Question

Golden Nugget Airlines has opened a free bar in the tail of their airplanes in an attempt to lure customers. In order to automatically adjust for the sudden weight shift due to passengers rushing to the bar when it first opens, the airline is mechanizing a pitch-attitude autopilot. The figure below shows the block diagram of the proposed arrangement. We will model the passenger moment as a step distubance W(s)Wos, with a maximum expected value for W of 0.6. Kr A. what value of K is required to keep the steady-state error in θ to less than 0.02 rad (~ 1")? B. Draw a root locus with respect to K C. Based on your root locus, what is the value of K when the system becomes unstable? D. Suppose the value of K required for acceptable steady-state behavior is 600. Show that this value yields un unstable system with roots at s =-29,-13.5" +1.2土16.6 E. You are given a black box with rate gyro written on the side and told that, when installed, it provides a perfect measure of , with output K. Assume that K 600 as in part D. and draw a block diagram indicating how you would incorporate the rate gyro into the autopilot. (Include transfer function boxes.) E. For the rate gyro in part E., sketch a root locus with respect to Ky G. What is the maximum damping factor of the complex roots obtainable with the configuration in part E.? H. what is the value of KT, for part G.? 25 I. Suppose you are not satisfied with the steady-state errors and damping ratio of the system with a rate gyro in parts E. through H. Discuss the advantages and disadvantages of adding an integral term and extra lead networks in the control law. Support your comments using SCILAB or with rough root-locus sketches.

Answer 1

117ว่า K CS3 าาา ら十10 31K 5 x10 50 given 代 21-

K (st)

clc: cïose дії; clear all: numerator-[1 3]: denominator-conv([1 10 0], [1 4 5]); sys-tf (numerator, denominator): rlocus (sys)

Root Locus System: sys Gain: 148 Pole: 0.0193.77i mping:-0.00503 Overshoot (%): 102 Frequency (rad/s): 3.77 0 0 -10 35 -30 25 20 15 10 5 0 5 10 15 Real Axis (seconds')

k=600 ven iS 6o0 Cst3)

Goo Cs+3)

>> chareuation-[1 14 45 650 1800] chareuation - 1800 650 45 14 >>roots (chareuation) ans -13.5014 0.0000i 1.2183 6.62841 1.2183 - 6.62841 -2.9352 0.0000i

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