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hwold3 - AE 383 System Dynamics HW#3 Due Dec 27 2005 1...

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AE 383 System Dynamics HW#3 Due: Dec. 27, 2005 1. Using Routh’s stability test, examine the stability of the systems whose characteristic equations are given below. a. 7 6 5 4 3 2 2.3 4 5.6 7 11 18 12.3 s s s s s s s + + + + + + + b. 5 4 3 2 1 2 20 32 164 200 400 s s s s s s + + + + + + c. 8 7 6 5 4 3 2 3 48 21 35 19 4 14 56 s s s s s s s s + + + + + + + + 2. Following feedback control system is given. Using Routh’s stability test, find the range of values on K for the system to be stable. 3. Approximately plot the unit step response of the following system whose characteristic equation roots are at: 1 8 j − ± . 4. The following 2 nd order system is given: 2 100 ( ) 20 100 G s s s ζ = + + . Using Simulink obtain the response of this system to step input for various values of the damping ratio, ( 0.1, 0.3, 0.7, 1., 1.5) ζ = . Comment on your results. (Hint:
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