# hw4 - y t to stay in the following time-template | y t |...

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J.M. Gon¸ calves Fall 2003 CDS 212 - Introduction to Modern Control Homework # 4 Date Given: October 23rd, 2003 Date Due: October 30th, 2003, in class P1. DFT: Chapter 6, Exercise 4. P2. DFT: Chapter 6, Exercise 5. P3. DFT: Chapter 6, Exercise 6. P4. DFT: Chapter 6, Exercise 7. P5. [ Zhou 6.5 and 6.7 ] Show that a non-minimum phase system cannot be stabilized by a very high-gain controller. Show also that an unstable system cannot be stabilized by a very low gain controller. (Hint: use the root locus method). P6. [ Zhou 6.9 ] Let a plant P have a zero on the right half-plane at z = a (where a is real). Let Y = ( I + P K ) - 1 D be the output due to a unit step disturbance D starting at t = 0. Suppose we want the output
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Unformatted text preview: y ( t ) to stay in the following time-template | y ( t ) | ≤ ± M ≤ t < T m t ≥ T where M > 1 > m > 0, and T > 0. Show that for a stabilizing controller to meet these speci±cations we must have aT ≥ ln ² M-m M-1 ³ Explain the tradeo²s in this problem. P7. [ Zhou 6.9 ] Let K be a stabilizing controller for the nominal plant P = s-α ( s-β )( s + γ ) where α > 0, β > 0, and γ ≥ 0. Suppose | S ( jw ) | ≤ δ < 1 for all w ∈ [-w , w ]. Find a lower bound for k S k ∞ and calculate the lower bound for α = 1, β = 2, γ = 10, δ = 0 . 2, and w = 1....
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## This note was uploaded on 01/04/2012 for the course CDS 212 taught by Professor Tarraf,d during the Fall '08 term at Caltech.

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