The roll control autopilot of a jet fighter is shown in Figure DP5.1. The goal is to select a suitable K so that the response to a unit step command Ï•d(t) = A, t ‰¥ 0, will provide a response Ï•(t) that is a fast response and has an overshoot of less than 20%.
(a) Determine the closed-loop transfer function Ï•(s)/Ï•d(s).
(b) Determine the roots of the characteristic equation for K = 0.7, 3, and 6.
(c) Using the concept of dominant roots, find the expected overshoot and peak time for the approximate second-order system.
(d) Plot the actual response and compare with the approximate results of part (c).
(e) Select the gain K so that the percentage overshoot is equal to 16%. What is the resulting peak time?
Figure DP5.1
Roll angle control.

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Aircraft dynamics 12.2 s(s +2.2) Aileron actuator ф(s) Roll angle Gyro