Simulink Modeling of Fighter Aircraft Longitudinal Motion: Pitch Rate Control

This article aims to utilize Simulink for simulating a simplified model of a fighter aircraft's longitudinal motion.

The 'angle of attack' represents the angle between the aircraft's pointing direction and its actual movement through the air. For an aircraft flying at a relatively constant altitude, this angle equates to the 'pitch angle', as depicted in Fig. 3. This angle is crucial as it generates a lift force perpendicular to the aircraft's axis, resulting in a 'normal acceleration', also illustrated in the figure.

Pilots aim to control the pitch angle, achieving this through the rotation of the aircraft's front fins and tail elevators, shown in Fig. 4. Consequently, the first task involves modeling the effect of these movements on the 'pitch rate', q.

b. Pitch Rate, q

The rate of change in the pitch angle, the 'pitch rate', q, is primarily influenced by the angle of the aircraft's front fins, as illustrated in Fig. 4. Aerodynamic modeling reveals that this relationship can be expressed by the following differential equation:

Q(s)/d(s)=(7.25s+11.27)/(s^2+3.1s-8.82)

where the gain refers to the gears, with a value of -5.

Before conducting real-world experiments, designers utilize simulations to analyze the aircraft's response. They then refine the response by measuring the output (i.e., the actual pitch rate) and subtracting it from the input (i.e., the desired outcome), generating an error signal. This error signal is amplified and employed to drive the actuator (see Fig. 5). This setup enables the actuator to automatically adjust and minimize any discrepancies between the input demand and the output response.

Note that this is a proportional controller.

A simulation with a gain of -0.5 was implemented, resulting in the following response.

Response Evaluation

The response can be evaluated using the following metrics:

1. Peak Time: The time elapsed from the starting point to the peak of the curve.

2. Settling Time: The time elapsed from the starting point to the point where the curve stabilizes.

3. Overshoot: The difference between the peak value and the steady-state value, divided by the steady-state value.

4. Steady-State Error: The difference between the stabilized curve and the target value.

Simulink Simulation Results

The response obtained through Simulink simulation is depicted in the following image:

Based on the image, the peak time is approximately 0.32s, the settling time is approximately 0.8s, the overshoot is around 2.8%, and the steady-state error is 0.

Conclusion

Based on the simulation results, the controller demonstrates satisfactory performance, meeting the design requirements.