast terminal SMC strategy is introduced to realize height control for quadrotors with variable mass and external disturbance [25]. Based on the back-stepping method, a fractional order sliding mode controller is proposed to attenuate wind disturbance and effects of variations in both loads and momentums of inertia [26]. In [27], a novel adaptive multilayer neural dynamic-based controller is used to control the height of a multirotor UAV. A multiple-model adaptive controller architecture is designed for height control of a quadrotor when transporting an unknown constant load [28]. It is known from [29] that a fault-tolerant control algorithm can control the altitude of quadrotor UAVs even in the presence of possible multiple actuator faults and modeling uncertainties. These height controllers have achieved satisfying results, but discussions about using ESOs to further improve control performance have been limited. In this paper, a dual closed-loop control method is designed to estimate and compensate for disturbances in the height control of quadrotor UAVs and improve the anti-disturbance ability.