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lec13

# lec13 - PID Controller Design 3(Complex zeros K(s z1(s z 2...

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PID Controller Design 3 ( Complex zeros ) s ) z s )( z s ( K ) s ( G 2 1 c - - = where ϖ σ - = j z 1 Slide 1 ME 475 Session 13: Root Locus Compensation Galen King Purdue University ϖ - σ - = j z 2

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PID Controller Design 3 Im s j4 j3 j2 j5 j6 Slide 2 ME 475 Session 13: Root Locus Compensation Galen King Purdue University Re s j1 - j4 - j3 - j2 - j1 - 2 - 4 - 6 - j5 - j6 - 8
Apply Angle Criterion 1 2 d z z 198.4 φ = = φ + φ ringoperator 1 2 z 1 z 2 1 2 180 , 180 161.6 φ = - α φ = - α α + α = ringoperator ringoperator ringoperator choose 5.5: σ = Slide 3 ME 475 Session 13: Root Locus Compensation Galen King Purdue University 1 2 1 2 1 2 1 2 6 6 tan 2(6 ) 6 0.5 6 6 tan 2(6 ) 6 0.5 tan tan 2(6 ) 2(6 ) tan( ) 1 tan tan 1 2(6 )2(6 ) - ϖ - ϖ α = = = - ϖ - σ + ϖ + ϖ α = = = + ϖ - σ α + α - ϖ + + ϖ α + α = = - α α - - ϖ + ϖ

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Apply Magnitude Criterion 1 2 1 2 2 2 p p z z r r (6.3)(8.5) 4K K 6.0 r r (1.86)(10.22) = = = 6(s 5.5 j4.2)(s

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lec13 - PID Controller Design 3(Complex zeros K(s z1(s z 2...

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