Question

Consider the aircraft model shown in Figure 1. We will assume that the aircraft is in steady-cruise at constant altitude and velocity; thus, the thrust, drag, weight and lift forces balance each other in the x- and y directions. We will also assume that a change in pitch angle will not change the speed of the aircraft under any circumstance (unrealistic but simplifies the problem a bit). Under these assumptions the longitudinal equations of motion for the aircraft can be written as, Drag Wnight Figure 1 a Angle of atack q-Pitch rate θ-Pitch angle δ«Elevator defection angle s Platform area of the wing さ Average chord length mMass of the aircraft U:Equilibrunnnght speed CrCooficient of thrust C Coefficient of drag CLCoefficient of lit Cw Coefficient of weight CM : Coefficient of pitch moment Density of air γ Flight path angle Normalzed moment ofinerta q = m.ic,1-r(Cu + cola + [CM +oCM (1-pCzle + (pCw sinh Using values taken from one of Boeing's commercial aircraft the state space model is given by, á l -0.313 56.7 01 al ral 0.232 0.0139 0.426 o 0.0203 0 56.7 oj Design a lead compensator cascade controller for the system shown in Figure 1 such that for a step input in the commanded pitch attitude the settle time less is than 10 seconds, the system overshoot is less than 30%, and the steady state tracking error is zero. Settle time is defined to be the time beyond which the response is within 2% of the final value. 2) Design values of your lead compensator gain, zero, and pole, i.e. Ge(s) = Kc . 3) MATLAB plots of the compensated and uncompensated root locus 4) MATLAB plots of the compensated and uncompensated step response showing the requirements are met s+pc)

Answer 1

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