problem_11_15

problem_11_15 - Problem 11.15 of the Palm textbook...

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Unformatted text preview: Problem 11.15 of the Palm textbook (MODIFIED) Plant TF: G P s ( 29 = 2 2- - 26 + 2 ( 29 + 3 ( 29 Sketch the root locus. Determine the range of proportional control gains K for which the system response is stable. Determine the value of K required for a time constant of = 2 / 3 . SOLUTION Closed-loop characteristic equation: = 1 + 2 2- - 26 + 2 ( 29 + 3 ( 29 = 1+ 2 2- - 26 3 + 5 2 + 6 = 1 + ( 29 ( 29 1. Number of branches : max N P , N Z { } = 3,2 { } = 2. Start/end points : OL zeros : z 1 = -3.36, 2 = 3.86 1 = 0, 2 = -2, 3 = -3 Therefore, the RL START at poles p 1 , p 2 , p 3 . Two RL branches ENDS at z 1 and z 2 while one branch ends at . 4. Since the RL can exist on the real axis only to the left of an ODD number of real OL zeros/poles, the regions on the real axis containing the RL are:...
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problem_11_15 - Problem 11.15 of the Palm textbook...

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