filled11 - amplification. ME 475 Handouts - Spring 2011 4...

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ME 475 Handouts - Spring 2011 1 Slide 1 ME 475 Session 11: Root Locus Design Galen King Purdue University Design Example Design G c to meet the following specs: ζ = 0.707 t s | 2% = 0.667 sec G c R(s) Y(s) Controller Plant + - ) 4 s ( s 4 + Slide 2 ME 475 Session 11: Root Locus Design Galen King Purdue University Root Locus for Proportional Control Im s Re s j4 j3 j2 j1 - j4 - j3 - j2 - j1 - 1 - 2 - 3 - 4 - 5 - 6 j5 j6 - j5 - j6
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ME 475 Handouts - Spring 2011 2 Slide 3 ME 475 Session 11: Root Locus Design Galen King Purdue University Use Angle Criterion for New Design Im s Re s j4 j3 j2 j1 - 1 - 2 - 3 - 4 - 5 - 6 j5 j6 - 7 - 8 - 9 Slide 4 ME 475 Session 11: Root Locus Design Galen King Purdue University Design PD Controller (Compensator)
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ME 475 Handouts - Spring 2011 3 Slide 5 ME 475 Session 11: Root Locus Design Galen King Purdue University Compensated Root Locus Im s Re s j8 j6 j4 j2 - j8 - j6 - j4 - j2 - 4 - 8 - 12 j10 j12 - j10 - j12 - 16 Slide 6 ME 475 Session 11: Root Locus Design Galen King Purdue University Lead (Lag) Compensator Design The PD controller is not a good design since it tends to amplify higher frequency noise. We want to design a compensator that reduces high-frequency
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Unformatted text preview: amplification. ME 475 Handouts - Spring 2011 4 Slide 7 ME 475 Session 11: Root Locus Design Galen King Purdue University Use Angle Criterion for New Design Im s Re s j4 j3 j2 j1-1-2-3-4-5-6 j5 j6 Slide 8 ME 475 Session 11: Root Locus Design Galen King Purdue University Design Lead Compensator ME 475 Handouts - Spring 2011 5 Slide 9 ME 475 Session 11: Root Locus Design Galen King Purdue University Compensated Root Locus Im s Re s j8 j6 j4 j2-j8-j6-j4-j2-4-8-12 j10 j12-j10-j12-16 Slide 10 ME 475 Session 11: Root Locus Design Galen King Purdue University Step Response Comparison Time (sec.) Amplitude Step Response 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 1.2 1.4 PD Lead ME 475 Handouts - Spring 2011 6 Slide 11 ME 475 Session 11: Root Locus Design Galen King Purdue University Check Steady-State Error R(s) Y(s) Controller Plant +-E(s) U(s) ) 4 s ( s 4 + 18 s 6 s 30 + +...
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filled11 - amplification. ME 475 Handouts - Spring 2011 4...

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