![]() ![]() Since our output is pitch angle, the output equation is the following. Recognizing the fact that the modeling equations above are already in the state-variable form, we can rewrite them as matrices The Laplace transform of the aboveĪfter few steps of algebra, you should obtain the following transfer function. Recall that when finding a transfer function, zero initial conditions must be assumed. To find the transfer function of the above system, we need to take the Laplace transform of the above modeling equations. These values are taken from the data from one of Boeing's commercial aircraft. The Extras: Aircraft Pitch System Variables page to see a further explanation of what each variable represents.įor this system, the input will be the elevator deflection angle and the output will be the pitch angle of the aircraft.īefore finding the transfer function and state-space models, let's plug in some numerical values to simplify the modeling Please refer to any aircraft-related textbooks for the explanation of how to derive these equations. Under these assumptions, the longitudinal equations of motion for the aircraft (unrealistic but simplifies the problem a bit). We will also assume that a change in pitch angle will not change the speed of the aircraft under any circumstance Lift forces balance each other in the x- and y-directions. We will assume that the aircraft is in steady-cruise at constant altitude and velocity thus, the thrust, drag, weight and The basic coordinate axes and forces acting on an aircraft are shown in the figure given below. In this example we will design an autopilot that controls the pitch of an ![]() Pitch is governed by the longitudinal dynamics. However, under certain assumptions, they can be decoupled and linearized into longitudinal and lateral equations. The equations governing the motion of an aircraft are a very complicated set of six nonlinear coupled differential equations. Transfer function and state-space models. ![]()
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