Simulink Modeling 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:

Convert this relationship into a transfer function form:

Sketch of pitch rate response to a step change in the control input here Comment on the response

The transfer function for the pitch rate, q, is given by:

q(s)/d(s) = Kq/(Ts + 1)

where d(s) is the input control signal (angle of the front fins), Kq is the gain, and T is the time constant.

When a step change is applied to the input control signal, the pitch rate responds as shown in the sketch below:

The response starts from zero and rises quickly to reach a steady-state value, which is proportional to the magnitude of the input control signal. The rise time and settling time depend on the time constant T, with a larger T resulting in a slower response.

Overall, the response is a first-order system with a characteristic exponential decay, and the steady-state gain reflects the sensitivity of the pitch rate to changes in the input control signal.