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# HW8 - points and the points of intersection with the...

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ECE 313 – Fall 2008 Homework # 8 Due Friday, October 24, 2008 1. Consider a unity feedback system with ) 4 )( 2 )( 1 ( ) ( + + + = s s s K s G (a) Sketch the root locus and find the break-in/breakaway points and the points of intersection with the imaginary axis. (b) Find the range of the gain to keep the system stable. (c) Find the value of K for 20% overshoot. What is the settling time and what is the peak time? (d) Is the second-order approximation used in part (c) justified? Test your answer by using MATLAB to calculate the overshoot, settling time, and peak time of the closed-loop step response, and compare with what you found in part (c). 2. Consider a unity feedback system with ) )( 1 ( 1 ) ( α + + = s s s s G Sketch the root locus as varies from zero to infinity. Find the break-in/breakaway
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Unformatted text preview: points and the points of intersection with the imaginary axis. 3. Consider a unity feedback system with ) 6 )( 4 )( 2 )( 2 2 ( ) 3 )( 1 ( ) ( 2 + + + + + + + = s s s s s s s K s G Use MATLAB to answer the following questions. (a) Plot the root locus. (b) Find the ω j-axis crossing and the gain , K , at the crossing. (c) Find the break-in and breakaway points. (d) Find the gain K to yield a damping ratio of 0.3 for the closed-loop dominant poles. What is the expected overshoot? (e) Plot the closed-loop step response and determine the overshoot. Hand in a plot of the root locus from MATLAB and mark on it the answers to parts (b) to (d)....
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