1. 1 CBE 491 /433 15 Oct 12 Model of Stirred Tank Heater Goal: set up models to simulate and see effect of tuning parameters 1 st principles (Chaps 3 – 6); transfer functions (just looked at this a bit) process simulators (AspenPlus Dynamics; CBE 450/550 class)

2. 2 + + - + energy balance on tank w/o control Stirred Tank Heater (w/ PI Controller) PI controller equation

3. 3 Let: Stirred Tank Heater (w/ PI Controller)

4. 4 ODE Solver (POLYMATH; MATLAB; MATHCAD; etc) Polymath code: step= if (t<1) then (0) else (1) Ti = 0 + step * 10

5. 5 ODE Solver: POLYMATH Polymath code (stirred tank heater): d(C) / d(t) = -1/tau*C + KT/tau*Ti + K1KT/tau*M C(0) = 0 d(errsum) / d(t) = R – C errsum(0) = 0 tau = 5 # min KT = 0.5 # %TO/degC K1KT = 0.8 # %TO/%CO R = 0 # set point stays same M = Kc*(R-C) + Kc/tauI*errsum step = if (t<1) then (0) else (1) Ti = 0 + step * 10 # step change disturbance Kc = 1.3 # %CO/%TO tauI = 10 # min t(0) = 0 t(f) = 100 # min In Class Demo / Exercise: Polymath Demonstration Build model in Polymath (ODE solver) Solve; graph C vs t Explore: Try P-only controller Adjust Kc and tauI to get QAD Try different Kc/tauI sets Can you get underdamped response? What is response to step change in R(t); holding Ti at the SS value?

6. 6 CBE 491 / 433 Model of Stirred Tank Heater Goal: set up models to simulate and see effect of tuning parameters 1 st principles (Chaps 3 – 6); transfer functions (just looked at this a bit) process simulators (AspenPlus Dynamics; CBE 450/550 class)

7. 7 + + - + Stirred Tank Heater (transfer function simulator) Transfer function simulator: Loop Pro Developer (Control Station) In Class Demo / Exercise: Build model in Loop Pro Developer (Custom Process) Turn on PI Controller and set Kc and tauI Explore: Change load (Ti) up by 10 to 60%; observe system response Change back to 50%; observe response Try P-only controller Adjust Kc and tauI to get QAD Try different Kc/tauI settings Can you get underdamped response? What is response to step change in R(t) to 60%?

8. 8 CBE 491 / 433 Model of Stirred Tank Heater Goal: set up models to simulate and see effect of tuning parameters 1 st principles (Chaps 3 – 6); transfer functions (just looked at this a bit) process simulators (AspenPlus Dynamics; CBE 450/550 class)

9. 9 SAVE your Polymath and Loop Pro Developer Models !!