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# PID Control addendum filled - ME375 Handouts Effect of...

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ME375 Handouts 1 School of Mechanical Engineering Purdue University ME375 PID Control - 1 Effect of Proportional Control Effect of Proportional Control Objective Objective : Design a system that has zero steady state error for step inputs for step inputs with %OS with %OS < 10% and T S S (2%) < < 6 [sec]. (A) (A) Let Let ’s try s try Proportional (P) control Proportional (P) control : : G C C ( s ) = ) = K P Closed loop transfer functions : 4 () 4 (2 1)(0.5 1) 4 1 ( ) ( ) ( ) (2 1)(0.5 4 1 (2 1)(0.5 4 1( )( ) ( ) ( 2 1 ) ( 0 . 5 1 ) 4 P CP P YR P P P YD P K GsGs K ss Gs GsGsHs s s K K s s K ++ == = +⋅⋅ + + + +⋅ + + + Output Y (s) Disturbance D (s) Plant G P ( s ) Control Input U ( s ) G C ( s ) + Reference Input R ( s ) Error E ( s ) + + ) 1 5 . 0 )( 1 2 ( 4 + + s s 1 Sensor H ( s ) Controller School of Mechanical Engineering Purdue University ME375 PID Control - 2 Effect of Proportional Control Effect of Proportional Control Design P Control: Design P Control: Closed Loop Characteristic Equation : 2 (2 1)(0.5 4 0 2.5 1 4 0 P P ssK K + = + = 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 K P = 0.1 K P = 0.5 K P = 1 K P = 2 K P = 5 Step Response Time (sec) Amplitude -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 Real part of s Imag part of s K P = 0.1 K P = 0.5 K P = 1 K P = 2 K P = 5

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ME375 Handouts 2
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PID Control addendum filled - ME375 Handouts Effect of...

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