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Example: PI-control of integrating process

Example: PI-control of integrating process. Simulink, tunepid4. 2.5. 2. 1.5. 1. 0.5. 0. 0. 5. 10. 15. 20. 25. 30. 35. 40. PI-control of integrator (level control). G = 1/s, taui =1. VARY Kc. NO DELAY , theta = 0. %tunepid4 s= tf ('s') theta=0

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Example: PI-control of integrating process

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  1. Example: PI-control of integrating process

  2. Simulink, tunepid4

  3. 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 35 40 PI-control of integrator (level control). G = 1/s, taui=1. VARY Kc NO DELAY, theta = 0 %tunepid4 s=tf('s') theta=0 g=(1/s)*exp(-theta*s) % integrating taud=0 taui=1 Kc=0.5 % oscillations (Kc*k'*taui = 0.5 < 4) sim tunepid4; plot(Tid,y); hold on % Kc=0.25 % more oscillations (Kc*k'*taui = 0.25 < 4) sim tunepid4; plot(Tid,y,'red'); Kc=1 % less oscillations (Kc*k'*taui = 1) sim tunepid4; plot(Tid,y,'green'); hold off Kc=0.25 Kc=1 Kc=0.5 Conclusion: Get “slow” oscillations if controller gain is too small Input disturbance at t=20 Setpoint change at t=0

  4. 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 30 35 40 PI-control of integrator (level control). G = 1/s, Kc=1. VARY taui NO DELAY, theta = 0 taui=0.5 taui=2 taui=4 Conclusion. Kc=1, taui=4 looks OK (no oscillations) Conclusion: Get “slow” oscillations if integral time is too small Input disturbance at t=20 Setpoint change at t=0

  5. 4 3.5 3 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 35 40 PI-control of integrator (level control). G = 1/s, taui=4 ADD DELAY, theta = 1 %tunepid4 s=tf('s') theta=1 g=(1/s)*exp(-theta*s) % integrating with delay (level control) taud=0 taui=4 Kc=1 % Too high Kc. % -> “fast” oscillations because of delay!! sim tunepid4; plot(Tid,y); hold on % Kc=0.5 % OK sim tunepid4; plot(Tid,y,'red'); Kc=0.25 % Too low Kc. % -> “slow” oscillations from integrator sim tunepid4; plot(Tid,y,'green'); hold off Kc=1 Kc=0.5 Kc=0.25 Comment. SIMC-rule, Kc=0.5, taui=8 Input disturbance at t=20 Setpoint change at t=0 CONCLUSION Kc too small (Kc=1): “Slow” oscillations (integrator not stabilized) Kc too large (Kc=0.25): “Fast” oscillations (because of time delay)

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