The motion of an aircraft in the atmosphere is inherently complex, characterized by nonlinearity, strong coupling, and uncertainty. This makes it challenging to develop an accurate mathematical model, as the system is also vulnerable to random disturbances such as wind gusts. Moreover, aerodynamic parameters can vary significantly under different flight conditions. As a result, designing a reliable attitude control system is essential for ensuring that the aircraft follows its intended trajectory accurately. While PID control is widely used due to its simplicity, reliability, and stable performance, it often falls short in harsh environments where high accuracy and stability are required. In such cases, traditional PID or even improved versions may not be sufficient to meet the demands.
To address these challenges, this paper integrates PID control with fuzzy control techniques in the aircraft attitude control system. Fuzzy control is an intelligent method that mimics human decision-making and does not rely on precise mathematical models. It is particularly effective in handling uncertainties and random disturbances. However, fuzzy control alone may struggle with steady-state errors. By combining it with PID control, we can compensate for these shortcomings and achieve better overall performance. Additionally, an automatic correction factor is introduced to dynamically adjust the fuzzy controller’s parameters in real time, ensuring optimal dynamic response across a wide range of operating conditions.
### 1. Fuzzy-PID Controller Design
#### 1.1 Overall Design
The fundamental principle of the Fuzzy-PID control system is illustrated in Figure 1. The system comprises two main components: a fuzzy controller and a PID controller. The inputs to the system are the error (e) and the rate of change of the error (ec), while the output is the control signal (u). The system selects between fuzzy and PID control based on the magnitude of the error. When the error is large, the fuzzy control algorithm is activated to enhance the control action, reduce overshoot, and speed up the system's response. Conversely, when the error is small, the PID controller takes over to minimize steady-state error and improve static performance. This hybrid approach offers superior control performance compared to using either method alone. The design of the PID controller itself is not repeated here.
#### 1.2 Fuzzy Controller Design with Automatic Correction Factor
Designing a fuzzy controller involves five key steps: (1) defining the structure of the controller, (2) selecting quantization and scaling factors to determine input and output variables, (3) defining fuzzy linguistic values and membership functions, (4) establishing fuzzy rules and choosing an approximate reasoning algorithm, and (5) determining the defuzzification method. Among these, the formulation of fuzzy control rules based on operator experience is critical to the performance of the controller.
Let the input variables be the error (e) and the rate of change of error (ec), and the output variable be the control signal (u). The fuzzy sets commonly used include {Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Medium (PM), Positive Big (PB)}. The selection of control actions depends on the size of the error: when the error is large, the goal is to eliminate it quickly; when it is small, the focus shifts to maintaining system stability and avoiding overshoot. Based on expert knowledge, the fuzzy control rules are summarized in Table 1.
The quantization factors for the error (K1) and the error change rate (K2) play a significant role in determining the performance of the fuzzy controller. A larger K1 increases the system’s overshoot and prolongs the transient process, while a smaller K1 leads to slower responses and lower steady-state accuracy. Similarly, a higher K2 reduces overshoot but slows down the system’s response, whereas a lower K2 results in faster response but increased overshoot. The scaling factor K3 influences the system’s dynamic behavior and is closely related to the specific control object.
In practical applications, to ensure rapid response and reduced overshoot, an automatic correction factor (n) is introduced into the conventional fuzzy controller. This factor adjusts the weighting of the error and error change rate during the control process, allowing the system to adapt in real time and achieve improved control performance.
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