# hw2 - J.M. Gonalves c Fall 2003 CDS 212 - Introduction to...

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J.M. Gon¸ calves Fall 2003 CDS 212 - Introduction to Modern Control Homework # 2 Date Given: October 9th, 2003 Date Due: October 16th, 2003, 1PM P1. Consider the transfer functions: G 1 ( s ) = s - 1 s 2 + 2 s + 2 , G 2 ( s ) = ( s + 1)( s - 1) s 3 + 2 s 2 + s + 1 . Compute, using MATLAB, the 2- and -norm of G 1 , G 2 , G 1 G 2 and G 1 + G 2 . How do the last two expressions compare to the individual norms? (Some MATLAB commands you may ±nd useful are tf , ss , norm , ssdata ). P2. Given the two block diagrams: 1 1 s 1 s i - i - - - - - 6 6 ± ± 1 2 s i - - - - 6 ± (a) Are they equivalent? (b) Analyze internal stability for both of them. (c) Explain the result. P3. DFT: Chapter 3, Exercise 2. P4. DFT: Chapter 3, Exercise 3. P5. Consider the standard block diagram: i - C ( s ) - - - P ( s ) 6 - r y u Take C ( s ) = 1 s + α and P ( s ) = s + α s +1 .

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J.M. Gon¸ calves Homework # 2 (Page 2 of 2) Fall 2003 (a) For what values of α is the system internally stable? (b)
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## hw2 - J.M. Gonalves c Fall 2003 CDS 212 - Introduction to...

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