07_PID_RoT2_S10

07_PID_RoT2_S10 - Step Response of Simulink PIDalpha...

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Unformatted text preview: Step Response of Simulink PIDalpha (Opened-loop Servo) CHE 461 ⎛ τ s + 1 ⎞⎛ τ D s + 1 ⎞ Commercial "real" PID controller has Gc , real ( s ) = K c ⎜ I ⎟⎜ ⎟ ⎝ τ I s ⎠⎝ ατ D s + 1 ⎠ P, PI, PID Controllers: K c = 1.0 , τ I = 0.5 , τ D = 0.2 , α = 0.05 (τ D = 0 or α = 1 is no D action) Output from PI Controller for Unit Step in E 25 E_step PC_graph PID_real Output from P Controller for Unit Step in E 20 15 20 15 10 5 0 0 0.5 1 Time 1.5 2 10 Output from PID Controller for Unit Step in E 25 0 0 0.5 1 Time 1.5 2 p' , Controller Output 5 20 15 10 5 0 0 0.5 1 Time 1.5 2 Output from PID Controller for Unit Step in E 25 p' , Controller Output p' , Controller Output 25 p' , Controller Output PIDalpha 20 15 10 5 0 0 0.02 0.04 0.06 Time 0.08 0.1 Step Response of Simulink PIDalpha (Regulator) CHE 461 ⎛ τ s + 1 ⎞⎛ τ D s + 1 ⎞ Commercial "real" PID controller has Gc , real ( s ) = K c ⎜ I ⎟⎜ ⎟ ⎝ τ I s ⎠⎝ ατ D s + 1 ⎠ PIDs: Base Case + changes for K c = 1.0 , τ I = 0.5 , τ D = 0.2 , α = 0.05 (τ D = 0 or α = 1 is no D action) CHE 461 PID_RoTD.mdl Time delay = 0.05 4 0.5s2+1.5s+1 D_step Time DelayD Gd T ime delay = 0.05 Sum 4 PIDalpha 0.5s2+1.5s+1 Ysp_step Time Delay PID_real Sum2 Y_graph Gp1 PID = Base Case A Performance for Unit Step in D PID Case B = 50% P-Action Performance for Unit Step in D 0.8 0.6 0.6 y' , Process Output Variable 1 0.8 y' , Process Output Variable 1 0.4 0.2 0 -0.2 -0.4 0.4 0.2 0 -0.2 -0.4 -0.6 -0.6 -0.8 -0.8 -1 0 1 2 3 Time 4 5 -1 0 6 PID Case C = 50% I-Action Performance for Unit Step in D 2 3 Time 4 5 6 PID Case D = 200% D-Action Performance for Unit Step in D 1 0.8 0.8 0.6 0.6 y' , Process Output Variable 1 y' , Process Output Variable 1 0.4 0.2 0 -0.2 -0.4 0.4 0.2 0 -0.2 -0.4 -0.6 -0.6 -0.8 -0.8 -1 0 1 2 3 Time 4 5 6 -1 0 1 2 3 Time 4 5 6 Step Response of Simulink PIDalpha (Opened-loop Regulator) CHE 461 ⎛ τ s + 1 ⎞⎛ τ D s + 1 ⎞ Commercial "real" PID controller has Gc , real ( s) = K c ⎜ I ⎟⎜ ⎟ ⎝ τ I s ⎠⎝ ατ D s + 1 ⎠ P, PI, PID Controllers: K c = 1.0 , τ I = 0.5 , τ D = 0.2 , α = 0.05 (τ D = 0 or α = 1 is no D action) CHE 461 PID_RoTD.mdl PID Opened-loop for Unit Step in D 4 Time delay = 0.05 0.5s2+1.5s+1 D_step Time DelayD Gd T ime delay = 0.05 Sum 4 PIDalpha 0.5s 2+1.5s+1 Ysp_step Time Delay PID_real Sum2 Y_graph y' , Process Output Variable 3.5 4 3 2.5 2 1.5 1 Gp1 0.5 P_graph 0 0 P Controller Opened-loop for Unit Step in D 1 Time 1.5 2 PI Controller Opened-loop for Unit Step in D 0 0 -1 -1 -2 -2 p' , Controller Output -3 -4 -5 -6 -7 -8 -3 -4 -5 -6 -7 -8 -9 -9 -10 0 -10 0 0.5 1 Time 1.5 2 0.5 1 Time PID Controller Opened-loop for Unit Step in D 0 -1 -2 p' , Controller Output p' , Controller Output 0.5 -3 -4 -5 -6 -7 -8 -9 -10 0 0.5 1 Time 1.5 2 1.5 2 ...
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