Asynchronous Tilt Transition Control of Quad Tilt Rotor UAV

Highlights

What are the main findings?

• An asynchronous transition control scheme is developed for quad tilt-rotor (QTR) unmanned aerial vehicles (UAVs), enabling feasible and stable transition flight under variations in center of gravity (CG) and forward acceleration limits.
• A two-level control allocation framework combining nonlinear dynamic inversion control (NDIC) and an extended state observer (ESO) (denoted as NDIC–ESO) achieves accurate transition trajectory tracking while coordinating rotor and aerodynamic surface control subsystems.

What are the implications of the main findings?

• The proposed approach improves robustness and adaptability during the transition phase, thereby expanding the operational envelope of QTR UAVs.
• The control framework provides a practical solution for control authority distribution in QTR UAVs with heterogeneous actuators.

Abstract

To address the challenges inherent in the transition flight control of QTR UAVs, this paper proposes an asynchronous tilt transition control framework that integrates NDIC with an ESO. First, a heterogeneous control allocation strategy is introduced to coordinate the rotors and aerodynamic surfaces, thereby maintaining consistent matching between control demands and actuator capabilities. Furthermore, compared with the synchronous tilt strategy, the proposed asynchronous tilt strategy improves pitch moment balance and forward acceleration capability, thereby enhancing robustness against CG variations and extending the achievable forward acceleration range. Finally, based on the asynchronous tilt transition strategy, a transition flight control method combining NDIC with ESO is presented to achieve precise transition control performance under the lumped disturbances. The simulation results demonstrate that the proposed tilt method achieves a safe and smooth transition, satisfies dynamic performance requirements, and exhibits strong robustness and high control accuracy.

1. Introduction

Tilt-rotor UAVs combine the vertical takeoff and landing capabilities of helicopters with the high-speed cruise advantage of fixed-wing aircraft, offering exceptional operational flexibility for military and civilian missions. The QTR configuration [1,2,3,4] is derived from the conventional dual tilt-rotor one [5,6,7] and exhibits significant improvements in payload capacity, flight envelope, and operational reliability [8]. However, safe and smooth transition control for QTR UAVs under time-varying CG shift and continuously changing actuator effectiveness remains insufficiently addressed, especially in an integrated framework that combines transition scheduling, capability-based control allocation, and robust tracking control. This gap motivates the present work.

Regardless of the tilt-rotor configuration [9,10,11], the transition phase remains the most critical segment of flight. As illustrated in Figure 1, this phase bridges the helicopter and fixed-wing modes, realizing the configuration conversion with two models. Due to complex actuation and inherent aerodynamic coupling, the transition phase involves several critical challenges [12,13,14]:

(1)

Time-varying CG shift with nacelle angle changes alters rotor moment arms and may induce pitch oscillations, degrading stability and lift establishment; thus, an effective transition strategy is required to mitigate pitch fluctuations.

(2)

The QTR UAV is equipped with rotor and aerodynamic-surface control systems [12,15,16], the control effectiveness of which is governed by the nacelle angle and the dynamic pressure, respectively. During the tilt transition phase, both variables vary continuously, leading to a dynamic redistribution of control authority between these systems. Consequently, developing an appropriate control allocation strategy [17] is essential for ensuring safe transition flight.

(3)

The transition control laws [18,19] must address not only the challenges posed by the time-varying CG and control-system effectiveness but also the nonlinearities inherent in transition dynamics and the unmodeled dynamic introduced by rotor downwash [20]. Therefore, the proposed control law must exhibit strong robustness to ensure stable transition flight.

To address the first challenge, forward CG shift is an inherent issue for tilt-rotor aircraft during the transition phase. From the perspective of mitigating CG-induced pitch disturbances, previous studies have handled this problem by either neglecting the CG disturbance or treating it as a perturbation [18,21] and then enhancing the robustness of the transition control law to accommodate it; however, such approaches increase the controller design complexity. In contrast, proactively mitigating CG-induced pitch disturbance via nacelle scheduling is still limited, motivating the asynchronous transition strategy proposed herein. Specifically, during forward transition, the front nacelle angles tilt more slowly than the rear ones. This strategy increases the vertical component of the front rotor thrust, compensating for the shortened moment arm caused by the CG shift and mitigating pitch fluctuations.

Control allocation provides another route to match control demands with heterogeneous actuator capabilities. For example, a velocity-segmented weighting allocation strategy was proposed for a dual tilt-rotor aircraft [22], where rotor and aerodynamic-surface subsystems dominate at low and high speeds, respectively, with a linear blending in the intermediate regime. However, although straightforward to implement, this method causes actuator underutilization at both speed extremes and fails to allocate authority according to actual control effectiveness, thereby reducing redundancy and compromising safety. Similar allocation schemes based on airspeed or nacelle angle [9,19,23,24] suffer from the same mismatched authority distribution and idle actuator issues. In addition, performance-function-based optimal control allocation methods have been extensively studied for tilt-rotor aircraft. For example, the method in Reference [17] integrates a min–max optimization framework with a force decomposition algorithm, achieving effective actuator saturation handling with low computational complexity. Moreover, Reference [25] formulates the control redundancy problem as a multi-objective optimization, enabling authority allocation based on actual control effectiveness and improving actuator utilization. Overall, many existing allocation schemes do not explicitly redistribute authority according to time-varying effectiveness throughout the transition, which may cause authority mismatch and actuator idleness/saturation under rapidly changing conditions.

Extensive research has also been conducted into control-law design. In [2], stage-wise longitudinal control strategies were designed based on actuator allocation; these demonstrate robustness in simulations, but the tilt transition lacks smoothness. In [17,26], the transition control problem was formulated as a nonlinear optimal control task solved online with performance-based cost functions. Moreover, with modern embedded hardware and efficient solvers, real-time computation is increasingly feasible. However, the design of suitable cost functions remains a critical and nontrivial issue for achieving satisfactory control performance. In [27,28], active disturbance rejection control (ADRC) was proposed for enhanced dynamic performance during the tilt-wing transition, but many of the parameters rely on experience for their values. In [29], a robust attitude control law was proposed for the longitudinal dynamics of the McART3 QTW-UAV, aiming to improve robustness and performance. In [19], an adaptive neural extended state observer with finite-time convergence was used for enhanced transition robustness, but the controller structure is difficult to design for applications. In [16], a model predictive controller was designed to control a tilt-rotor aircraft in autorotation and forward flight, whereas the control method requires an accurate model. Similarly, in [30,31], model predictive control was employed to solve an optimal control problem subject to constraints, but it typically requires online optimization and likewise depends on high-fidelity models. Nevertheless, it remains nontrivial to integrate robust tracking control with effectiveness-based allocation and transition scheduling in a unified framework that is both implementable and reliable for transition flight.

Based on the above analysis, this paper proposes an asynchronous transition control scheme for a QTR UAV. The main contributions are as follows.

(1)

Asynchronous transition strategy. Compared with the traditional synchronous transition strategy, the proposed asynchronous one offers superior adaptability to variations in CG and maximum forward acceleration. In particular, under CG shift conditions, the asynchronous tilt strategy maintains a safe and controllable transition, whereas the synchronous strategy suffers from actuator saturation and loss of transition feasibility. Consequently, the proposed approach enhances transition capability and extends the range of feasible flight conditions.

(2)

Two-level control allocation. The proposed two-level control allocation method dynamically distributes control authority between two control subsystems based on their real control capability. This approach enables automatic and reasonable matching of control demand with actuator capacity, avoiding actuator saturation or idleness and ensuring coordinated utilization of the rotor and aerodynamic-surface control subsystems.

(3)

NDIC-ESO control law. An NDIC–ESO control framework is developed for precise trajectory tracking. The NDIC is responsible for tracking the desired trajectory, while the ESO estimates and compensates for lumped disturbances, thereby enhancing system robustness and dynamic performance.

To further clarify the novelty of this work, we compare the proposed framework with representative nonlinear transition control strategies. Sliding-mode-based robust control can provide strong disturbance rejection but may suffer from chattering and requires careful boundary-layer and bandwidth considerations for heterogeneous actuators [32,33,34]. Adaptive nonlinear controllers can handle uncertainties [19], yet they often introduce coupled tuning and increased implementation complexity when CG shift and aerodynamic effectiveness vary continuously during transition. Nonlinear MPC explicitly handles constraints and multivariable coupling [30,31], but it typically relies on online optimization and accurate high-fidelity models. ADRC/ESO-based methods improve robustness by estimating lumped disturbances [27,28]; however, existing designs are not always straightforward to integrate with control allocation and transition scheduling. In contrast, our approach integrates: (i) asynchronous nacelle scheduling to proactively mitigate CG-induced pitch disturbance; (ii) capability-based two-level allocation to match time-varying actuator effectiveness while avoiding idleness/saturation; and (iii) NDIC–ESO tracking for accurate trajectory tracking with disturbance compensation, providing a practical trade-off among robustness, computational complexity, and implementability for QTR transition flight.

The remainder of this paper is organized as follows. Section 2 presents the integrated modeling of the QTR UAV, Section 3 describes the proposed control allocation strategy, Section 4 introduces the control-law design and Section 5 discusses the simulation results. Finally, Section 6 concludes the paper.

2. Integrated Modeling of QTR UAV

The configuration of the QTR is shown in Figure 2. Depending on the nacelle angle, the QTR operates in helicopter ($\tau ={90}^{°}$), transition ($0^{°}<\tau <{90}^{°}$), or fixed-wing ($\tau =0^{°}$) mode. Besides the tilt mechanism, the QTR also employs rotors ($n_{i=1~4}$) and aerodynamic-surface control systems; the inner surfaces (nos. 6, 8, 10, 12) act as elevators ${\delta }_e$, the outer surfaces (nos. 5, 7, 9, 11) as ailerons ${\delta }_a$, and the tail surface (no. 13) as the rudder ${\delta }_r$.

Based on the fixed-wing/rotorcraft modeling approaches, an integrated and full-state nonlinear model of the QTR is established as follows [35,36,37]:

$$\underset{{\dot{\mathit{X}}}_F}{\underbrace{\left[\begin{array}{c}{a}_x\\ a_z\end{array}\right]}}=\underset{h_{\mathbf{1}\mathit{F}}}{\underbrace{{\mathit{S}}_{\mathit{b}}^{\mathit{e}}\left[\begin{array}{c}vr-wq\\ uq-vp\end{array}\right]}}+\underset{h_{\mathbf{2}\mathit{F}}}{\underbrace{S_b^e\left[\begin{array}{c}-g\sin \theta \\ g\cos \theta \cos \varphi \end{array}\right]}}+\underset{U_F}{\underbrace{S_b^e\left[\begin{array}{c}{\displaystyle \frac{F_x}{m}}\\ \frac{F_z}{m}\end{array}\right]}}$$

(1)

$$\underset{{\dot{X}}_M}{\underbrace{\left[\begin{array}{c}\dot{p}\\ \dot{q}\\ \dot{r}\end{array}\right]}}=\underset{h_{\mathbf{1}\mathit{M}}}{\underbrace{\left[\begin{array}{c}{\displaystyle \frac{\left(I_y-I_z\right)qr}{I_x}}\\ {\displaystyle \frac{\left(I_z-I_x\right)pr}{I_y}}\\ {\displaystyle \frac{\left(I_x-I_y\right)pq}{I_z}}\end{array}\right]}}+\underset{h_{\mathbf{2}\mathit{M}}}{\underbrace{\left[\begin{array}{c}{\displaystyle \frac{\left(M_{x0}+M_{x\alpha \beta }\right)}{I_x}}\\ {\displaystyle \frac{\left(M_{y0}+M_{y\alpha \beta }\right)}{I_y}}\\ {\displaystyle \frac{\left(M_{z0}+M_{z\alpha \beta }\right)}{I_z}}\end{array}\right]}}+\underset{U_M}{\underbrace{\left[\begin{array}{c}{\displaystyle \frac{M_x}{I_x}}\\ {\displaystyle \frac{M_y}{I_y}}\\ {\displaystyle \frac{M_z}{I_z}}\end{array}\right]}}$$

(2)

$$\left[\begin{array}{c}\dot{x}\\ \dot{z}\end{array}\right]=\left[\begin{array}{c}{V}_x\\ V_z\end{array}\right]$$

(3)

$$\left[\begin{array}{c}\dot{\varphi }\\ \dot{\theta }\\ \dot{\psi }\end{array}\right]=\left[\begin{array}{c}p+\left(r\cos \varphi +q\sin \varphi \right)\tan \theta \\ q\cos \varphi -r\sin \varphi \\ {\displaystyle \frac{1}{\cos \theta }}\left(r\cos \varphi +q\sin \varphi \right)\end{array}\right]$$

(4)

Here, $X_F,X_M$ are the force and moment state vectors, respectively; $h_{1F},h_{1M}$ are the coupling terms; $U_F,U_M$ are the control input forces and moments, respectively; $a_x,a_z$ are the forward and vertical accelerations in the inertial frame, while $V_x,V_z$ are the corresponding velocities; $S_b^e$ is the transformation matrix from the body frame to the inertial frame; $u,v,w$ are the velocity components along the body axes; $\varphi ,\theta ,\psi$ are the roll, pitch, and yaw angles, respectively; $p,q,r$ are the body angular rates.

Furthermore, $F={\left[F_x,F_z\right]}^{\mathrm{T}}$ and $M={\left[M_x,M_y,M_z\right]}^{\mathrm{T}}$ are the body-frame force and moment vectors, respectively, composed of the rotor and aerodynamic systems and expressed as

$$\left\{\begin{array}{l}F=F_n+F_d\\ M=M_n+M_t+M_d\end{array}\right.$$

(5)

where ${\mathit{F}}_n,F_d$ are the forces generated by the rotor and aerodynamic systems, respectively, and $M_n,M_t,M_d$ are the rotor thrust moment, rotor anti-torque moment, and aerodynamic moment, respectively. These are expressed as

$$\left\{\begin{array}{l}{F}_d=S_{\alpha }^{b}Q{S}_{ref}{\left[\begin{array}{cc}{C}_D& C_L\end{array}\right]}^T\\ F_n={\left[\begin{array}{cc}{\displaystyle \sum _{i=1}^4\left(K_f{n}_i^2\cos {\tau }_i\right)}& {\displaystyle \sum _{i=1}^4\left(-K_f{n}_i^2\sin {\tau }_i\right)}\end{array}\right]}^T\\ M_n={\displaystyle \sum _{i=1}^4\left(-K_f{n}_i^2{\left[l_{iy}\sin {\tau }_i,-l_{ix}\sin {\tau }_i,l_{iy}\cos {\tau }_i\right]}^T\right)}\\ M_t={\displaystyle \sum _{i=1}^4{\left(-1\right)}^i\left({\left[-K_m{n}_i^2\cos {\tau }_i,0,K_m{n}_i^2\sin {\tau }_i\right]}^T\right)}\\ M_d=Q{S}_{ref}\overline{\mathit{b}}\cdot diag\left(C_{mx},C_{my},C_{mz}\right)\end{array}\right.$$

(6)

where $K_f,K_m$ are the rotor thrust and torque coefficient, respectively, ${\tau }_i$ is the nacelle angle of the $i$-th rotor, $S_{\alpha }^b$ is the transformation matrix from the wind axis to the body axis, $Q$ is the dynamic pressure, and $\overline{\mathit{b}}$ is a vector expressed as $\overline{\mathit{b}}={\left[b,c_A,b\right]}^{\mathrm{T}}$. Furthermore, $C_D,C_L$ are the aerodynamic drag and lift coefficients, respectively, and $C_{mx},C_{my},C_{mz}$ are the aerodynamic moment coefficients. All these aerodynamic data are obtained from wind tunnel experiments.

3. Design of Two-Level Control Allocation Strategy

This section proposes a two-level control allocation strategy, as illustrated in Figure 3. In the first level, the total control demands are allocated based on the control capabilities of the rotor and aerodynamic-surface subsystems. Performed without loss of precision, the first-level allocation enhances the reasonableness of the distribution and reduces the design complexity of the parameters for the second-level SQP (sequential quadratic programming) allocation. Building on this, our strategy adaptively matches the control demands with actuator effectiveness.

3.1. Control Weight Allocation for Rotor and Aerodynamic-Surface Subsystems

During the transition process, the force control demands primarily compensate for gravity and generate forward acceleration, while the moment control demands govern the attitude angles. Although both are influenced by flight dynamic pressure, their control objectives differ fundamentally. Therefore, considering the distinct mechanisms through which the rotor and aerodynamic control subsystems generate forces and moments, two separate physically meaningful weight allocation strategies are designed as follows:

$$\left\{\begin{array}{l}\mathrm{Force} \mathrm{Weight}:w_F\left(Q\right)=\left\{\begin{array}{cc}1-{\displaystyle \frac{C_{L}Q{S}_{ref}}{mg}}& 0\le Q\le Q_{str}\\ 0& Q>Q_{str}\end{array}\right.,w_{\alpha }=1-w_F\\ \mathrm{Moment} \mathrm{Weight}:w_n\left(\tau ,Q\right)={\displaystyle \frac{\sin \tau }{\sin \tau +\frac{Q}{Q_{str}}}},w_{\delta }=1-w_n\end{array}\right.$$

(7)

where $C_{L}Q{S}_{ref}$ denotes the aerodynamic lift, $w_{F,\alpha },w_{n,\delta }$ are the weighting coefficients for the force and moment control of the rotor and aerodynamic-surface control subsystems, respectively, $Q=0.5\rho V^2$ and $Q_{str}=0.5\rho V_{str}^2$ are the real dynamic pressure and the safety threshold dynamic pressure corresponding to level flight speed $V_{str}$, respectively; $\rho$ is the air density; and the role of $\tau =\max [{\tau }_{\mathrm{f}},{\tau }_{\mathrm{r}}]$ is to reduce the control load on the aerodynamic subsystem during the initial transition phase.

The essence of tilt transition is that the aircraft’s weight support gradually shifts from rotor-borne lift to wing-borne aerodynamic lift. Therefore, the force weight $w_F$ is intentionally linked to the lift fraction ($C_{L}Q{S}_{ref}/mg$) to schedule the redistribution of the vertical force demand: the wing is assigned a larger portion of vertical force only when the aerodynamic lift becomes sufficiently meaningful. This capability-based design helps avoid altitude excursions caused by insufficient lift or aerodynamic model mismatch. The moment/control authority is reflected by the moment weights $w_n$. Physically, the rotor subsystem’s moment-generation capability varies mainly with the nacelle tilt angle, whereas the aerodynamic-surface subsystem’s moment-generation capability is strongly dependent on the real dynamic pressure $Q$. The term $Q/Q_{str}$ is introduced as a dimensionless normalization to eliminate dimensional inconsistency and to obtain a bounded, well-conditioned weighting indicator over the transition envelope.

Notably, the first-stage weight computation is formulated based on the physical meaning of control authority. However, the force weight is based on the aerodynamic lift coefficient. Because of uncertainties in the aerodynamic model, discrepancies may arise between the required and actual aerodynamic lift, which can lead to altitude fluctuations. To mitigate this issue, an aerodynamic lift regulator is proposed, which compensates for the aerodynamic lift by adjusting the angle of attack. The detailed design process is presented in Section 4.4.

Remark 1. 

The proposed allocation strategy effectively exploits the control capability of the aerodynamic subsystem during high-speed flight in helicopter mode. Moreover, the capability-based weighting strategy mitigates the strong constraint between nacelle angle and airspeed in the transition phase.

3.2. Subsystem Control Allocation with SQP

Building on the system weighting allocation, the primary task of the subsystem control allocation is to achieve a rational and precise mapping of the force and moment control demands of the rotor and aerodynamic-surface subsystems to the actuators. To balance optimization efficiency with practical engineering applicability, an SQP algorithm is used to solve the subsystem control allocation problem [38]. The main design framework is summarized as follows.

First, to minimize the discrepancy between the desired and actual forces and moments, the deviation between the commanded and generated control outputs is formulated as the main optimization objective. Second, to ensure the smoothness of rotor thrust and control-surface deflection rates, the differential terms of rotor thrust and nacelle tilt angle are incorporated into the objective function. On this basis, an allocation optimization model for rotor and aerodynamic-surface control subsystems is established:

$$\begin{array}{l}\min f_2=S_2^T{W}_2{S}_2+P_2^T{M}_2{P}_2\hfill \\ \left\{\begin{array}{l}\mathit{Rotor} \mathit{Control} \mathit{Subsystem}\hspace{1em}s.t.\left\{\begin{array}{l}{S}_{2n}=\left[\begin{array}{c}{\mathit{diag}(1,w}_F)\times F_c-F_n\\ w_n\times M_c-M_n\end{array}\right]\\ P_{2n}={\left[{\dot{F}}_f,{\dot{F}}_r,{\dot{\tau }}_f,{\dot{\tau }}_r\right]}^T\end{array}\right.\hfill \\ Aerodynamic \mathrm{C}ontrol \mathit{Subsystem}\hspace{1em}s.t.\left\{\begin{array}{l}{S}_{2\delta }=\left[\begin{array}{c}{w}_{\alpha }\times F_c\left(2\right)-F_{\delta }\\ w_{\delta }\times M_c-M_{\delta }\end{array}\right]\\ P_{2\delta }={\left[{\dot{\delta }}_a,{\dot{\delta }}_e,{\dot{\delta }}_r\right]}^T\end{array}\right.\hfill \end{array}\right.\hfill \end{array}$$

(8)

Remark 2. 

Because the aerodynamic subsystem cannot generate forward thrust, ${\mathrm{diag}(1,\mathrm{w}}_F)\times \mathit{F}$ indicates that the forward thrust does not require weight allocation, and only the vertical force is distributed according to the control weighting coefficient ${\mathrm{w}}_F$.

4. Transition Control Based on NDIC and ESO

This section presents an asynchronous transition control scheme with NDIC based on a two-level allocation strategy, as illustrated in Figure 4, using feedforward compensation for unmodeled aerodynamic effects by ESO. Additionally, an aerodynamic lift regulator is proposed to compensate for the discrepancies between the database and the actual aerodynamics.

4.1. Design Concept of NDIC-ESO Controller

Considering the unmodeled aerodynamic and data fitting errors, Equations (1) and (2) can be formulated as

$$\dot{\mathit{X}}=h_1+h_2+\underset{U}{\underbrace{U_1+U_2+U_3}}+\Delta \left(h_1,h_2,\mathit{\zeta }\right)$$

(9)

where $\Delta \left(h_1,h_2,\mathit{\zeta }\right)$ represents the lumped disturbance term, including data fitting errors, external disturbances and modeled uncertainties. Furthermore, $U_1$ is the feedforward control input, $U_2$ is the reference control input derived from NDIC, and $U_3$ is the control input generated by the ESO.

4.2. Design of Inner-Loop Control Law

The inner-loop control includes a forward acceleration controller, a vertical acceleration controller, and a three-axis angular rate controller. Based on Equation (9), the control law consists of three components: a feedforward control law, an NDIC law, and an ESO control law. The design procedures of each component are described as follows.

Step 1: Feedforward Control Design. Based on Equation (9), the feedforward generic control law is given by

$$U_1=-h_1-h_2$$

(10)

Based on Equations (1) and (2), we obtain

$$\left\{\begin{array}{l}{U}_{\mathit{F}\mathbf{1}}=-h_{\mathbf{1}\_\mathit{F}}-h_{\mathbf{2}\_\mathit{F}}\\ U_{\mathit{M}\mathbf{1}}=-h_{\mathbf{1}\_\mathit{M}}-{\widehat{\mathit{h}}}_{\mathbf{2}\_\mathit{M}}\end{array}\right.$$

(11)

Consequently, the body-axis forces and moments are written as

$$\left\{\begin{array}{l}\left[\begin{array}{c}{F}_{xc1}\\ F_{zc1}\end{array}\right]=-m\left[\begin{array}{c}vr-wq\\ uq-vp\end{array}\right]-m\left[\begin{array}{c}-g\sin \theta \\ g\cos \theta \cos \varphi \end{array}\right]\\ \left[\begin{array}{c}{M}_{xc1}\\ M_{yc1}\\ M_{zc1}\end{array}\right]=-\left[\begin{array}{c}\left(I_y-I_z\right)qr\\ \left(I_z-I_x\right)pr\\ \left(I_x-I_y\right)pq\end{array}\right]-\left[\begin{array}{c}\left({\widehat{M}}_{x0}+{\widehat{M}}_{x\alpha \beta }\right)\\ \left({\widehat{M}}_{y0}+{\widehat{M}}_{y\alpha \beta }\right)\\ \left({\widehat{M}}_{z0}+{\widehat{M}}_{z\alpha \beta }\right)\end{array}\right]\end{array}\right.$$

(12)

Remark 3. 

$h_{\mathbf{1}\_\mathit{F}},h_{\mathbf{2}\_\mathit{F}},h_{\mathbf{1}\_\mathit{M}}$ are known parameters associated with the QTR or measurable from onboard sensors, while ${\widehat{\mathit{h}}}_{\mathbf{2}\_\mathit{M}}$ denotes the three-axis aerodynamic non-control moments derived from data fitting.

Step 2: Design of NDIC Law. Following the feedforward control law in step 1, the inner-loop model can be written as

$$\dot{\mathit{X}}=U_2$$

(13)

Defining the tracking error as $\mathit{e}=\mathit{X}-X_c$, its differential can be expressed as

$$\dot{\mathit{e}}=\dot{\mathit{X}}-{\dot{\mathit{X}}}_c$$

(14)

By substituting Equation (13) into Equation (14), we obtain

$$\dot{\mathit{e}}=\dot{\mathit{X}}-{\dot{\mathit{X}}}_c=U_2-{\dot{\mathit{X}}}_c+\Delta \left(h_1,h_2,\mathit{\zeta }\right)$$

(15)

To explicitly shape the transient performance of each component of the error vector, we consider the weighted Lyapunov function:

$$\mathit{V}={\displaystyle \frac{1}{2}}{e}^{T}Qe$$

(16)

where $Q=\mathrm{diag}(q_1,q_2,q_3,q_4,q_5)>0$. Its time derivative is

$$\dot{\mathit{V}}=e^{T}Q\dot{e}$$

(17)

The NDIC reference input is chosen as

$${\mathit{U}}_2=-\Delta \left(h_1,h_2,\mathit{\zeta }\right)+{\dot{\mathit{X}}}_{\mathit{c}}-\mathit{K}e$$

(18)

where $K=diag(k_{a_x},k_{a_z},k_p,k_q,k_r)>0$ is the feedback gain matrix.

Substituting Equation (18) into Equation (15) gives

$$\dot{\mathit{e}}=-Ke$$

(19)

Therefore,

$$\dot{V}=-e^{T}QKe\le -{\lambda }_{\min }\left(QK\right){‖e‖}^2$$

(20)

which proves exponential convergence of $e$ to zero. In practice, the disturbance term $\Delta \left(h_1,h_2,\mathit{\zeta }\right)$ is estimated and compensated by the ESO described in Step 3, further improving robustness under model uncertainties and external disturbances.

Combining Equations (1) and (13), the decoupled force–motion equation can be written as

$$\left[\begin{array}{c}{\dot{V}}_x\\ {\dot{V}}_z\end{array}\right]=S_b^e\left[\begin{array}{c}\dot{u}\\ \dot{w}\end{array}\right]=S_b^e\left[\begin{array}{c}{\displaystyle \frac{1}{m}}{F}_x\\ {\displaystyle \frac{1}{m}}{F}_z\end{array}\right]$$

(21)

By substituting Equation (18) into Equation (21), the force control command is obtained as

$$\left[\begin{array}{c}{F}_{xc2}\\ F_{zc2}\end{array}\right]=m{\left(S_b^e\right)}^T\left[\begin{array}{c}-K_{a_x}\left(a_x-a_{xg}\right)+{\dot{V}}_{xg}\\ -K_{a_z}\left(a_z-a_{zg}\right)+{\dot{V}}_{zg}\end{array}\right]$$

(22)

and, similarly, the required three-axis moments are given by

$$\left[\begin{array}{c}{M}_{xc2}\\ M_{yc2}\\ M_{zc2}\end{array}\right]=diag(I_x,I_y,I_z)\left[\begin{array}{c}-K_p(p-p_c)+{\dot{p}}_c\\ -K_q(q-q_c)+{\dot{q}}_c\\ -K_r(r-r_c)+{\dot{r}}_c\end{array}\right]$$

(23)

Remark 4. 

${\dot{V}}_{xg},{\dot{V}}_{zg},{\dot{p}}_c,{\dot{q}}_c,{\dot{r}}_c$ are obtained using a tracking differentiator [39,40].

Step 3: Design of ESO Control Law. By substituting the control laws obtained in steps 1 and 2 into Equation (9), the inner-loop dynamics can be written as

$${\dot{\mathit{X}}}_1=U_3+\Delta \left(h_1,h_2,\mathit{\zeta }\right)$$

(24)

To mitigate the influence of the disturbance term on the transition-flight control performance, we define $X_2=\Delta \left(h_1,h_2,\mathit{\zeta }\right)$. Assuming ${\dot{\mathit{X}}}_2=\eta$ (a bounded, varying disturbance), the augmented system is given by

$$\left\{\begin{array}{l}{\dot{\mathit{X}}}_1=U_3+X_2\\ {\dot{\mathit{X}}}_2=\mathit{\eta }\end{array}\right.$$

(25)

The ESO is constructed as follows:

$$\left\{\begin{array}{l}{\widehat{\dot{\mathit{X}}}}_1=U_3+{\widehat{\mathit{X}}}_2+{\beta }_1\left(X_1-{\widehat{\mathit{X}}}_1\right)\\ {\widehat{\dot{\mathit{X}}}}_2={\beta }_2\left(X_1-{\widehat{\mathit{X}}}_1\right)\end{array}\right.$$

(26)

Combining Equations (25) and (26), the system can be rewritten in state-space form as

$$\left[\begin{array}{c}{\widehat{\dot{\mathit{X}}}}_1\\ {\widehat{\dot{\mathit{X}}}}_2\end{array}\right]=\left[\begin{array}{cc}-{\beta }_1& 1\\ -{\beta }_2& 0\end{array}\right]\left[\begin{array}{c}{\widehat{\mathit{X}}}_1\\ {\widehat{\mathit{X}}}_2\end{array}\right]+\left[\begin{array}{cc}1& {\beta }_1\\ 0& {\beta }_2\end{array}\right]\left[\begin{array}{c}{U}_3\\ X_1\end{array}\right]$$

(27)

Based on the definitions of the estimation errors $e_1=X_1-{\widehat{\mathit{X}}}_1$ and $e_2=X_2-{\widehat{\mathit{X}}}_2$, the corresponding differential equations are given by

$$\left[\begin{array}{c}{\dot{e}}_1\\ {\dot{e}}_2\end{array}\right]=\underset{A}{\underbrace{\left[\begin{array}{cc}-{\beta }_1& 1\\ -{\beta }_2& 0\end{array}\right]}}\left[\begin{array}{c}{\dot{e}}_1\\ {\dot{e}}_2\end{array}\right]+\underset{B}{\underbrace{\left[\begin{array}{c}0\\ 1\end{array}\right]}}\eta$$

(28)

The characteristic equation of the error system is

$$\det \left(sI-A\right)=0$$

(29)

Let the eigenvalues be $s=-{\omega }_0,{\omega }_0>0$, and the system is stable, and thus the gain ${\beta }_1=2{\omega }_0$, ${\beta }_2={\omega }_0^2$ is determined. Setting $U_3=-{\widehat{\mathit{X}}}_2$ cancels lumped disturbances. Therefore, the compensation force and moment demands are expressed as

$$\left[\begin{array}{c}\begin{array}{c}{F}_{xc3}\\ F_{zc3}\end{array}\\ M_{xc3}\\ M_{yc3}\\ M_{zc3}\end{array}\right]=-diag(m,m,I_x,I_y,I_z){\widehat{\mathit{X}}}_2$$

(30)

Thus, the design of the inner-loop control law is completed.

4.3. Design of Outer-Loop Control Law

4.3.1. Design of Attitude-Angle Control Law

Within the controller bandwidth, we have $p\approx p_c,q\approx q_c,r\approx r_c$. Accordingly, Equation (4) can be formulated as

$$\underset{\dot{\mathsf{\Omega }}}{\underbrace{\left[\begin{array}{c}\dot{\varphi }\\ \dot{\theta }\\ \dot{\psi }\end{array}\right]}}=\left[\begin{array}{c}{p}_c+\left(r\cos \varphi +q\sin \varphi \right)\tan \theta \\ q_c\cos \varphi -r\sin \varphi \\ {\displaystyle \frac{1}{\cos \theta }}\left(r_c\cos \varphi +q\sin \varphi \right)\end{array}\right]$$

(31)

Defining the attitude error as $e_{\varphi \theta \psi }=\mathit{\Omega }-{\Omega }_c$, its differential can be written as

$${\dot{\mathit{e}}}_{\varphi \theta \psi }=\dot{\mathit{\Omega }}-{\dot{\mathit{\Omega }}}_c$$

(32)

According to the NDIC design procedure in step 2 of Section 4.2 and Equation (31), the attitude control law is formulated as

$$\left[\begin{array}{c}{p}_c\\ q_c\\ r_c\end{array}\right]=\left[\begin{array}{c}{\dot{\varphi }}_c-\tan \theta \left(r\cos \varphi +q\sin \varphi \right)\\ {\displaystyle \frac{1}{\cos \varphi }}\left({\dot{\theta }}_c+r\sin \varphi \right)\\ {\displaystyle \frac{\cos \theta }{\cos \varphi }}{\dot{\psi }}_c-q\tan \varphi \end{array}\right]-\left[\begin{array}{c}{K}_p^{\varphi }\\ K_p^{\theta }\\ K_p^{\psi }\end{array}\right]e_{\varphi \theta \psi }$$

(33)

where $K_p^{\varphi }>0,K_p^{\theta }>0,K_p^{\psi }>0$.

4.3.2. Design of Airspeed Control Law

Within the controller bandwidth, we have $a_x\approx a_{xg},a_z\approx a_{zg}$. Defining the airspeed error as $e_V=X_V-X_{Vc}$, its time derivative is obtained as

$${\dot{\mathit{e}}}_V={\dot{\mathit{X}}}_V-{\dot{\mathit{X}}}_{Vc}=\left[\begin{array}{c}{\dot{V}}_x\\ {\dot{V}}_z\end{array}\right]-\left[\begin{array}{c}{\dot{V}}_{xg}\\ {\dot{V}}_{zg}\end{array}\right]\approx \left[\begin{array}{c}{a}_{xg}\\ a_{zg}\end{array}\right]-\left[\begin{array}{c}{\dot{V}}_{xg}\\ {\dot{V}}_{zg}\end{array}\right]$$

(34)

Thus, the velocity control law is designed as

$$\left[\begin{array}{c}{a}_{xg}\\ a_{zg}\end{array}\right]=-K_V{e}_V+\left[\begin{array}{c}{\dot{V}}_{xg}\\ {\dot{V}}_{zg}\end{array}\right]$$

(35)

where $K_V=diag(k_{vx},k_{vz})$ and $k_{vx}>0,k_{vz}>0$.

4.3.3. Design of Altitude Control Law

Similar, when $\dot{H}=V_z$ and $V_z\approx V_{zg}$ hold within the bandwidth of the controller, the altitude control law is designed as

$$V_{zg}=-K_p^H\left(H-H_g\right)+{\dot{H}}_g$$

(36)

where $K_p^H>0$ and $H_g$ denotes the altitude command.

4.4. Design of Aerodynamic Lift Regulator

As described in Section 3.1, due to aerodynamic uncertainties, discrepancies may arise between the required and actual aerodynamic lift, leading to altitude fluctuations. Specifically, if the actual lift coefficient is smaller than its nominal value, the generated lift falls short of the required lift and the UAV descends; conversely, an overestimated lift coefficient yields excess lift and the UAV climbs.

To mitigate this issue, we propose an aerodynamic lift regulation and compensation strategy through pitch angle commands. The underlying principle is to adjust the aerodynamic lift by modifying the flight angle of attack. The aerodynamic lift is reformulated as

$$L=Q{S}_{ref}\left(C_{L0}+k_a\left(a_r+\Delta a\right)\right)$$

(37)

where $k_a$ is the slope of the lift coefficient and $C_{L0}$ is the zero-lift coefficient. Based on the principle that the demanded lift equals the lift generated at the current angle of attack, the compensatory increment of angle of attack $\Delta \alpha$ is derived as

$$\Delta \alpha ={\displaystyle \frac{{\mathrm{w}}_{\alpha }\times F_c\left(2\right)-Q{S}_{ref}{C}_{L0}}{k_{\alpha }Q{S}_{ref}}}-{\alpha }_r$$

(38)

To prevent stall, the compensation term of the angle-of-attack regulator satisfies: $\left|\Delta \alpha \right|\le 5^{°}$.

5. Simulations and Results

This section presents validation results that demonstrate the rationale of the proposed control scheme shown in Figure 4. The simulations are conducted on a software platform using MATLAB/SIMULINK 2023B. The solver is set to ode4, the Runge–Kutta method is employed in a fixed-step simulation mode, and the simulation step size is set to 0.01 s.

The initial simulation hover altitude, airspeed, and attitude of the QTR UAV were set as $\left(H_0,V_{x0},{\varphi }_0,{\theta }_0,{\psi }_0\right)=\left(100 \mathrm{m},0 \mathrm{m}/\mathrm{s},0^{°},0^{°},0^{°}\right)$, and the transition terminal fixed-wing flight state was selected as $\left(H_t,V_{xt},{\varphi }_t,{\theta }_t,{\psi }_t\right)=\left(100 \mathrm{m},30 \mathrm{m}/\mathrm{s},0^{°},5^{°},0^{°}\right)$. For a thorough assessment of the method’s effectiveness under different performance requirements and transition strategies, two cases featuring various forward accelerations are outlined in

Table 1. Desired airspeed commands.

Case	Transition Command
1	$\left(H_c,{\dot{V}}_{xc},{\varphi }_c,{\theta }_c,{\psi }_c\right)=\left(100 \mathrm{m},1 {\mathrm{m}/\mathrm{s}}^2,0^{\circ },5^{\circ },0^{\circ }\right)$
2	$\left(H_c,{\dot{V}}_{xc},{\varphi }_c,{\theta }_c,{\psi }_c\right)=\left(100 \mathrm{m},3 {\mathrm{m}/\mathrm{s}}^2,0^{\circ },5^{\circ },0^{\circ }\right)$

, and the physical QTR parameters and the proposed control parameters are presented in

Table 2. Physical parameters and flight control parameters of QTR.

Parameter	Value
Mass $m$ (kg)	100
Nacelle angle $\tau$ (°)	$\left[0,95\right]$
Nacelle deflection rate $\dot{\tau }$ (°/s)	[−20, 20]
Thrust coefficient $k_f$	[1.70, 1.55, 1.64, 1.60, 1.55, 1.55, 1.45, 1.40] × ${10}^{-5}$
Torque coefficient $k_m$	[8.86, 8.61, 8.67, 9.11, 9.00, 10.01, 9.97, 10.68] × ${10}^{-7}$
Rotor speed $n$ (rpm/min)	[0, 5500]
Aerodynamic surfaces (°)	$\left|{\delta }_e\right|\le 20,\left|{\delta }_a\right|\le 20,\left|{\delta }_r\right|\le 20$
Reference area $S_{ref}$ (m2)	2.317
Wing span/chord [$b,c_A$] (m)	[1.55, 0.55]
Distance from CG to i-th rotor along x/y axis (m)	$l_{ix}=1.2,l_{iy}=1.4$
Moments of inertia $I_{xyz}$ ($\mathrm{kg}\cdot {\mathrm{m}}^2$)	$\left(44.8,0,-4.82;0,80.6,0;-4.82,0,122.4\right)$
NDIC gains	$K_{pqr}=\left(4,4,4\right)$, $K_p^{\mathsf{\Omega }}=\left(10,10,5\right)$, $k_p^{a_x}=2$, $k_p^{a_z}=1$, $k_p^{V_x}=2$, $k_p^{V_z}=1$, $k_p^H=0.2$
ESO parameters	${\beta }_1=\left[10,10,20,20,20\right],{\beta }_2=\left[25,25,100,100,100\right]$
PID gains	$k_{PID}^{pqr}=\left(\begin{array}{l}3.5,1.1,0.1\\ 5.6,1.6,0.3\\ 3.7,0.8,0.1\end{array}\right)$, $k_{PID}^{\mathsf{\Omega }}=\left(\begin{array}{l}3.5,0,0.6\\ 2.6,0.5,0.2\\ 1.7,0,0.2\end{array}\right)$ $k_{PID}^{a_{x\mathrm{z}}}=\left(\begin{array}{l}2.6,1.2,0.4\\ 1.5,0.7,0.3\end{array}\right)$, $k_{PID}^{V_{x\mathrm{z}}}=\left(\begin{array}{l}3.5,0,0.4\\ 2.6,0,0.2\end{array}\right)$ $k_{PID}^H=\left(0.2,0,0\right)$

.

5.1. Simulation Results of Asynchronous Tilt Control Scheme

In this part, to validate the effectiveness of the designed NDIC-ESO control scheme, simulations were conducted under the asynchronous tilt transition strategy and two different desired forward acceleration conditions as outlined in Table 1.

5.1.1. Analysis of Control Allocation Strategy

The simulation results of the proposed two-level control allocation for the two cases are presented in Figure 5. As shown in Figure 5a, the results for the first-level control allocation weights indicate that the force weight exchanges faster than the moment weight. When the aerodynamic force weight transition is completed, the rotor-subsystem moment control weight accounts for about 47% of the total aircraft control authority. This suggests that when the fixed-wing flight condition is safely established, the rotor subsystem still retains good control capability. Consequently, the proposed weight allocation strategy ensures a smooth transition between the rotor and aerodynamic subsystems without any uncontrollable areas, while maintaining a control margin overlap region that enhances tilt transition safety.

Figure 5b–f present the results of the proposed two-level control allocation compared to the SQP method without the first-level control strategy.

Table 3. Maximum steady-state errors under cases 1 and 2.

Cases 1 and 2	Proposed Control Allocation	Only SQP Control Allocation
Forward force	2.6% and 3.3%	5.6% and 6.3%
Vertical force	3.1% and 3.7%	5.5% and 6.9%
Roll moment	5.2% and 6.1%	9.2% and 10.1%
Pitch moment	3.6% and 4.3%	5.1% and 7.3%
Yaw moment	5.6% and 6.3%	7.1% and 9.6%

summarizes the maximum steady-state allocation errors for cases 1 and 2. Notably, these results confirm that the proposed two-level control allocation strategy is not only feasible but also achieves higher control accuracy and better dynamic performance compared to the SQP strategy, demonstrating its effectiveness in maintaining precise and stable control during the transition flight regime.

5.1.2. Analysis of Control Performance with NDIC and ESO

The simulation results of the proposed control scheme for the two cases are illustrated in Figure 6a. The transition procedure is divided into four phases: hovering (0–10 s), transition-attitude adjustment (10–20 s), forward-acceleration transition (case 1: 20–50 s; case 2: 20–30 s), and fixed-wing cruise (case 1: 50–70 s; case 2: 30–70 s). Because of the different desired forward accelerations in Table 2, the corresponding tilt-transition durations are 30 s and 10 s, respectively.

To provide an ablation study, we compare NDIC–ESO with NDIC (without ESO) under the same allocation scheme. PID is only used as a conventional baseline for reference. As shown in Figure 6b–f, the results indicate that the NDIC-ESO controller achieves significantly more accurate tracking performance compared with the NDIC controller.

The maximum control errors of different control methods under two transition cases are summarized in

Table 4. Maximum control errors under cases 1 and 2.

Cases 1 and 2	NDIC–ESO	NDIC	PID
Max airspeed error	[0.1, 0.1] m/s	[0.3, 0.4] m/s	[0.6, 0.7] m/s
Max pitch error	[0.1, 0.1]°	[0.2, 0.2]°	[0.4, 0.5]°
Max roll error	[0.2, 0.2]°	[0.9, 1.0]°	[2.1, 3.5]°
Max yaw error	[0.2, 0.2]°	[1.5, 1.7]°	[2.2, 5.5]°
Max altitude deviation	[1.8, 1.9] m	[1.8, 2.0] m	[1.9, 2.2] m

. Clearly, the maximum airspeed tracking error remains within 0.1 m/s, the maximum attitude error does not exceed 0.2°, and the peak altitude fluctuation is approximately 1.9 m. For lateral motion, the maximum roll and yaw errors remain below 0.3°, both outperforming the NDIC controller. Furthermore, the dynamic response characteristics during the tilt transition demonstrate good smoothness and stability.

Figure 7a–c present the control inputs of the NDIC-ESO controller for cases 1 and 2. The rotor speeds, nacelle angles, and elevator deflections vary smoothly and remain within their respective safety limits. Therefore, the above analyses verify that the proposed asynchronous transition strategy with the NDIC-ESO control framework has high-quality transition-flight performance and robustness.

5.1.3. Robustness Analysis

To further verify the robustness of the proposed approach in the transition process, performance evaluations are conducted under both external disturbance and model uncertainty conditions in case 1. As listed in

Table 5. Robustness verification conditions.

A: External Disturbances	B: Model Uncertainties
Wind: Dryden gust model	Mass variation: ±15%
Sensor noise: White Gaussian Noise	Surface effectiveness: ±15%
Time delay: 50 ms	Aerodynamic efficiency: ±15%

, the external disturbances simultaneously consider wind effects, sensor noise, and time delays, whereas the model uncertainties encompass mass variations, control surface effectiveness deviations, and aerodynamic efficiency variations.

Figure 8 presents the simulation results under the simultaneous presence of multiple external disturbances. Specifically, Figure 8a–c illustrate the transitional state responses, while Figure 8d–f show the corresponding control input responses. The maximum state tracking errors under combined disturbances are summarized in

Table 6. Maximum state tracking errors under combined disturbances.

Cases 1	External Disturbances	Model Uncertainties
Max airspeed error	0.5 m/s	0.2 m/s
Max pitch error	0.5°	0.6°
Max altitude deviation	3.5 m	6.2 m

. The results indicate that the maximum airspeed error is 0.5 m/s, the maximum pitch-angle error is approximately 0.5°, and the maximum altitude fluctuation is about 3.5 m. Compared with the results in Table 4, the transition performance under multiple disturbances exhibits a slight degradation; however, the transition responses remain within a safe and acceptable range, thereby satisfying the tilt-transition performance requirements.

Figure 9 shows the simulation results under model uncertainties. The model uncertainties include the mass, the control-surface effectiveness, and the aerodynamic model effectiveness, with a perturbation magnitude of ±15%. In the figure, the case denoted by (+−−) corresponds to a 15% increase in mass, together with a 15% decrease in control-surface effectiveness and aerodynamic model effectiveness; whereas the case (−++) indicates a 15% decrease in mass and a 15% increase in both surface effectiveness and aerodynamic model effectiveness. Specifically, Figure 9a–c present the transitional state responses, and Figure 9d–f depict the corresponding control input responses. The simulation results demonstrate that, after model uncertainties, the steady-state terminal pitch angle is 4.5° for the (+−−) case and 1.2° for the (−++) case. The corresponding aerodynamic trim elevator deflections are −5° and −3°, respectively. Compared with the nominal results in Table 4, the transition response under model uncertainties converges to a different steady-state trim condition; however, the system remains within a safe operating envelope, thereby meeting the tilt-transition performance requirements.

In summary, although the proposed control architecture exhibits a slight degradation in transition performance under external disturbances and model uncertainties, the desired state responses remain within the prescribed safety limits and continue to satisfy the tilt-transition handling quality and safety requirements. Therefore, the proposed control architecture is validated to be robust, maintaining acceptable transition performance in the presence of both external disturbances and model uncertainties.

5.2. Simulation Results of Tilt Transition Strategies

In this part, we evaluated the control quality of CG fluctuations and the maximum forward acceleration capability under both asynchronous and synchronous tilt transition strategies.

5.2.1. Sensitivity Analysis of CG

With the nacelle angle tilting level, we assumed that the CG was shifted forward with $\Delta CG=0.1m\cdot \cos \tau$, and the simulation results of the asynchronous and synchronous tilt strategies are presented in Figure 10.

Notably, as shown in Figure 10a, all rotor speeds remain within the allowable operating range under the asynchronous strategy. However, the synchronous strategy leads to the complete stoppage of rotors 3 and 4 to counteract the increased pitch moment. Given the considerable restart delay inherent in electric propulsion systems, such rotor shut-down behavior is infeasible for practical flight operations. In addition, as shown in Figure 10b,c, the altitude fluctuation under the asynchronous strategy is about 2 m, which is significantly smaller than the 4.2 m under the synchronous strategy. The pitch angle exhibits a 0.2° tracking error under the asynchronous strategy, whereas a non-negligible and gradually increasing pitch-angle tracking error occurs under the synchronous strategy, with the maximum reaching 1.2°. Furthermore, as indicated by the velocity and forward acceleration dynamics in Figure 10e,f, the asynchronous tilt transition exhibits better control quality.

Based on the above analysis, when the CG shifts forward, the asynchronous tilt strategy exhibits improved control performance compared to the synchronous one, as summarized in

Table 7. Performance comparison under CG shift: Asynchronous vs. Synchronous Strategies.

	Asynchronous Strategy	Synchronous Strategy
Max airspeed error	0.1 m/s	0.5 m/s
Max pitch angle error	0.2°	1.2°
Max altitude deviation	2.0 m	4.2 m

. More importantly, under CG shift conditions, the synchronous strategy results in rotor shutdowns to balance the pitching moment, which significantly degrades transition safety and is therefore unacceptable. In contrast, the asynchronous strategy maintains all rotor speeds within safe and reasonable operating ranges. These results demonstrate the highlight advantages of the asynchronous tilt transition strategy.

5.2.2. Capability Analysis of Maximum Acceleration

To further investigate the maximum acceleration capability of the tilt transition strategy, an impulse airspeed command was applied, and the simulation results are presented in Figure 11a. It can be seen that the asynchronous tilt strategy completes a transition duration of approximately 3.2 s and a maximum forward acceleration of about 16.1 m/s², whereas the synchronous tilt strategy requires about 6.6 s and reaches a maximum acceleration of 9.0 m/s². Thus, the transition time of the asynchronous strategy is reduced by approximately 50% compared with the synchronous strategy, and its peak acceleration is nearly twice as high. In addition, Figure 11b,c show that the altitude fluctuations with the asynchronous strategy are only 50% of those observed with the synchronous strategy.

Based on the above analysis, the asynchronous transition strategy not only provides better control performance compared with the synchronous strategy but also offers improved adaptability to dynamic flight conditions, enhancing transition safety and expanding the operational envelope.

6. Discussion

The proposed asynchronous NDIC–ESO transition framework is designed for practical onboard implementation. The asynchronous tilt schedule can be realized using a simple command generator, without requiring additional sensing or computationally intensive online optimization. CG-sensitivity simulations further indicate that a synchronous transition can trigger undesirable actuator behaviors—for example, rotor shutdown to counter excessive pitch moments under forward CG shifts—which is impractical in light of non-negligible restart delays in electric propulsion and the associated risks to safety and controllability. By keeping all actuators within allowable limits and avoiding prolonged idleness, the asynchronous strategy enhances feasibility and increases safety margins during transition.

The two-level control allocation is likewise suitable for real-time execution. At the first level, capability-based weighting explicitly redistributes control authority between rotors and aerodynamic surfaces according to their instantaneous effectiveness, thereby reducing both tuning effort and numerical burden for the second-level SQP allocator. The SQP layer then enforces actuator constraints and command smoothness objectives, helping to prevent saturation and abrupt control inputs. Finally, the NDIC–ESO controller is computationally lightweight and relies only on standard onboard measurements (IMU, airspeed estimate, nacelle angle, and rotor speed). The ESO compensates for lumped disturbances, improving robustness without requiring a high-fidelity aerodynamic model. Overall, the achieved tracking performance with bounded control inputs suggests that the proposed framework is well suited for embedded transition-flight control.

7. Conclusions

An asynchronous tilt-transition control framework coordinated with NDIC and an ESO is proposed for a QTR UAV to improve transition performance under varying flight conditions. The asynchronous transition strategy reduces sensitivity to CG variations and substantially increases the achievable forward acceleration, demonstrating better adaptability than the conventional synchronous strategy. To ensure control accuracy and meet performance requirements, a two-level control allocation scheme is introduced to coordinate the rotor and aerodynamic-surface subsystems, enabling effective matching between the demanded control effort and the available actuation capability. Building on this allocation architecture, an NDIC controller augmented with an ESO is developed to achieve accurate tracking of the asynchronous transition commands. The simulation results under the tested conditions show that the proposed NDIC–ESO approach achieves high-precision tracking and favorable flight-dynamic behavior with bounded actuator inputs. Overall, the asynchronous NDIC–ESO-based framework provides an effective and reliable solution for transition-flight control of QTR UAVs. Future work will focus on flight experiments involving the QTR UAV to further validate the proposed method.