# l24 - 16.06 Lecture 24 Compensator Design Karen Willcox...

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Unformatted text preview: 16.06 Lecture 24 Compensator Design Karen Willcox October 30, 2003 Today’s Topics 1. Phase-lead compensator design 2. Phase-lag compensator design Reading : 6.6, 6.7 1 1 Phase-lead compensator design We have the following system: where Consider the pole-zero diagram: 2 Phase-lead compensation has a stabilizing effect. At A 1 , angle of plant = At A 2 , angle of plant + angle of compensator = At A 2 , angle of plant will be So the compensator must contribute From the triangle, we have Now we can establish a design procedure. 2 Design Procedure 7 steps on handout. 3 insert phase-lead design procedure here 4 3 Phase-lead compensator design example 1 G ( s ) = s ( s + 2) Design G c ( s ) to meet the following closed-loop specifications: (i) Dominant time constant should be 0.25 sec (ii) P.O. for step response ≈ 16% 5 • Step 1 Specifications imply: Therefore, the dominant closed-loop poles are at • Step 2 Angle condition: • Step 3 Place zero at-4 6 • Step 4 tan 46 . 1 ◦ = • Step 5 Magnitude condition: K c = 7 •...
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l24 - 16.06 Lecture 24 Compensator Design Karen Willcox...

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