In recent years, drone technology has revolutionized various fields, including military reconnaissance, environmental monitoring, and disaster response, due to its versatility and efficiency. Unmanned Aerial Vehicles (UAVs), particularly fixed-wing types, offer advantages such as long endurance and high payload capacity, making them ideal for complex missions. However, controlling the longitudinal attitude of these drones poses significant challenges, including model uncertainties and external disturbances like wind gusts. Traditional control methods, such as PID, often fall short in handling these nonlinearities, leading to reduced performance. This paper addresses these issues by proposing an adaptive sliding mode control approach integrated with Radial Basis Function Neural Networks (RBFNN). By leveraging drone technology advancements, this method enhances robustness and precision in Unmanned Aerial Vehicle operations, ensuring stable flight under adverse conditions.
The longitudinal dynamics of a fixed-wing Unmanned Aerial Vehicle can be modeled as a nonlinear rigid-body system with uncertainties. The equations of motion involve key parameters like angle of attack, pitch angle, and pitch rate, which are critical for attitude control. Let $$ \alpha $$ represent the angle of attack, $$ \theta $$ the pitch angle, and $$ q $$ the pitch rate. The dynamics are described by:
$$ \dot{\alpha} = f_\alpha + \Delta f_\alpha $$
$$ \dot{q} = f_q + \Delta f_q $$
$$ \dot{\theta} = q $$
where $$ f_\alpha $$ and $$ f_q $$ are the known modeled terms, and $$ \Delta f_\alpha $$ and $$ \Delta f_q $$ represent the composite disturbances, including unmodeled dynamics and external interferences. For instance, $$ f_\alpha $$ can be expressed as:
$$ f_\alpha = q – \frac{g \sin \theta}{V} + \frac{\bar{q} S C_L}{m V} $$
and $$ f_q $$ as:
$$ f_q = \frac{\bar{q} S c C_m}{I_y} $$
Here, $$ m $$ is the mass, $$ V $$ the velocity, $$ g $$ gravity, $$ \bar{q} $$ dynamic pressure, $$ S $$ wing area, $$ c $$ mean aerodynamic chord, $$ C_L $$ lift coefficient, $$ C_m $$ pitching moment coefficient, and $$ I_y $$ the moment of inertia. The disturbance terms $$ \Delta f_\alpha $$ and $$ \Delta f_q $$ encapsulate uncertainties such as aerodynamic variations and external torques, which are approximated using RBFNN in the control design. This modeling foundation is essential for advancing drone technology in Unmanned Aerial Vehicle applications.
To design the attitude controller, we focus on tracking a desired pitch angle command $$ \theta_d $$. Define the tracking error as $$ e = \theta – \theta_d $$. The sliding surface is chosen as:
$$ s = \dot{e} + \lambda e $$
where $$ \lambda > 0 $$ is a design parameter. The derivative of the sliding surface is:
$$ \dot{s} = \ddot{e} + \lambda \dot{e} = \dot{q} + \lambda \dot{e} – \ddot{\theta}_d = f_q + \Delta f_q – \ddot{\theta}_d + \lambda \dot{e} $$
A sliding mode reaching law is adopted:
$$ \dot{s} = -k \text{sgn}(s) – \eta s $$
with $$ k > 0 $$ and $$ \eta > 0 $$. Ignoring disturbances initially, the control law for the elevator deflection $$ \delta_e $$ is derived as:
$$ \delta_e = \left( -k \text{sgn}(s) – \eta s – f_q + \ddot{\theta}_d – \lambda \dot{e} \right) / \left( \frac{\bar{q} S c C_{m_{\delta_e}}}{I_y} \right) $$
However, to handle the unknown disturbance $$ \Delta f_q $$, an RBF neural network is employed. The RBFNN approximates $$ \Delta f_q $$ as:
$$ \Delta f_q = W^T \phi(x) + \epsilon $$
where $$ x = [\theta, q]^T $$ is the input vector, $$ \phi(x) $$ is the Gaussian basis function vector, $$ W $$ is the ideal weight vector, and $$ \epsilon $$ is the approximation error bounded by $$ |\epsilon| \leq \bar{\epsilon} $$. The Gaussian function for each node $$ i $$ is:
$$ \phi_i(x) = \exp\left( -\frac{\|x – c_i\|^2}{2\sigma_i^2} \right) $$
To reduce computational complexity, a minimal learning parameter method is used, where a single parameter $$ \hat{\Theta} $$ estimates the upper bound of the weights. The adaptive control law becomes:
$$ \delta_e = \left( -k \text{sgn}(s) – \eta s – f_q – \frac{1}{2} \hat{\Theta} \phi^T \phi + \ddot{\theta}_d – \lambda \dot{e} \right) / \left( \frac{\bar{q} S c C_{m_{\delta_e}}}{I_y} \right) $$
with the adaptive update law:
$$ \dot{\hat{\Theta}} = \frac{\gamma}{2} s^2 \phi^T \phi – \sigma \gamma \hat{\Theta} $$
where $$ \gamma > 0 $$ and $$ \sigma > 0 $$ are adaptation gains. Stability is proven using Lyapunov theory. Consider the Lyapunov function:
$$ V = \frac{1}{2} s^2 + \frac{1}{2\gamma} \tilde{\Theta}^2 $$
where $$ \tilde{\Theta} = \hat{\Theta} – \Theta $$ is the estimation error. Its derivative yields:
$$ \dot{V} = s \dot{s} + \frac{1}{\gamma} \tilde{\Theta} \dot{\hat{\Theta}} $$
Substituting the control and adaptive laws, it can be shown that $$ \dot{V} \leq – \eta s^2 – \frac{\sigma}{2} \tilde{\Theta}^2 + \Delta $$, where $$ \Delta $$ is a bounded term, ensuring uniform ultimate boundedness of the system. This approach significantly enhances the robustness of Unmanned Aerial Vehicle control in drone technology applications.
Simulation studies were conducted to validate the proposed method. The fixed-wing UAV parameters are summarized in Table 1.
| Parameter | Value | Unit |
|---|---|---|
| Mass (m) | 1400 | kg |
| Wing Area (S) | 10 | m² |
| Mean Chord (c) | 1.3 | m |
| Moment of Inertia (I_y) | 5400 | kg·m² |
| Initial Velocity (V) | 516 | km/h |
| Initial Altitude | 5000 | m |
The desired pitch angle is set to 3°, and external disturbances are applied as $$ \Delta \tau = 500 \times [0.2 \sin(3t) + 0.3 \cos(t)] $$ N·m. Aerodynamic parameters are perturbed by 20% to simulate uncertainties. The controller parameters are: $$ \lambda = 1.5 $$, $$ k = 30 $$, $$ \eta = 0.01 $$, $$ \gamma = 150 $$, and $$ \sigma = 0.1 $$. For comparison, PID and conventional SMC are also implemented. The PID gains are tuned to $$ K_p = 0.25 $$, $$ K_i = 0.33 $$, $$ K_d = 0.19 $$.
The simulation results demonstrate the superiority of the RBFNN-based adaptive SMC. Under nominal conditions, all controllers achieve tracking, but the proposed method shows faster response and lower steady-state error. With disturbances and parameter variations, the PID controller exhibits oscillations, while SMC has minor fluctuations. The RBF-SMC maintains precise tracking, highlighting its robustness. Table 2 summarizes the performance metrics.
| Controller | Rise Time (s) | Overshoot (%) | Steady-State Error (°) |
|---|---|---|---|
| PID | 10.2 | 5.1 | 0.15 |
| SMC | 2.5 | 0.0 | 0.02 |
| RBF-SMC | 1.8 | 0.0 | 0.01 |
Further analysis involves the control input and angular rate responses. The RBF-SMC generates smoother control signals, reducing chattering common in traditional SMC. The angular rate $$ q $$ converges rapidly with the proposed method, ensuring stability. The external disturbance torque profile is plotted to illustrate the challenging conditions. These results affirm that the integration of neural networks with sliding mode control elevates the capabilities of drone technology in handling real-world uncertainties for Unmanned Aerial Vehicles.
In conclusion, this paper presents a novel adaptive sliding mode control strategy using RBF neural networks for the longitudinal attitude control of fixed-wing UAVs. The method effectively compensates for model uncertainties and external disturbances, proven through Lyapunov stability analysis. Simulations show that it outperforms PID and conventional SMC in terms of accuracy and robustness. This advancement in drone technology paves the way for more reliable and autonomous Unmanned Aerial Vehicle operations in dynamic environments. Future work will focus on experimental validation and extension to full six-degree-of-freedom control.
The application of such intelligent control systems is crucial for the evolution of drone technology, as Unmanned Aerial Vehicles become increasingly integral to modern aviation. By addressing key challenges in attitude control, this research contributes to safer and more efficient UAV deployments, highlighting the transformative potential of adaptive neural networks in aerospace engineering.