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hw_prj_6 - Dr Atilla Dogan MAE 4310 Automatic Control Fall...

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Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 Homework–6 (Due date: Tuesday, Oct 31, 2006) Textbook Readings: Sections 6–1, 6–2, 6–3, 6–4, 6–5, 6–6 1. Determine the angle and magnitude of G ( s ) = 16( s + 1) s ( s + 2)( s + 4) at the following points in the s–plane: (a) s = i 2 , (b) s = - 2 + i 2 , (c) s = - 4 + i 2 , (d) s = - 6 , (e) s = - 3 . 2. Consider the following unity feedback control system: K G(s) For each transfer function, find the breakaway points on the root–locus: (i) G ( s ) = 1 s ( s + 6)( s + 8) (ii) G ( s ) = s + 5 ( s + 2)( s + 4) (iii) G ( s ) = s + 1 s 2 ( s + 9) 3. Find the departure angle of the root–locus from the pole at s = - 10 + i 10 for the system given in problem 2 with the transfer function G ( S ) = s + 8 ( s + 14)( s + 10 + i 10)( s + 10 - i 10) 4. Find the arrival angle of the root–locus to the zero at s = - 7 + i 5 for the system given in problem 2 with the transfer function G ( S ) = ( s + 7 + i 5)( s + 7 - i 5) ( s + 3)( s + 5)( s + 10) 5. Using the rules given in the class, sketch the root-loci for the system given in problem 2 (i). Mechanical and Aerospace Engineering - UTA 1 of 3
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Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 6.
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