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Unformatted text preview: AE361 Advanced Stability and Control
Homework 3 Due Wednesday, September 30, 2009 1. A control scheme is shown in the block diagram shown below: The initial conditions are x(0) = 0 , 36(0) = 0
Use the following parameter values
M=1000, K=332 ,a=1,,6’=4,71=7, 2'2 =10, 0'=l. Use ODE45 to solve for the response of the system with the two cases of the input
x f (t) given below: xf(z)=1 t=0 —O't =e t>0 (a) Does the system go in the direction of the force or opposite to it at small time? xf(r)=0 [=0 =e"” t>0 (b) Does the system go in the direction of the force or opposite to it at small time?
Why is case (b) different from case (a) 2. Place the following differential equation in proper LTI form 3E+53i+10x+3x=f(t)+5% The desired output for the system is X. Give the matrices [a] , [b] , [c] , [d] in the LTI
representation [alz+[b]u
[c]r+[d]z i
Z 3. For Problem 1, increase K from 332 and show and describe what happens to the
response as K increases. Estimate the maximum value of K before the system becomes
unstable. ...
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 Fall '10
 WalterEversman
 5%, AE361 ADVANCED STABILITY

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