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Tuning PI Control for Integrating Processes in Simulink with Delay and Oscillation Analysis

This document explores the tuning of Proportional-Integral (PI) controllers for integrating processes using Simulink. It demonstrates how varying the controller gain (Kc) and integral time (taui) affects system behavior, specifically highlighting oscillations under different conditions. We analyze cases with no delay and with time delay. The results suggest that a high Kc can lead to fast oscillations, while a low Kc results in slow oscillations. Simulation results are presented, and key conclusions on optimizing PI parameters are drawn for effective control.

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Tuning PI Control for Integrating Processes in Simulink with Delay and Oscillation Analysis

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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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