Simulink Simulation of Fighter Aircraft Longitudinal Motion: Pitch Rate Control

The purpose is to use Simulink to simulate a (much simplified) model of the longitudinal motion of a fighter aircraft. The 'angle of attack' is the angle between the direction a plane is pointing, and the direction in which it actually moves through the air. For a plane flying at approximately constant altitude, this is equivalent to the 'pitch angle', as illustrated in Fig. 3. This angle is important because it produces a lift force perpendicular to the axis of the plane, and hence a 'normal acceleration', (also shown in the figure).

The pilot wants to be able to control the pitch angle, and does so ultimately by rotating the front fins, and tail elevators of the aircraft, shown in Fig. 4. The first task is therefore to model the effect of these movements on the 'pitch rate', where

b. Pitch Rate, q The rate at which the pitch angle changes, (the 'pitch rate', q), is determined mainly by the angle of the front fins of the aircraft shown in Fig. 4. Indeed aerodynamic modelling shows that this relationship can be described by the differential equation: Q(s)/d(s)=(7.25s+11.27)/(s^2+3.1s-8.82)
其中，gain 是指 gears，数值是-5

Sketch of pitch rate response to a step change in the control input here 输出的response图显示从0开始直到16s开始大幅下降 Comment on the response The response shows that the pitch rate initially increases, and then decreases sharply after 16 seconds. This indicates that the front fins of the aircraft are initially causing the pitch angle to increase, but then the tail elevators are being used to bring the pitch angle back down to the desired level. The steep drop in pitch rate after 16 seconds suggests that the tail elevators are very effective at controlling the pitch angle. The negative gain value of -5 also indicates that the front fins and tail elevators are opposing each other, with the front fins causing the pitch angle to increase and the tail elevators causing it to decrease. Overall, the response shows that the aircraft is able to maintain a stable pitch angle through the use of these control surfaces.