The control of the roll angle of an airplane is achieved by using the torque developed by the ailerons. A linear model of the roll control system for a small experimental aircraft is shown in Figure DP4.2, where

The goal is to maintain a small roll angle θ due to disturbances. Select an appropriate gain KK1 that will reduce the effect of the disturbance while attaining a desirable transient response to a step disturbance, with θd(t) = 0. To obtain a desirable transient response, let KK1 Figure DP4.2
Control of the roll angle of an airplane.

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s)=s2 + 4s + 9 Tsts) K, T(s) θ(s) Roll angle ?is)