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hw_prj_5

# hw_prj_5 - Dr Atilla Dogan MAE 4310 Automatic Control Fall...

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Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 Homework–5 (Due date: Thursday, Oct 19, 2006) Textbook Readings: Sections 5–7, 5–9, Examples A–5–15, A–5–16, A–5–18, A–5–23, A–5–25 1. Consider the satellite attitude control system below K 1 J s 2 R(s) C(s) Show that the output of this system exhibits continued oscillations by determining the damp- ing ratio of the closed loop system. This system can be stabilized by the following control structure K J s R(s) C(s) 1 s K h If K/J = 4, what value of K h will yield the damping ratio to be 0.6. 2. Determine the range of K for stability of a unity feedback control system whose open–loop transfer function is G ( s ) = K ( s - 1) ( s + 2)( s 2 + 2 s + 2) You should use Routh–Hurwitz Stability Criterion to answer this question. 3. Consider the unity–feedback control system with the following open–loop transfer function. G ( s ) = 10 s ( s - 1)( s + 3) Determine the stability of the closed loop system by using Routh–Hurwitz Method. 4. Consider the following characteristic polynomial s 3 + (4 + K ) s 2 + 6 s + 12 For what values of K does this polynomial have roots with negative real parts? Use Routh– Hurwitz Method.

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hw_prj_5 - Dr Atilla Dogan MAE 4310 Automatic Control Fall...

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