Blown Yaw: A Novel Yaw Control Method for Tail-Sitter Aircraft by Deflected Propeller Wake During Vertical Take-Off and Landing

Highlights

What are the main findings?

• A novel “blown yaw” concept is introduced, enhancing yaw control using propeller-induced slipstream over aerodynamic rudders.
• An optimization-based control allocation method is designed to handle actuator redundancy and nonlinear actuator characteristics.

What is the implication of the main finding?

• The proposed method significantly improves yaw authority for large tail-sitter UAVs without sacrificing power efficiency.
• Simulations verify that the optimization-based control allocation method supports accurate and robust trajectory tracking under challenging flight conditions.

Abstract

In recent years, tail-sitter unmanned aerial vehicles (UAVs), capable of vertical take-off and landing (VTOL) and long-range flight, have garnered extensive attention. However, the challenge of yaw control, particularly for large-scale UAVs, has become a significant obstacle. It is challenging to generate sufficient yaw moments by motor differential thrust without compromising control authority in other channels or increasing mechanical complexity. Therefore, this paper proposes the concept of blown yaw, which utilizes the high-velocity airflow over rudders, induced by the propellers slipstream, to enhance the yaw control torque actively. An over-actuated, hundred-kilogram-class, tail-sitter UAV is designed to validate the effectiveness of the proposed method. To address the control allocation problem introduced by the implementation of blown yaw, an optimization-based control allocation module is developed, capable of precisely mapping the required forces and torques to all actuators. The proposed method, combined with computational fluid dynamics (CFD) simulations, accounts for the propeller model and the significant differences in actuator effectiveness across various flight conditions. Simulation results demonstrate that the proposed blown-yaw method significantly enhances the yaw control performance, achieving an overall energy savings of approximately 8.0% and a 60% reduction in the mean-squared error. Furthermore, the method exhibits robust performance against variations in control parameters and external disturbances.

1. Introduction

Due to many advanced features, such as low cost, simple structure, and good maintainability, unmanned aerial vehicles (UAVs) have attracted widespread attention from both academia and industry due to their immense potential application value [1,2,3]. Unfortunately, the inherent limitations of traditional UAVs restrict their applications in larger-scale scenarios. Multirotor UAVs possess excellent vertical maneuverability, enabling vertical take-off and landing (VTOL) as well as stationary hovering. However, they suffer from low flight efficiency and limited flight range, as the majority of the thrust generated by propellers is used to counteract gravity. Fixed-wing UAVs with superior aerodynamic characteristics rely on wing-generated lift to counteract gravity, resulting in an extended flight range and enhanced flight efficiency, but runways are required for take-off and landing, increasing the cost of constructing related infrastructure.

Therefore, to meet the requirements of the long flight range and VTOL, VTOL aircraft have received considerable attention, and various configurations of VTOL aircraft have been developed, which can primarily be categorized into the following types based on flight mode transition methods: tilt-rotor, compound-wing, and tail-sitter aircraft [4]. Tilt-rotor VTOL aircraft achieve forward propulsion during cruise flight by tilting a portion of the propellers (tilt-rotor) or by tilting both the wings and propellers (tilt-wing) to provide the necessary lift and thrust during cruise. However, the additional tilting mechanism increases the weight of the aircraft. Compound-wing aircraft incorporate both VTOL propellers and cruise flight propellers, but only one set operates during a given flight phase, resulting in unnecessary weight. In contrast, tail-sitter aircraft mount propellers on the wings to simplify the mechanical structure, eliminating the need for additional tilting mechanisms or redundant propulsion systems. Consequently, the vehicle weight and potential failure points are reduced [5].

A tail-sitter UAV named “The Eagle of Taihu” is designed in this paper, which integrates the advantages of VTOL, long flight range, and high cruise speed, establishing it as an exceptional aerial platform. The typical flight profile of this UAV is illustrated in Figure 1, including take-off, forward transition, cruise flight, backward transition, and landing. The aircraft achieves vertical take-off in rotorcraft mode, propelled by thrust from its propellers. Upon activation of the transition command, the aircraft pitches downward approximately 90 degrees to transition from vertical to cruise flight. Following completion of the forward transition, the UAV enters horizontal cruise flight mode, operating as a fixed-wing aircraft. During this phase, aerodynamic lift is provided by wings and the propellers generate thrust to counteract drag forces. For landing, the aircraft first performs the backward transition, pitching upward approximately 90 degrees to revert to rotorcraft mode, then descends vertically to the ground.

Yaw control for large-scale platforms with limited thrust-to-weight ratios remains a significant challenge, particularly when relying solely on motor differential thrust. While small UAVs can tolerate limited yaw torque due to their low moment of inertia, larger platforms suffer from sluggish yaw response as a result of increased inertia, mass distribution complexity, and insufficient motor-generated torque. This inefficiency compromises energy performance and accelerates the degradation of the battery and propulsion, increasing the risk of failure. To enhance yaw authority, a distributed electric propulsion (DEP) system is proposed in [6] to decouple yaw from flight speed control. However, the introduction of DEP inherently increases the weight and complexity, which may be impractical for large-scale vehicles. An alternative approach, adopted in [7,8,9,10], involves inclining motors along their diagonal axes at a fixed angle to increase the yaw-axis torque. Although effective in enhancing the yaw capability, this configuration sacrifices part of the available thrust needed to counteract gravity, which is undesirable for large tail-sitter UAVs with constrained power margins, and also introduces significant structural design challenges. More recently, advanced control strategies, such as reinforcement learning [11], backstepping [12], and fuzzy control [13], are employed to improve the yaw performance. Nevertheless, these methods often involve trade-offs, such as reduced control authority or degraded performance in other control channels. Consequently, achieving a precise yaw control through the motor differential thrust in large UAVs necessitates advanced control strategies to improve the responsiveness and stability in dynamic flight environments.

Blown lift is an aerodynamic concept where the airflow over the wings or other control surfaces of an aircraft is actively manipulated to increase the lift [14]. This effect is typically achieved by directing high-velocity air over the wing surface, frequently through leading-edge slats or trailing-edge flaps positioned along the wing. The injected air stream enhances the aerodynamic performance by augmenting the wing lift, enabling increased lift production at reduced airspeeds or elevated angles of attack. This method is particularly advantageous for short take-off and landing (STOL) aircraft and VTOL vehicles, enhancing their performance and operational flexibility [15]. However, the existing literature on blown aerodynamics largely focuses on lift augmentation or roll/pitch control in fixed configurations, with limited attention to yaw control [16]. Moreover, prior studies generally lack rigorous modeling of propeller–control surface interactions, particularly the coupling between slipstream flow and rudder effectiveness. Therefore, inspired by the concept of blown lift, this paper proposes and experimentally validates a blown-yaw control strategy, where the propeller slipstream is directed over rudders to generate substantial yaw moments. This approach directly addresses the limitation of yaw control for large tail-sitter UAVs by harnessing aerodynamic enhancement to boost the yaw performance without significantly increasing the mechanical complexity or power demand. However, practical deployment in large UAVs introduces complex, over-actuated, nonlinear control allocation challenges, particularly when multiple rudders operate within the propeller slipstream across different flight modes.

The pseudoinverse method, as one of the most commonly used control allocation approaches, maps the desired forces and moments to actuator commands by computing the pseudoinverse of the control allocation matrix [17,18]. However, the issue of actuator saturation inherent in pseudoinverse methods often results in poor control performance or even loss of control [19]. To address this issue, a cascaded inverse control allocation method is proposed by Marks et al. [20], which ensures controller commands are allocated to actuators without inducing saturation. Based on the zero-space pseudoinverse of the control matrix (PAN), Tohidi et al. introduce an adaptive control allocation approach [21], which is then applied in fault-tolerant control scenarios [22]. The null space transfer method is utilized to search for minimum-energy control inputs for actuators by Xu et al. [23]. In [24], a novel pseudoinverse-based control allocation algorithm is presented, which utilizes the null space transfer method to resolve global constraints. Although these approaches can prevent actuator saturation, they do not account for the significant variations in the actuator efficiency of VTOL UAVs under different flight conditions, leaving a gap in real-world applicability. Daisy-chaining is another approach for handling control allocation by dividing actuators into two groups and defining a priority sequence [25]. A daisy-chaining control allocation strategy for tilt-rotor VTOL aircraft, which involves the primary generation of torque by control surfaces, with the rotors taking over for the remaining torque upon saturation, is proposed by Spannagl et al. [26,27]. While this approach considers actuator prioritization, it still relies on idealized actuator models and does not fully capture nonlinearities or variations due to changing flight conditions. For tail-sitter UAVs, the actuator efficiency under different flight conditions has been partially addressed by introducing the flight speed into the allocation strategy [7,8,9], where rotors dominate in hover mode, and control surfaces dominate in fixed-wing cruise mode. However, these studies generally assume an ideal propeller model. Although [28] considers the nonlinear relationship between propeller-generated force and torque, it neglects the influence of the incoming flow velocity on thrust and torque. To sum up, although considerable progress has been made in control allocation methods, existing approaches generally exhibit two major limitations. First, many methods assume idealized actuator behavior and fail to fully account for actuator nonlinearities, such as the nonlinear relationship between motor speed and thrust/torque, or efficiency variations across different flight conditions. Second, the influence of inflow velocity on propeller-generated forces and torques is frequently neglected, leading to inaccuracies under different flight conditions. These gaps underscore the need for more realistic modeling and advanced control allocation strategies tailored to large-scale tail-sitter UAVs.

In conclusion, despite extensive research on various UAV platforms, challenges still persist. The primary difficulty lies in the fact that platforms with limited thrust-to-weight ratios cannot rely solely on motor differential thrust to generate sufficient yaw moments without compromising control authority in other channels or increasing mechanical complexity. Additionally, considering the number of actuators and the drastic changes in their efficiency across different flight states, it is challenging to map the control forces and torques to all actuators accurately. Therefore, the purpose of this study is to propose a method to improve the yaw control capability of the tail-sitter UAVs. Meanwhile, significant variations in actuator effectiveness must be considered in various flight conditions. The contributions of this article are as follows:

• The blown yaw concept is proposed to address and scale the challenge of insufficient yaw control authority in large-scale tail-sitter UAVs. To validate this approach, a hundred-kilogram-class tail-sitter UAV equipped with 12 actuators is designed. The interaction between the propeller slipstream and the control surfaces is rigorously modeled using high-fidelity CFD simulations, accurately capturing the slipstream velocity field and the resulting forces on the rudders, thereby providing a solid foundation for evaluating the effectiveness of the proposed method.
• An optimization-based control allocation framework is employed to address the control allocation challenges associated with implementing a blown yaw. The proposed framework not only accurately maps the required control forces and torques to the actuators but also accounts for the actual physical model of the actuators and their varying execution efficiencies. This module is integrated into a comprehensive control system, including a cascaded PID position controller and an Active Disturbance Rejection Control (ADRC) attitude controller, to track the specified trajectory.
• A series of simulation experiments is conducted to demonstrate the effectiveness of the blown yaw as well as the robustness of the complete control system, such as aggressive trajectory tracking under noise and wind disturbances.

The subsequent sections of this paper are organized as follows: Section 2 presents the platform for blown yaw and related dynamic analysis. Section 3 introduces the tail-sitter UAV control allocation model and optimization strategies, followed by relevant simulation experiments in Section 4. Lastly, Section 5 presents the key conclusions.

2. Platform for Blown Yaw and Dynamic Analysis

In this section, the design of the tail-sitter UAV is introduced, followed by the dynamic modeling. For clarity, the designed vehicle and the relevant coordinate systems are explained in Section 2.1. Subsequently, the detailed model for the propeller is established in Section 2.2, followed by the development of the tail-sitter UAV dynamic model in Section 2.3.

2.1. Aircraft Introduction and Frame Definition

While the inclined installation of motors can enhance yaw control authority, it also imposes greater mechanical stress on the airframe, potentially accelerating structural fatigue and diminishing the long-term reliability of the UAV. Consequently, this approach presents significant challenges in the structural design of large-scale tail-sitter UAVs. Additionally, the inclined motors lead to a reduction in power output, consequently diminishing the thrust-weight ratio of the vehicle and adversely affecting the flight efficiency. A logical approach to address this issue is to utilize higher-power motors to enhance the yaw control capability. However, larger motors, while capable of providing more thrust, come with increased weight and power consumption. This added weight can lead to slower response times and less precise control due to the increased inertia of larger motors, which is not a feasible solution.

Drawing inspiration from the principle of blown lift, the concept of blown yaw has been proposed to enhance the yaw control capabilities of tail-sitter UAVs. Blown lift leverages high-velocity airflow generated by propellers to improve lift efficiency, a technique that has proven beneficial in various aircraft designs. Similarly, blown yaw aims to utilize the high-velocity airflow induced by the propeller slipstream over rudders to actively enhance yaw control torque. This innovative approach allows for more precise and effective control of yaw movements, particularly during VTOL operations, where maneuverability is critical. Therefore, the realization of blown yaw in this work is achieved through a unique structural layout, as shown in Figure 1. The four rudders, mounted on pylons, are strategically placed in the slipstream of the propellers. The increased airflow speed over the rudder surfaces within the propeller slipstream zones significantly enhances the control efficiency of the rudders in rotor mode. Consequently, the deflection of the rudders substantially improves the yaw control capability of the tail-sitter UAV. In the rotor mode, the necessary control torque is provided by both the motor differential speed and the rudder deflection. Yaw torque is produced by deflecting rudders 1 and 3 in one direction and rudders 2 and 4 in the opposite direction. This methodology potentially enhances the operational performance of large-scale, over-actuated UAVs. By maximizing the efficiency of yaw control through blown yaw, UAVs can achieve better agility and control in complex flight environments, ultimately leading to more successful mission outcomes. Moreover, the designed tail-sitter adopts a canard layout, comprising a main fuselage, a pair of wings, four symmetrically arranged pylons, and two canards. The wings employ a Liebeck airfoil and are equipped with segmented trailing edges. Winglets are installed at the rear of the wings. Pylons symmetrically mounted on the upper and lower surfaces of the wings support the power nacelles. Each power nacelle houses a complete propulsion system, including a rotor, an Electronic Speed Controller (ESC), and a propeller. The bottom of each nacelle is equipped with landing gears. The Liebeck airfoil is also utilized for the canard. The inherent redundancy not only enhances robustness against uncertainties and external disturbances but also improves fault tolerance by allowing for flexible redistribution of control demands among multiple actuators in the event of a partial failure. The overall parameters of the discussed tail-sitter UAV are summarized in

Table 1. Physical parameters of the aircraft.

Parameter	Symbol	Value (Unit)
Mass	m	101.4 kg
Inertia about x-axis	$I_{xx}$	76.872 kg·m2
Inertia about y-axis	$I_{yy}$	82.305 kg·m2
Inertia about z-axis	$I_{zz}$	128.773 kg·m2
Wingspan	b	4.674 m
Chord length	$\overline{c}$	0.6381 m
Main wing surface area	$S_w$	3.2323 m2
Length and width	$[l_1,l_2]$	[2.5, 1.5] m

.

For the purpose of facilitating the modeling of the flight dynamics and the design of the control system, the coordinate systems mentioned in this paper are defined as follows: the local east–north–up (ENU) coordinate system is considered as the inertial frame during the whole flight envelope. The body frame used in this paper is shown in Figure 1, where the rotation along the $x_b,y_b\mathrm{and}{z}_b$ are defined as roll, pitch, and yaw in the rotor mode. While the proposed control allocation method is developed for yaw control in the rotor mode of large tail-sitter UAVs, it is also applicable during the fixed-wing phase to strengthen control authority about the $x_b$ and $z_b$ axes.

2.2. Propeller Model

The propeller plays a crucial role throughout the entire flight process of the tail-sitter UAV. However, in most research on propeller-driven aircrafts, it is commonly assumed that the magnitude of the force and torque generated by the propeller depends solely on the rotation speed of the propeller, i.e.,

$$\begin{array}{cccc}& & \hfill \begin{array}{c}\hfill T=C_f{n}^2,M=C_m{n}^2,\end{array}& \end{array}$$

(1)

where n is the rotation speed of the propeller, and $C_f$ and $C_m$ denote the thrust and torque coefficients of the propeller. Due to the mild flight speeds of conventional rotor craft, the inflow velocity has little effect on the propeller, allowing for approximating the relationship between the forces and torques generated by the propeller as linear. Moreover, due to the simple structure of rotor craft, a modeling error can usually be compensated for through robust controllers and redundant power systems.

However, during the full-flight process of the tail-sitter UAV, the aircraft switches between the low-speed rotor mode, the complex transition phase, and the high-speed fixed-wing mode. As a result, the inflow velocity experienced by the propeller undergoes a wide range of variations. Many studies have revealed that the force and torque generated by the propeller decrease significantly with increasing inflow velocity and exhibit strong non-linearity [29,30]. Consequently, the aforementioned model is no longer applicable to the full-flight process of the tail-sitter UAV.

Accordingly, the aerodynamic forces and torques generated by the propeller can be modeled as functions of the inflow velocity and rotation speed. For the given vehicle configuration, a specific propulsion system has been selected, with propeller characteristics described by a polynomial approximation, mapping the advance ratio and rotational speed to the corresponding thrust and torque coefficients.

$$\begin{array}{cccc}& & \hfill \begin{array}{cc}\hfill C_f& =f_{C_f}(J,n)\hfill \\ & =f_{00}+f_{01}n+f_{02}{n}^2+f_{10}J+f_{11}Jn+f_{20}{J}^2,\hfill \\ \hfill C_m& =f_{C_m}(J,n)\hfill \\ & =m_{00}+m_{01}n+m_{02}{n}^2+m_{10}J+m_{11}Jn+m_{20}{J}^2,\hfill \end{array}& \end{array}$$

(2)

where $J={\displaystyle \frac{∥\mathbf{V}∥}{nD}}$, $∥\mathbf{V}∥$ refers to the magnitude of inflow velocity, D refers to the diameter of the propeller, and $n_i$ refers to the rotation speed. $f_{00}\sim f_{20}$ and $m_{00}\sim m_{20}$ are both characteristic parameters of the propeller, whose estimated values can be obtained by fitting the original data points simulated in the CFD software (Available online: https://www.simscale.com/product/cfd/, accessed on 8 September 2025) using the least squares method. The fitting results are illustrated in Figure 2.

Equation (2), with $R^2>0.99$, accurately models the thrust and torque coefficients of the propeller across different rotation speeds and advance ratios, as shown in Figure 2. The polynomial representation provides a detailed understanding of force and torque behavior over various flight conditions, enabling optimal aircraft control. Furthermore, as the advance ratio increases, both coefficients demonstrate a notable decrease, even reaching negative values. This phenomenon is primarily due to the major section of the propeller airfoil experiencing negative angles of attack at high inflow velocity, resembling aerodynamic drag. Therefore, the combination of rotation speed and advance ratio produces thrust, torque, and power:

$$\begin{array}{cccc}& & \hfill \begin{array}{c}\hfill F_T=C_f\rho D^4{n}^2,M_T=C_m\rho D^5{n}^2,P=M_{T}n,\end{array}& \end{array}$$

(3)

where $\rho$ is the air density.

Generally, the induced velocity of the propeller is estimated from the momentum theory [31] as follows:

$$\begin{array}{cccc}& & \hfill \begin{array}{c}\hfill v_{in}={\displaystyle \frac{1}{2}}\left(-w+\sqrt{w^2+{\displaystyle \frac{2F_T}{\rho A}}}\right),\end{array}& \end{array}$$

(4)

where A is the propeller disk area, and w denotes the inflow velocity.

Although Equation (4) models the induced velocity of the propellers as a function of inflow velocity and rotation speed, it is evident from Figure 3 that the slipstream velocity varies spatially within the flow field. Specifically, the velocity in the slipstream decreases progressively with increasing distance from the propeller, highlighting the non-uniform nature of the induced flow. Since the rudder is positioned 0.5 m behind the propeller, the previous model fails to describe the airflow velocity over the rudder accurately. To address this, CFD simulations were conducted under 18 different flight conditions, varying the propeller speed from 1500 to 4000 RPM and the inflow speed from 0 to 5 m/s. A multilayer perceptron (MLP) model is then used to fit the slipstream velocity, i.e.,

$$\begin{array}{cccc}& & \hfill \begin{array}{c}\hfill v_{in}=f\left(w,n,p\right),\end{array}& \end{array}$$

(5)

where p denotes the position on the propeller disk. It should be noted that, although the $R^2$ value in the above equation exceeds 0.99 on the test set, the slipstream is still influenced by the pylon and becomes highly complex. Therefore, our focus is on characterizing the characteristics of the airflow velocity over the rudder surface as affected by its position, rather than on constructing a perfect model.

In summary, the analysis of propeller characteristics demonstrates that both linear approximations and momentum-theory-based estimates of induced velocity are insufficient to fully capture the complex propeller characteristics across the full-flight process. Employing fitting-based methods provides a more comprehensive and reliable means of modeling these nonlinear effects.

2.3. Dynamic Model of the Tail-Sitter

Ignoring the effects of earth curvature and rotation, we can establish the dynamics model of the tail-sitter UAV by applying Newton’s second law to a rigid body as follows:

$$\left\{\begin{array}{c}{\dot{\mathbf{p}}}_e=\mathbf{R}{\mathbf{v}}_b\hfill \\ m{\dot{\mathbf{v}}}_e=\mathbf{R}{\mathbf{F}}_b\hfill \\ \dot{\mathbf{R}}=\mathbf{R}{\left({\mathit{\omega }}_b\right)}^{\times }\hfill \\ \mathbf{J}{\dot{\mathit{\omega }}}_b={\mathbf{M}}_b-{\mathit{\omega }}_b\times \left(\mathbf{J}{\mathit{\omega }}_b\right)\hfill \end{array},\right.$$

(6)

where ${\mathbf{p}}_e$ refers to the position in the inertial coordinate system. ${\mathbf{v}}_b={\left[u,v,w\right]}^T$ and ${\mathit{\omega }}_b$ refer to the velocity and angular velocity in the body coordinate system, respectively. $\mathbf{R}$ is the rotation matrix from the body coordinate system to the inertial coordinate system with the rotation order of Z-Y-X. ${\mathbf{F}}_b={\mathbf{F}}_g+{\mathbf{F}}_t+{\mathbf{F}}_a$, the external force acting on the center of mass (CM) in the body coordinate system, is the sum of gravity, thrusts, and aerodynamic forces. Similarly, ${\mathbf{M}}_b={\mathbf{M}}_t+{\mathbf{M}}_a$, the external torque acting at CM of the tail-sitter UAV in the body coordinate system, is the sum of the torques generated by the actuators and the aerodynamic torques, where ${\mathbf{M}}_a$, with the rudder effects taken into account, can be modeled with Equation (7) [32,33]:

$$\begin{array}{cc}\hfill {\mathbf{M}}_a=\left[\begin{array}{c}{\mathbf{M}}_l+{\mathbf{M}}_{\delta ,\mathrm{roll}}\\ {\mathbf{M}}_m+{\mathbf{M}}_{\delta ,\mathrm{pitch}}\\ {\mathbf{M}}_n+{\mathbf{M}}_{\delta ,\mathrm{yaw}}\end{array}\right]& =\left[\begin{array}{c}{\displaystyle \frac{1}{2}}\rho {∥{\mathbf{V}}_{\mathrm{unwashed}}∥}^2{S}_{w}b{C}_{\mathrm{roll}}+\sum _{i=1}^4\left({\displaystyle \frac{1}{2}}\rho {∥{\mathbf{V}}_{\mathrm{i},\mathrm{washed}}∥}^2{S}_{r}b{C}_{\mathrm{roll}}^{{\delta }_r}{\delta }_{r_i}\right)\\ {\displaystyle \frac{1}{2}}\rho {∥{\mathbf{V}}_{\mathrm{unwashed}}∥}^2{S}_w\overline{c}{C}_{\mathrm{pitch}}\\ {\displaystyle \frac{1}{2}}\rho {∥{\mathbf{V}}_{\mathrm{unwashed}}∥}^2{S}_{w}b{C}_{\mathrm{yaw}}+\sum _{i=1}^4\left({\displaystyle \frac{1}{2}}\rho {∥{\mathbf{V}}_{\mathrm{i},\mathrm{washed}}∥}^2{S}_{r}b{C}_{\mathrm{yaw}}^{{\delta }_r}{\delta }_{r_i}\right)\end{array}\right].\hfill \end{array}$$

(7)

The subscripts “washed” and “unwashed” denote whether the propeller-induced slipstream augments the local velocity. $S_w$ and $S_r$ denote the area of wing and rudder, b refers to the wingspan of the tail-sitter UAV, and $\overline{c}$ denotes the mean aerodynamic chord length. $C_{\mathrm{roll}}$, $C_{\mathrm{pitch}}$, and $C_{\mathrm{yaw}}$ represent the coefficients of rolling, pitching, and yawing torques, respectively. The effectiveness of the rudder is denoted by $C_{\mathrm{yaw}}^{{\delta }_{r_i}}$ and $C_{\mathrm{roll}}^{{\delta }_{r_i}}$, respectively. These coefficients are obtained through CFD simulations. ${\mathbf{V}}_{\mathrm{unwashed}}=\left[u,w\right]$, ${\mathbf{V}}_{\mathrm{washed}}=\left[u,w+v_{in}\right]$.

3. Control Framework

After developing the platform, this section proceeds to address the control problem introduced by implementing blown yaw. Section 3.1 provides an overview of the control system, followed by a detailed introduction to the design of the optimization-based control allocation algorithm in Section 3.3.

3.1. Overview of Control Structure

The complete control system, comprising trajectory planning, a position controller, an attitude controller, control allocation, and the dynamic model of the tail-sitter UAV, is illustrated in Figure 4. Initially, the trajectory planner generates a smoothed trajectory with associated timestamps. The cascaded PID position controller then utilizes the desired trajectory and sensor data to calculate the desired thrust $u_1$, as well as the desired attitudes ${\varphi }_{\mathrm{des}}$ and ${\theta }_{\mathrm{des}}$ [34,35].

Subsequently, the attitude controller introduced in Section 3.2 takes the desired attitude from both the trajectory and position controllers, integrating it with actual attitude feedback from sensors to compute the attitude-related control commands.

Next, the control allocation module maps the desired thrust and control torques to the actuators, which will be discussed in Section 3.3. Finally, the rotation speeds of the four motors and the deflection angles of the control surfaces are fed into the tail-sitter UAV model to generate the required control forces and torques, enabling the vehicle to track the desired trajectory effectively.

3.2. Attitude Control

Given the large windward area, the tail-sitter UAV is particularly susceptible to wind disturbances in rotor mode. Therefore, a robust attitude controller is essential for enhancing trajectory-tracking performance. The ADRC technique is employed for attitude control due to its strong disturbance rejection capabilities, high control precision, and rapid tracking speed [36,37]. The block diagram of ADRC, consisting of a tracking differentiator (TD), nonlinear law of state error feedback (NLSEF), and extended state observer (ESO), is shown in Figure 4.

3.2.1. Tracking Differentiator

The tracking differentiator facilitates a smooth transition process, generating both the tracking signal and its derivative, thereby serving as a filter and reducing initial errors. It is formulated as follows:

$$\left\{\begin{array}{c}fh\left(k\right)=f_{\mathrm{TD}}(x_1\left(k\right)-\nu \left(k\right),x_2\left(k\right),r_0,h_0)\hfill \\ x_1(k+1)=x_1\left(k\right)+h{x}_2\left(k\right)\hfill \\ x_2(k+1)=x_2\left(k\right)+hfh\left(k\right)\hfill \end{array}\right.,$$

(8)

where $x_1$ refers to the tracking signal for the input signal $\nu$, $x_2$ is the differential signal of $x_1$, h denotes the step size, $r_0$ represents the tracking velocity factor, and $h_0$ stands for the filtering factor. $f_{\mathrm{TD}}$ is formulated as follows:

$$\left\{\begin{array}{c}d=r_0{h}_0^2\hfill \\ a_0=h_0{x}_2\hfill \\ y=x_1+a_0\hfill \\ a_1=\sqrt{d(d+8|y\left|\right)}\hfill \\ a_2=a_0+{\displaystyle \frac{sign\left(y\right)(a_1-d)}{2}}\hfill \\ s_y={\displaystyle \frac{sign(y+d)-sign(y-d)}{2}}\hfill \\ a=(a_0+y-a_2)s_y+a_2\hfill \\ s_a={\displaystyle \frac{sign(a+d)-sign(a-d)}{2}}\hfill \\ f_{\mathrm{TD}}=-r_0\left({\displaystyle \frac{a}{d}}-sign\left(a\right)\right)s_a-r_{0}sign\left(a\right)\hfill \end{array}\right..$$

(9)

3.2.2. Nonlinear Law of State Error Feedback

The nonlinear law of state error feedback adopts the concept of error elimination to construct a nonlinear error feedback control law, integrating the output of TD and the error between system states, which is more suitable for nonlinear systems. The NLSEF can be expressed as follows:

$$\left\{\begin{array}{c}{u}_0={\beta }_1{f}_{\mathrm{NL}}(e_1,a_1,\delta )+{\beta }_2{f}_{\mathrm{NL}}(e_2,a_2,\delta )\hfill \\ f_{\mathrm{NL}}(x,a,\delta )=\left\{\begin{array}{cc}{\displaystyle \frac{x}{{\delta }^{1-a}}},\hfill & \mathrm{if}\left|x\right|\le \delta \hfill \\ {sign\left(x\right)\left|x\right|}^a,\hfill & \mathrm{if}\left|x\right|>\delta \hfill \end{array}\right.\hfill \end{array}\right.,$$

(10)

where ${\beta }_1$ and ${\beta }_2$ are parameters used to adjust the NLSEF, e is the tracking error, $\alpha \in (0,1)$ is the nonlinear gain exponent, and $\delta >0$ defines the linear region threshold.

3.2.3. Extended State Observer

ESO, capable of simultaneously estimating internal disturbances and external unknown disturbances and providing compensation in feedback to eliminate the influence of disturbances, is the core of the entire ADRC. The algorithm is shown below:

$$\left\{\begin{array}{c}{\epsilon }_1=z_1-y\hfill \\ {\dot{z}}_1=z_2-{\beta }_{01}{\epsilon }_1\hfill \\ {\dot{z}}_2=z_3-{\beta }_{02}{f}_{\mathrm{NL}}\left({\epsilon }_1,{\displaystyle \frac{1}{2}},\delta \right)+b_{0}u\hfill \\ {\dot{z}}_3=-{\beta }_{03}{f}_{\mathrm{NL}}\left({\epsilon }_2,{\displaystyle \frac{1}{4}},\delta \right)\hfill \end{array}\right.,$$

(11)

where ${\beta }_{01},{\beta }_{01}$, and ${\beta }_{03}$ are parameters used to adjust the ESO.

3.3. Control Allocation

Unlike conventional approaches to control allocation in rotorcraft, this work emphasizes the coordinated use of four motors and four rudders to generate the required control forces and torques. In our framework, the forces and moments produced by the propellers are modeled as nonlinear functions of rotor speed and inflow velocity. This nonlinear representation complicates the control allocation problem, rendering traditional pseudoinverse methods less applicable. Furthermore, the redundancy in actuation facilitates the generation of required control forces and moments while also providing the flexibility to pursue secondary objectives, such as energy efficiency or actuator load balancing. Therefore, an optimization-based approach will be employed to address the control allocation challenges introduced by blown yaw in this section.

3.3.1. Design of the Cost Function

As outlined in the control structure overview detailed in Section 3.1, the actuators receive commands $\mathbf{n}=\left[n_1,n_2,n_3,n_4\right]$ and $\mathit{\delta }=\left[{\delta }_{r_1},{\delta }_{r_2},{\delta }_{r_3},{\delta }_{r_4}\right]$ from the control allocation module, which are then combined to produce the achieved thrust and torques ${\mathbf{u}}_{\mathrm{now}}={\left[u_1,u_2,u_3,u_4\right]}^{\mathrm{T}}$. Therefore, ${\mathbf{u}}_{\mathrm{now}}$ can be represented by $\mathit{\delta }$ and $\mathbf{n}$ as follows:

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill \left\{\begin{array}{c}{u}_1=F_{T_1}+F_{T_2}+F_{T_3}+F_{T_4}\hfill \\ u_2=M_x={\displaystyle \frac{l_1}{2}}\left(-F_{T_1}+F_{T_2}+F_{T_3}-F_{T_4}\right)+M_{\delta ,\mathrm{roll}}\hfill \\ u_3=M_y={\displaystyle \frac{l_2}{2}}\left(-F_{T_1}+F_{T_2}-F_{T_3}+F_{T_4}\right)\hfill \\ u_4=M_z=-M_{T_1}-M_{T_2}+M_{T_3}+M_{T_4}+M_{\delta ,\mathrm{yaw}}\hfill \end{array}\right..\end{array}& \end{array}$$

(12)

Assuming ${\mathbf{u}}_{\mathrm{des}}={\left[F_{\mathrm{des}},M_{\mathrm{roll}},M_{\mathrm{pitch}},M_{\mathrm{yaw}}\right]}^{\mathrm{T}}$ represents the desired control thrust and torques conveyed to the control allocation module. To achieve precise trajectory tracking, the actuator commands generated from the control allocation module should minimize the deviation between ${\mathbf{u}}_{\mathrm{now}}$ and ${\mathbf{u}}_{\mathrm{des}}$. Consequently, the first term of the cost function can be formulated as follows:

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill {\mathbf{J}}_{\mathrm{u}}={\mathbf{K}}_{\mathrm{u}}{∥{\mathbf{u}}_{\mathrm{des}}-{\mathbf{u}}_{\mathrm{now}}∥}^2.\end{array}& \end{array}$$

(13)

It is worth mentioning that the primary optimization effort of the control allocation module goes toward minimizing the difference between desired and achieved thrust/torques. Therefore, the elements of the weighting matrix ${\mathbf{K}}_{\mathrm{u}}={\mathbf{I}}_{4\times 4}$ are much larger than others.

Furthermore, for the over-actuated tail-sitter UAV studied in this paper, there are non-unique solutions for allocating the actuators to achieve the desired control thrust and torques. However, both the motors and servo motors experience inherent mechanical and electrical delays, which limit their ability to track rapidly changing control commands. Allowing unrestricted selection among these solutions may result in erratic control commands that the actual actuators struggle to follow. Therefore, to prevent sudden changes in motor speeds or abrupt deflections of the rudders, the second term of the cost function should be designed to impose strict constraints on the rate of change of control commands outputted by the control allocation module.

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill {\mathbf{J}}_{\mathrm{c}}={\mathbf{K}}_n{∥{\mathbf{n}}_{\mathrm{now}}-{\mathbf{n}}_{\mathrm{last}}∥}^2+{\mathbf{K}}_{\delta }{∥{\delta }_{\mathrm{now}}-{\delta }_{\mathrm{last}}∥}^2.\end{array}& \end{array}$$

(14)

It should be noted that, compared to motors, servo motors exhibit faster response speeds and lower energy costs. Additionally, considering that motor variations within smaller ranges are more conducive to maintaining their operational performance, greater penalties should be imposed on motor variations. This will be reflected in the weighting matrices ${\mathbf{K}}_n=1\times {10}^{-3}{\mathbf{I}}_{4\times 4}$ and ${\mathbf{K}}_{\delta }=1\times {10}^{-6}{\mathbf{I}}_{4\times 4}$.

Additionally, different actuators exhibit distinct operating ranges that must be considered in control allocation. For instance, the rotation speed of the motor used in this study varies from 0 RPM to 4000 RPM, whereas the deflection angle of the servo motor ranges from −30 to 30 degrees. Notably, the torque generated by a change of 1 RPM in motor speed is significantly smaller than the torque produced by a 1-degree deflection of the rudder. However, this observation does not imply that the maximum torque generated by varying motor speed is less than that produced via rudder deflection. The overall effectiveness of each actuator can vary depending on the specific operating conditions and configurations.

To facilitate accurate comparisons and characterizations of actuator performance, it is essential to normalize their operating ranges into a unified scale. This normalization process allows for a more coherent assessment of each actuator’s contributions, ensuring that the control allocation module can effectively utilize the capabilities of each actuator while considering their unique characteristics.

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill \left\{\begin{array}{c}\overline{\mathbf{n}}={\mathbf{W}}_n\mathbf{n},{\mathbf{W}}_n=\mathrm{diag}\left({\displaystyle \frac{1}{n_{max}}}\right)\hfill \\ \overline{\mathit{\delta }}={\mathbf{W}}_{\delta }\mathit{\delta },{\mathbf{W}}_{\delta }=\mathrm{diag}\left({\displaystyle \frac{1}{{\delta }_{max}}}\right)\hfill \end{array}\right..\end{array}& \end{array}$$

(15)

Although the eight actuators can generate sufficient force and torque, improper planning may lead to unexpected energy loss. It is well known that the control torque generated by the rudder is aerodynamically driven, resulting in lower required power and higher efficiency. Therefore, from an energy conservation perspective, it is preferable to generate a control torque through rudder deflection rather than motor differential thrust, which is achieved by imposing a higher penalty on the use of motor differential speed. Furthermore, ${∥{\mathbf{V}}_b∥}^2$ is introduced to reflect the efficiency of the rudder under different flight conditions. At lower flight speeds, the rudder and motor differential speed jointly generate the required torques. At higher flight speeds, the required torque in the yaw is primarily generated by the rudder.

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill {\mathbf{J}}_{\mathrm{W}}=& {\mathbf{K}}_{{\mathrm{W}}_n}{∥{\mathrm{W}}_n\left({\mathbf{n}}_{\mathrm{now}}-{\mathbf{n}}_{\mathrm{ideal}}\right)∥}^2+{\mathbf{K}}_{{\mathrm{W}}_{\delta }}{∥{\mathbf{W}}_{\delta }\left({\mathit{\delta }}_{\mathrm{now}}-{\mathit{\delta }}_{\mathrm{ideal}}\right)∥}^2,\hfill \end{array}\end{array}$$

(16)

where ${\mathbf{K}}_{{\mathrm{W}}_n}=1\times {10}^{-5}{∥{\mathbf{V}}_b∥}^2{\mathbf{I}}_{4\times 4}$, ${\mathbf{K}}_{{\mathrm{W}}_{\delta }}=3\times {10}^{-7}{\mathbf{I}}_{4\times 4}$, ${\mathbf{n}}_{\mathrm{ideal}}$ and ${\mathit{\delta }}_{\mathrm{ideal}}$ are the actuator setpoint configuration where no energy is used.

3.3.2. Optimization-Based Control Allocation Algorithm

This article not only investigates the nonlinear relationship between propeller thrust and torque but also accounts for the impact of inflow velocity on propeller efficiency. Furthermore, the aerodynamic effects on the rudder are modeled, further complicating the control allocation problem. If the eight commands to the actuators are directly regarded as optimization variables, the optimization problem can be formulated as follows:

$$\begin{array}{cc}\hfill \underset{{\mathbf{n}}_{\mathrm{now}},{\mathit{\delta }}_{\mathrm{now}}}{min}& {\mathbf{K}}_u\parallel {\mathbf{u}}_{\mathrm{des}}-{\mathbf{u}}_{\mathrm{now}}{\parallel }^2+{\mathbf{K}}_n\parallel {\mathbf{n}}_{\mathrm{now}}-{\mathbf{n}}_{\mathrm{last}}{\parallel }^2+{\mathbf{K}}_{\delta }{\parallel {\mathit{\delta }}_{\mathrm{now}}-{\mathit{\delta }}_{\mathrm{last}}\parallel }^2\hfill \\ \hfill & +{\mathbf{K}}_{{\mathbf{W}}_n}\parallel {\mathbf{W}}_n({\mathbf{n}}_{\mathrm{now}}-{\mathbf{n}}_{\mathrm{ideal}}){\parallel }^2+{\mathbf{K}}_{{\mathbf{W}}_{\delta }}{\parallel {\mathbf{W}}_{\delta }({\mathit{\delta }}_{\mathrm{now}}-{\mathit{\delta }}_{\mathrm{ideal}})\parallel }^2,\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& \left\{\begin{array}{c}{\mathbf{n}}_{\mathrm{now}}\in \left[{\mathbf{n}}_{min},{\mathbf{n}}_{max}\right],\hfill \\ {\mathit{\delta }}_{\mathrm{now}}\in \left[{\mathit{\delta }}_{min},{\mathit{\delta }}_{max}\right],\hfill \\ {\mathbf{n}}_{\mathrm{now}}-{\mathbf{n}}_{\mathrm{last}}\in \left[-{\dot{\mathbf{n}}}_{max},{\dot{\mathbf{n}}}_{max}\right]\Delta t,\hfill \\ {\mathit{\delta }}_{\mathrm{now}}-{\mathit{\delta }}_{\mathrm{last}}\in \left[-{\dot{\mathit{\delta }}}_{max},{\dot{\mathit{\delta }}}_{max}\right]\Delta t,\hfill \\ P_i\in \left[0,P_{i,max}\right],i=1,2,3,4.\hfill \end{array}\right.\hfill \end{array}$$

(17)

where ${\mathbf{n}}_{\mathrm{last}}$ and ${\mathit{\delta }}_{\mathrm{last}}$ refer to the actuator control commands obtained from the last control allocation optimization. Although the propulsion system is capable of providing power up to 13 kW, the maximum power is further restricted to 11 kW to protect the motor from sudden maneuvers.

It is somehow straightforward to recognize that the above cost function contains high-order terms of the variables to be optimized. While certain numerical optimization methods can effectively address such constrained optimization problems, it is necessary to consider that the attitude loop of the tail-sitter UAV typically operates at a frequency of 200 Hz. Given the high operating frequency, it remains challenging for numerical optimization methods to meet the real-time requirements of control allocation for tail-sitter UAVs. Furthermore, employing numerical optimization methods to solve high-order optimization problems frequently results in numerical instability, which can significantly impact the flight stability and safety of tail-sitter UAVs.

Fortunately, the most recent values of control variables can be dynamically acquired from sensors in real-time. This enables the adoption of a nonlinear iterative optimization algorithm to determine actuator control commands at each control step. Specifically, the optimization is formulated based on the incremental changes in control variables between two consecutive time steps. To achieve this, we approximate ${\mathbf{n}}_{\mathrm{now}}$ and ${\mathit{\delta }}_{\mathrm{now}}$ using a first-order Taylor expansion around the previous operating point, i.e., ${\mathbf{n}}_{\mathrm{last}}$ and ${\mathit{\delta }}_{\mathrm{last}}$. This approximation is feasible due to the high update rate typically available in UAV flight control systems. Therefore, Equation (17) can be rewritten as

$$\begin{array}{cc}\hfill \underset{\Delta \mathbf{n},\Delta \mathit{\delta }}{min}& {\mathbf{K}}_u{∥{\mathbf{u}}_{\mathrm{des}}-\left({\mathbf{u}}_{\mathrm{last}}+{\displaystyle \frac{\partial {\mathbf{u}}_{\mathrm{now}}}{\partial \mathbf{n}}}·\Delta \mathbf{n}+{\displaystyle \frac{\partial {\mathbf{u}}_{\mathrm{now}}}{\partial \mathit{\delta }}}·\Delta \mathit{\delta }\right)∥}^2+{\mathbf{K}}_n{∥\Delta \mathbf{n}∥}^2+{\mathbf{K}}_{\delta }{∥\Delta \mathit{\delta }∥}^2\hfill \\ \hfill & +{\mathbf{K}}_{{\mathbf{W}}_n}{∥{\mathbf{W}}_n\left({\mathbf{n}}_{\mathrm{last}}+\Delta \mathbf{n}-{\mathbf{n}}_{\mathrm{ideal}}\right)∥}^2+{\mathbf{K}}_{{\mathbf{W}}_{\delta }}{∥{\mathbf{W}}_{\delta }\left({\mathit{\delta }}_{\mathrm{last}}+\Delta \mathit{\delta }-{\mathit{\delta }}_{\mathrm{ideal}}\right)∥}^2,\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& \left\{\begin{array}{c}\Delta \mathbf{n}\in \left[{\mathbf{n}}_{min}-{\mathbf{n}}_{\mathrm{last}},{\mathbf{n}}_{max}-{\mathbf{n}}_{\mathrm{last}}\right],\hfill \\ \Delta \mathit{\delta }\in \left[{\mathit{\delta }}_{min}-{\mathit{\delta }}_{\mathrm{last}},{\mathit{\delta }}_{max}-{\mathit{\delta }}_{\mathrm{last}}\right],\hfill \\ \Delta \mathbf{n}\in \left[-{\dot{\mathbf{n}}}_{max},{\dot{\mathbf{n}}}_{max}\right]\Delta t,\hfill \\ \Delta \mathit{\delta }\in \left[-{\dot{\mathit{\delta }}}_{max},{\dot{\mathit{\delta }}}_{max}\right]\Delta t,\hfill \\ {\displaystyle \frac{d{\mathbf{P}}_{\mathrm{now}}}{d\mathbf{n}}}\Delta \mathbf{n}\le {\mathbf{P}}_{max}-{\mathbf{P}}_{\mathrm{last}}.\hfill \end{array}\right.\hfill \end{array}$$

(18)

The derivative in the above equation can be expanded as

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill {\mathbf{U}}_n\stackrel{\Delta }{=}{\displaystyle \frac{\partial {\mathbf{u}}_{\mathrm{now}}}{\partial \mathbf{n}}}={\left[{\displaystyle \frac{\partial u_1}{\partial \mathbf{n}}},{\displaystyle \frac{\partial u_2}{\partial \mathbf{n}}},{\displaystyle \frac{\partial u_3}{\partial \mathbf{n}}},{\displaystyle \frac{\partial u_4}{\partial \mathbf{n}}}\right]}^{\mathrm{T}},\\ \hfill {\mathit{U}}_{\mathit{\delta }}\stackrel{\Delta }{=}{\displaystyle \frac{\partial {\mathbf{u}}_{\mathrm{now}}}{\partial \mathit{\delta }}}={\left[{\displaystyle \frac{\partial u_1}{\partial \mathit{\delta }}},{\displaystyle \frac{\partial u_2}{\partial \mathit{\delta }}},{\displaystyle \frac{\partial u_3}{\partial \mathit{\delta }}},{\displaystyle \frac{\partial u_4}{\partial \mathit{\delta }}}\right]}^{\mathrm{T}},\\ \hfill {\mathbf{P}}_{\mathit{\delta }}\stackrel{\Delta }{=}{\displaystyle \frac{d\mathbf{P}}{d\mathit{\delta }}}={\left[{\displaystyle \frac{d{P}_1}{d{\mathit{\delta }}_1}},{\displaystyle \frac{d{P}_2}{d{\mathit{\delta }}_2}},{\displaystyle \frac{d{P}_3}{d{\mathit{\delta }}_3}},{\displaystyle \frac{d{P}_4}{d{\mathit{\delta }}_4}}\right]}^{\mathrm{T}}.\end{array}& \end{array}$$

(19)

According to Equations (3) and (12), Equation (19) can be further expanded as

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill {\displaystyle \frac{\partial u_1}{\partial {\mathit{\delta }}_r}}=& \left[0,0,0,0\right],\hfill \\ \hfill {\displaystyle \frac{\partial u_2}{\partial {\mathit{\delta }}_r}}=& \left[{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{roll}}}{\partial {\mathit{\delta }}_{r_1}}},{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{roll}}}{\partial {\mathit{\delta }}_{r_2}}},{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{roll}}}{\partial {\mathit{\delta }}_{r_3}}},{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{roll}}}{\partial {\mathit{\delta }}_{r_4}}}\right],\hfill \\ \hfill {\displaystyle \frac{\partial u_3}{\partial {\mathit{\delta }}_r}}=& \left[0,0,0,0\right],\hfill \\ \hfill {\displaystyle \frac{\partial u_4}{\partial {\mathit{\delta }}_r}}=& \left[{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{yaw}}}{\partial {\mathit{\delta }}_{r_1}}},{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{yaw}}}{\partial {\mathit{\delta }}_{r_2}}},{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{yaw}}}{\partial {\mathit{\delta }}_{r_3}}},{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{yaw}}}{\partial {\mathit{\delta }}_{r_4}}}\right].\hfill \end{array}\end{array}$$

(20)

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill {\displaystyle \frac{\partial u_1}{\partial \mathbf{n}}}=& \left[{\displaystyle \frac{d{F}_{T_1}}{d{n}_1}},{\displaystyle \frac{d{F}_{T_2}}{d{n}_2}},{\displaystyle \frac{d{F}_{T_3}}{d{n}_3}},{\displaystyle \frac{d{F}_{T_4}}{d{n}_4}}\right],\hfill \\ \hfill {\displaystyle \frac{\partial u_2}{\partial \mathbf{n}}}=& {\displaystyle \frac{l_1}{2}}\left[-{\displaystyle \frac{d{F}_{T_1}}{d{n}_1}},{\displaystyle \frac{d{F}_{T_2}}{d{n}_2}},{\displaystyle \frac{d{F}_{T_3}}{d{n}_3}},-{\displaystyle \frac{d{F}_{T_4}}{d{n}_4}}\right]+\left[{\displaystyle \frac{\partial M_{\mathit{\delta },\mathrm{roll}}}{\partial n_1}},{\displaystyle \frac{\partial M_{\delta ,\mathrm{roll}}}{\partial n_2}},{\displaystyle \frac{\partial M_{\delta ,\mathrm{roll}}}{\partial n_3}},{\displaystyle \frac{\partial M_{\delta ,\mathrm{roll}}}{\partial n_4}}\right],\hfill \\ \hfill {\displaystyle \frac{\partial u_3}{\partial \mathbf{n}}}=& {\displaystyle \frac{l_2}{2}}\left[-{\displaystyle \frac{d{F}_{T_1}}{d{n}_1}},{\displaystyle \frac{d{F}_{T_2}}{d{n}_2}},-{\displaystyle \frac{d{F}_{T_3}}{d{n}_3}},{\displaystyle \frac{d{F}_{T_4}}{d{n}_4}}\right],\hfill \\ \hfill {\displaystyle \frac{\partial u_4}{\partial \mathbf{n}}}=& \left[-{\displaystyle \frac{d{M}_{T_1}}{d{n}_1}},-{\displaystyle \frac{d{M}_{T_2}}{d{n}_2}},{\displaystyle \frac{d{M}_{T_3}}{d{n}_3}},{\displaystyle \frac{d{M}_{T_4}}{d{n}_4}}\right]+\left[{\displaystyle \frac{\partial M_{\delta ,\mathrm{yaw}}}{\partial n_1}},{\displaystyle \frac{\partial M_{\delta ,\mathrm{yaw}}}{\partial n_2}},{\displaystyle \frac{\partial M_{\delta ,\mathrm{yaw}}}{\partial n_3}},{\displaystyle \frac{\partial M_{\delta ,\mathrm{yaw}}}{\partial n_4}}\right].\hfill \end{array}\end{array}$$

(21)

To simplify the calculations, the following definitions are introduced:

$$\begin{array}{cc}\hfill \begin{array}{cc}& \Delta \mathbf{x}\stackrel{\Delta }{=}{\left[\Delta {\mathbf{n}}^{\mathrm{T}},\Delta {\mathit{\delta }}^{\mathrm{T}}\right]}^{\mathrm{T}}\in {\mathbb{R}}^{8\times 1},\hfill \\ & \mathbf{U}\stackrel{\Delta }{=}\left[{\mathbf{U}}_n,{\mathbf{U}}_{\delta }\right]\in {\mathbb{R}}^{4\times 8},\hfill \\ & \Delta {\mathbf{u}}_{\mathrm{real}}\stackrel{\Delta }{=}{\mathbf{u}}_{\mathrm{des}}-{\mathbf{u}}_{\mathrm{last}}\in {\mathbb{R}}^{4\times 1},\hfill \\ & {\mathbf{K}}_1\stackrel{\Delta }{=}\left[\begin{array}{cc}{\mathbf{K}}_n& {\mathbf{0}}_{4\times 4}\\ {\mathbf{0}}_{4\times 4}& {\mathbf{K}}_{\delta }\end{array}\right]\in {\mathbb{R}}^{8\times 8},\hfill \\ & {\mathbf{K}}_2\stackrel{\Delta }{=}\left[\begin{array}{cc}{\mathbf{K}}_{{\mathrm{W}}_n}& {\mathbf{0}}_{4\times 4},\\ {\mathbf{0}}_{4\times 4}& {\mathbf{K}}_{{\mathrm{W}}_{\delta }}\end{array}\right]\in {\mathbb{R}}^{8\times 8},\hfill \\ & \mathbf{W}\stackrel{\Delta }{=}\left[\begin{array}{cc}{\mathbf{W}}_n& {\mathbf{0}}_{4\times 4},\\ {\mathbf{0}}_{4\times 4}& {\mathbf{W}}_{\delta }\end{array}\right]\in {\mathbb{R}}^{8\times 8}.\hfill \end{array}& \end{array}$$

(22)

Building upon the aforementioned definition, the cost function can be rewritten as

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill \begin{array}{c}J=\Delta {\mathbf{x}}^{\mathrm{T}}\left({\mathbf{U}}^{\mathrm{T}}{\mathbf{K}}_{\mathrm{u}}\mathbf{U}+{\mathbf{K}}_1+{\mathbf{W}}^{\mathrm{T}}{\mathbf{K}}_2\mathbf{W}\right)\Delta \mathbf{x}+\left(2{\mathbf{x}}_{\mathrm{last}}^{\mathrm{T}}{\mathbf{W}}^{\mathrm{T}}{\mathbf{K}}_2\mathbf{W}-2\Delta {\mathbf{u}}_{\mathrm{real}}^{\mathrm{T}}{\mathbf{K}}_{\mathrm{u}}\mathbf{U}\right)\Delta \mathbf{x}+c,\hfill \end{array}\end{array}& \end{array}$$

(23)

where c is a constant independent of the variables being optimized. Since ${\mathbf{K}}_{\mathrm{u}}$, ${\mathbf{K}}_1$, and ${\mathbf{K}}_2$ are positive, definite, diagonal matrices, the quadratic term can be proven to be a semi-definite matrix. Moreover, $\mathbf{U}$ is a row full-rank matrix when all four motor speeds are nonzero, and the quadratic term matrix can be confirmed as a strictly definite matrix, making the problem a strictly convex quadratic programming problem. Furthermore, due to the dimension of the variables being optimized being eight, the above quadratic programming problem can be reformulated into a lower-dimensional quadratic programming problem with linear inequality constraints, making many QP solvers able to efficiently handle this problem. In this paper, the QP solver in MATLAB (v2024b) is used for solving, and simulations demonstrate that the performance meets the real-time requirement.

To sum up, the block diagram of control allocation is illustrated in Figure 4. Based on the desired control force and torques, as well as the relevant feedback information, an optimization problem concerning the control variables is formulated. By utilizing a first-order approximation, the optimization problem is transformed into a standard QP problem, which is subsequently solved using a standard QP solver to obtain the current actuator control commands. These commands are then utilized by the actuators to generate the required control forces and torques. Finally, in conjunction with other established modules, the closed-loop control system of the tail-sitter UAV is completed.

4. Simulation Experiments

The effectiveness of the blown yaw mechanism and the overall control framework is validated in this section through two distinct scenarios in the rotor mode. The first scenario, introduced in Section 4.1, involves a yaw control simulation that demonstrates the improved yaw authority enabled by the proposed method. The second scenario, detailed in Section 4.2, evaluates the robustness during aggressive trajectory tracking under measurement noise and external wind disturbances. To ensure realistic simulation conditions, the environment is configured with $\rho =1.225\mathrm{kg}/{\mathrm{m}}^3$, while the actuator dynamics are modeled using first-order responses with motor and servo time constants of $0.3\mathrm{s}$ and $0.01\mathrm{s}$, respectively. The key parameters involved in the control system are summarized in

Table 2. Primary parameters of the control system.

Variable	Value	Notation
${\mathbf{r}}_0$	$\left(10,20,10\right)$	ADRC
${\mathbf{b}}_0$	$\left(0.05,0.05,0.05\right)$	ADRC
${\mathit{\beta }}_1$	$\left(30,30,30\right)$	ADRC
${\mathit{\beta }}_2$	$\left(100,100,100\right)$	ADRC
${\mathit{\beta }}_{01}$	$\left(30,30,50\right)$	ADRC
${\mathit{\beta }}_{02}$	$\left(300,300,300\right)$	ADRC
${\mathit{\beta }}_{03}$	$\left(30,20,10\right)$	ADRC
${\mathbf{k}}_{\mathrm{px}}$	$\left(0.4,0.5,1\right)$	PID
${\mathbf{k}}_{\mathrm{ix}}$	$\left(0.02,0.03,0\right)$	PID
${\mathbf{k}}_{\mathrm{dx}}$	$\left(0.008,0,0\right)$	PID
${\mathbf{k}}_{\mathrm{pv}}$	$\left(0.4,0.5,0.5\right)$	PID
${\mathbf{k}}_{\mathrm{iv}}$	$\left(0.02,0.03,0\right)$	PID
${\mathbf{k}}_{\mathrm{dv}}$	$\left(0.3,0.5,0.5\right)$	PID

.

4.1. Yaw Channel Response Control Simulation

A standard procedure for assessing the efficacy of the control framework entails conducting simulations to evaluate the capacity of the tail-sitter UAV in adhering to prescribed trajectories. In order to verify the effectiveness of our proposed method in enhancing the yaw control capability, the first experimental scenario involves the UAV hovering at a fixed point in the air while tracking the yaw command specified in Equation (24):

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill \psi =sin{\displaystyle \frac{2\pi }{T}}t,\end{array}& \end{array}$$

(24)

where $T=7.5$.

For the purpose of demonstrating the enhancement of yaw capability achieved by blown yaw, simulations comparing the performance with and without the use of rudders while tracking the specified yaw commands are conducted. The results are presented in Figure 5.

By comparing the motor speeds shown in Figure 5a, it can be observed that the maximum instantaneous difference among the four motors decreased from 1722.06 RPM to 1492.05 RPM. This reduction indicates a significant decrease in the maximum yaw control torque provided by the motors. This improvement is primarily attributed to the proposed blown yaw technique, which leverages rudder deflection, as shown in Figure 5b, to utilize the propeller downwash for generating yaw control torque. This effect is further corroborated by Figure 5f, where, under a required maximum yaw moment exceeding 80 Nm, the deflection of the rudder provides nearly half of the necessary yaw torque. Consequently, the burden on the motors is substantially reduced, effectively preventing motor saturation when tracking aggressive trajectories.

From an energy perspective, Figure 5c shows that the maximum output power of a single motor decreased from 11,000.33 W to 10,319.80 W, corresponding to a reduction of approximately 6.2%. Meanwhile, the average output power decreased from 5714.49 W to 5329.05 W, a reduction of about 6.7%. Furthermore, the total control energy over the entire maneuver, illustrated in Figure 5d, indicates a total energy saving of 8.0%. The reduction in both peak power and overall energy consumption relaxes the requirements of the energy system, which implies lower manufacturing costs and extended endurance—factors that are particularly critical for eVTOL applications.

Finally, Figure 5e compares the trajectory-tracking performance. To quantitatively validate the effectiveness of blown yaw in trajectory tracking, the Mean-Squared Error (MSE) defined in Equation (25) is calculated:

$$\mathrm{MSE}={\displaystyle \frac{1}{T}}{\int }_0^T{∥{\mathbf{p}}_e-{\mathbf{p}}_{\mathrm{traj}}∥}_2^{2}dt,$$

(25)

where ${\mathbf{p}}_e$ and ${\mathbf{p}}_{\mathrm{traj}}$ denote the actual and desired trajectories, respectively. The MSE with rudder assistance is 0.20, compared to 0.51 without rudder contribution, representing an improvement of approximately 60%. Moreover, the maximum yaw-rate-tracking error after stabilization decreased from 0.8197 rad/s to 0.5749 rad/s. In summary, the proposed blown yaw approach effectively redistributes yaw control effort between the motors and the rudder, reducing both peak motor torque and energy consumption, while significantly improving the trajectory-tracking performance.

To investigate the influence of weighting parameters on the system performance, additional experiments are conducted. Three representative cases are considered for ${\mathbf{K}}_u$, namely ${10}^{-3}{\mathbf{K}}_u,{\mathbf{K}}_u$ and ${10}^3{\mathbf{K}}_u$. For each case, we calculate $\sum (\left|{\mathbf{u}}_{\mathbf{des}}-{\mathbf{u}}_{\mathbf{now}}\right|·\Delta t)$, $max\left(\left|{\mathbf{u}}_{\mathbf{des}}-{\mathbf{u}}_{\mathbf{now}}\right|\right)$ and the total motor energy consumption $\sum P\Delta t$. The results summarized in

Table 3. Effect of different ${\mathbf{K}}_u$ values on control errors and energy consumption.

Parameter	$\sum \left|{\mathbf{u}}_{\mathbf{des}}-{\mathbf{u}}_{\mathbf{now}}\right|·\mathbf{\Delta }\mathit{t}$	$max\left|{\mathbf{u}}_{\mathbf{des}}-{\mathbf{u}}_{\mathbf{now}}\right|$	$\sum \mathit{P}\mathbf{\Delta }\mathit{t}$
$1\times {10}^{-3}{\mathbf{K}}_u$	$[6.00,8.61\times {10}^{-7},5.16\times {10}^{-7},68.73]$	$[10.73,1.29\times {10}^{-6},1.27\times {10}^{-6},42.00]$	$3.83\times {10}^6$
${\mathbf{K}}_u$	$[0.70,1.43\times {10}^{-6},2.64\times {10}^{-7},11.21]$	$[7.09,6.61\times {10}^{-7},9.72\times {10}^{-7},38.51]$	$3.87\times {10}^6$
$1\times {10}^3{\mathbf{K}}_u$	$[0.69,1.42\times {10}^{-6},2.57\times {10}^{-7},10.31]$	$[7.09,5.90\times {10}^{-7},8.13\times {10}^{-7},38.50]$	$3.87\times {10}^6$

demonstrate that, as ${\mathbf{K}}_u$ increases, both the cumulative and maximum errors decrease to varying extents, indicating enhanced tracking performance. However, excessively large ${\mathbf{K}}_u$ also increases actuator effort, which leads to higher energy consumption and a greater risk of approaching actuator limits during aggressive maneuvers. This trade-off highlights the necessity of selecting a balanced baseline value for ${\mathbf{K}}_u$.

${\mathbf{K}}_n$ and ${\mathbf{K}}_{\delta }$ are designed to penalize rapid variations in actuator commands. Since further reductions in ${\mathbf{K}}_n$ and ${\mathbf{K}}_{\delta }$ produced negligible changes in system behavior, only two cases are tested: the baseline values of ${\mathbf{K}}_n$ and ${\mathbf{K}}_{\delta }$, and values scaled by ${10}^3$. With ${10}^3{\mathbf{K}}_n$ setting, the maximum absolute errors between consecutive motor PWM commands fell to a very small value, namely 0.2521, indicating substantially smoother motor behavior. This smoothing contributes to extending actuator lifespan and mitigating the risk of mechanical failures. Likewise, increasing ${\mathbf{K}}_{\delta }$ effectively slows the rate of rudder deflections. The trade-off observed is that high ${\mathbf{K}}_n$ or ${\mathbf{K}}_{\delta }$ reduces rapid variations but may shift the control burden. When ${\mathbf{K}}_n$ is large, blown-yaw contributes most of the yaw torque, which alleviates motor saturation. In contrast, a large ${\mathbf{K}}_{\delta }$ leads to greater reliance on differential motor thrust, resulting in higher energy consumption, as is shown in

Table 4. Effect of different ${\mathbf{K}}_n$ and ${\mathbf{K}}_{\delta }$ values on actuators and energy consumption.

Parameter	$max\left|\mathbf{n}(\mathit{k}+1)-\mathbf{n}\left(\mathit{k}\right)\right|$ or $max\left|\mathit{\delta }(\mathit{k}+1)-\mathit{\delta }\left(\mathit{k}\right)\right|$	$\sum \mathit{P}\mathbf{\Delta }\mathit{t}$
${\mathbf{K}}_n$	$[20,20,20,20]$	$3.87\times {10}^6$
$1\times {10}^3{\mathbf{K}}_n$	$[0.2521,0.2521,0.2521,0.2521]$	$3.83\times {10}^6$
${\mathbf{K}}_{\delta }$	$[0.1,0.1,0.1,0.1]$	$3.87\times {10}^6$
$1\times {10}^3{\mathbf{K}}_{\delta }$	$[0.0756,0.0756,0.0756,0.0756]$	$4.06\times {10}^6$

.

${\mathbf{K}}_{W_n}$ and ${\mathbf{K}}_{{\mathrm{W}}_{\delta }}$ are designed to discourage actuators from operating at high throttle levels. This can be evaluated by the total motor energy consumption $\sum P\Delta t$. With ${10}^4{\mathbf{K}}_{{\mathrm{W}}_{\delta }}$ setting, the system exhibits a stronger preference for motor-based control over control-surface usage, leading to an increase in total energy consumption from $3.87\times {10}^6$ to $4.13\times {10}^6$. Since the tail-sitter is performing yaw control at hover with $∥{\mathbf{V}}_{\mathbf{b}}∥=0$, the influence of ${\mathbf{K}}_{W_n}$ can not be tested. Fortunately, by observing the variations under adjusted ${\mathbf{K}}_{{\mathrm{W}}_{\delta }}$, we can draw an analogy to the expected effects of ${\mathbf{K}}_{W_n}$.

These findings underscore the effectiveness of the proposed blown yaw method in improving yaw control and energy efficiency. This approach allows for more effective control of the UAV yaw movement, particularly during VTOL. By strategically positioning the rudders within the propeller slipstream, the concept of blown yaw offers a more efficient and effective approach to yaw control, representing a substantial advancement in control strategies for large-scale tail-sitter UAVs.

4.2. Aggressive Trajectory Tracking Under Disturbances

The inherent characteristics of quadrotor UAVs, namely their low mass and powerful propulsion systems, render them particularly well-suited for aggressive trajectory tracking and large-amplitude maneuvers through the implementation of resilient or nonlinear control mechanisms. However, in the case of large-scale tail-sitter UAVs, the principal focus of control strategies pivots towards ensuring stability, safety, and robustness. Consequently, for the simulation exercise, a spiral trajectory delineated in Equation (26) is selected, representing a particularly challenging trajectory for the hundred-kilogram class tail-sitter UAV.

$$\begin{array}{cc}\hfill \begin{array}{c}\hfill x=Rsin{\displaystyle \frac{2\pi }{T}}t,y=R\left(1-cos{\displaystyle \frac{2\pi }{T}}t\right),z=kt,\end{array}& \end{array}$$

(26)

where $R=15$, $T=15$, and $k=1$.

The current flight status, obtained from the onboard sensors, is essential for both the position and attitude controllers. However, measurement noise is inevitably introduced into the control framework via these sensors. Therefore, in this section, to evaluate the noise resistance of the designed control framework, we artificially introduce measurement noise, as detailed in

Table 5. Amplitude of measurement noise.

Parameter	Observation Error Amplitude
Position	$\pm 1.5\mathrm{m}$
Velocity	$\pm 0.4\mathrm{m}/\mathrm{s}$
Attitude	$\pm 20\mathrm{deg}$
Angular velocity	$\pm 0.5\mathrm{rad}/\mathrm{s}$

, using the Band-Limited White Noise block in MATLAB. The noise is added to the feedback information of the vehicle model depicted in Figure 4.

Moreover, the large windward area of the tail-sitter UAV during vertical operations makes it highly susceptible to wind interference. Consequently, CFD is used to calculate the external forces and torques experienced by the tail-sitter UAV under level 5 wind conditions on the Beaufort scale, as listed in

Table 6. External forces and torques caused by Beaufort scale level 5 wind.

Parameter	Values
External forces	$[251.6,3.2,35.1]\mathrm{N}$
External torques	$[3.2,-48.6,-4.3]\mathrm{Nm}$

.

The behavior of the tail-sitter UAV tracking an aggressive trajectory under the influence of noise and wind is illustrated in Figure 6. Despite the presence of significant external perturbations, the vehicle is still able to follow the reference trajectory with only a certain degree of delay and error, as shown in Figure 6a,b. These deviations can be attributed to several factors. First, the vehicle’s substantial mass and large rotational inertia inherently slow its dynamic response, so even when corrective commands are issued, the system requires time to react. Second, although the integral term in a PID-based position controller is theoretically capable of eliminating steady-state errors, it is often conservatively tuned in practice to avoid excessive overshoot or oscillations, which can result in a small residual error. Third, actuator limitations, including response delays, rate constraints, and saturation, further restrict the controller’s ability to instantaneously compensate for disturbances. Finally, persistent external forces continuously act on the vehicle, and the PID controller can only respond based on measured errors, without predictive capability. In addition, it is straightforward to recognize from Figure 6e that external torques about the y-axis have a pronounced impact on the pitch dynamics, while external forces along the x-axis induce noticeable deviations in the x-direction at the onset of trajectory tracking. Nevertheless, the controller rapidly compensates for these effects, driving the vehicle back toward the desired trajectory. A closer examination of the motor speeds and rudder deflections shown in Figure 6c,d indicates that the rudder undergoes more pronounced oscillations within its operational range. This phenomenon arises because the motors respond more slowly than the servos, effectively introducing a natural low-pass filtering effect that attenuates high-frequency noise. By contrast, the faster response of the servos makes them more sensitive to high-frequency disturbances, resulting in the more evident oscillations observed in their deflections. These oscillations further manifest in the yaw moment distribution shown in Figure 6f. Nevertheless, the rapid responsiveness of the rudder enables the vehicle to react more effectively to abrupt changes in both external disturbances and control commands, thereby enhancing the tail-sitter’s capacity to maintain accurate tracking of aggressive trajectories despite significant disturbances. Overall, despite considerable external disturbances, the tail-sitter achieves a satisfactory trajectory-tracking performance, benefiting from the robustness of the proposed controller and the effectiveness of the control allocation module in precisely mapping control demands to the actuators.

As a comparison, the vehicle attempts to track the aggressive trajectory without utilizing rudder-assisted control. Due to constraints such as limited motor speed and power, differential thrust alone proves inadequate for effective yaw control in large tail-sitter UAVs, resulting in poor trajectory tracking. The control performance under this condition is presented in Figure 7. This indicates that fully leveraging the potential of all actuators can significantly enhance the vehicle’s maneuverability. The proposed blown yaw possesses a significant degree of robustness against sensor measurement noise and wind interference.

To further demonstrate the effectiveness of the control allocation algorithm proposed in this study, we record the control inputs required to track the aforementioned trajectory under ideal conditions. The control allocation is performed using both the conventional pseudoinverse method and the optimization-based allocation approach developed herein, and the results are compared, as illustrated in Figure 8. The mean tracking errors for the two methods are [35.02, 1.30, 1.93, 5.26] and [1.41, 0.59, 0.99, 0.05], respectively. As observed in Figure 8, the pseudoinverse control allocation exhibits significant oscillations and lower accuracy in the thrust and yaw moment directions compared to the proposed optimization-based method. This behavior can be attributed to several inherent limitations of the pseudoinverse approach. First, the pseudoinverse method does not account for variations in actuator efficiency across different operating speeds. During trajectory tracking, the inflow along the z-axis affects motor efficiency, thereby inducing corresponding variations in the generated forces and moments. Second, the influence of propeller-induced slipstreams on the effectiveness of control surfaces, particularly in yaw moment generation, is ignored, introducing further inaccuracies in actuator mapping. Third, the pseudoinverse method assumes a linear relationship between propeller inputs and the resulting forces and moments and presumes constant thrust and torque coefficients, whereas the actual propeller dynamics are nonlinear and speed-dependent. These unmodeled effects collectively result in discrepancies between the desired and actual actuator outputs, and because the pseudoinverse method does not incorporate feedback to correct for such errors, they manifest themselves as oscillations in the allocated commands. In contrast, the proposed optimization-based control allocation explicitly accounts for actuator efficiency variations, nonlinear propeller dynamics, and the interaction between propeller wake and control surfaces, thereby achieving more accurate and stable thrust and moment distribution.

5. Conclusions

This paper addresses the long-standing challenge of achieving effective yaw control in large-scale tail-sitter UAVs with limited thrust-to-weight ratios. To this end, we propose and scale the blown-yaw concept, leveraging propeller slipstream effects over rudders to generate substantial yaw moments without increasing design complexity or sacrificing control authority in other channels. Unlike prior studies that rely on simplified momentum theory or idealized actuator assumptions, our work employs high-fidelity CFD simulations to rigorously capture the nonlinear propeller–control surface interactions, thereby providing a more realistic aerodynamic foundation. In addition, by integrating ADRC, the proposed system enhances robustness against uncertainties and environmental disturbances. Finally, to resolve the over-actuation challenge inherent in multi-actuator configurations, we develop an optimization-based control allocation framework that accounts for actuator nonlinearities and efficiency variations across flight modes, enabling accurate and reliable force/torque distribution. Simulations are conducted to verify the effectiveness, demonstrating that fully exploiting all actuators substantially improves yaw control capability and maintains effective trajectory tracking, even in the presence of disturbances such as noise and wind. These findings highlight the robustness and efficiency of blown yaw, providing a significant advancement in control strategies for large-scale tail-sitter UAVs. Future work will focus on experimental validation and further optimization to enhance the system’s performance in real-world applications. Specifically, it will focus on refining the proposed algorithm and assessing its real-time feasibility through hardware-in-the-loop (HIL) simulations. Furthermore, it will focus on conducting full-scale experimental validation, including trajectory-tracking tests under both calm and windy conditions, to verify the robustness and practical applicability of the approach.