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CBE 491 /433 15 Oct 12 Model of Stirred Tank Heater Goal: set up models to simulate and see effect of tuning parameters • 1st principles (Chaps 3 – 6); • transfer functions (just looked at this a bit) • process simulators (AspenPlus Dynamics; CBE 450/550 class) 1 Stirred Tank Heater i s (w/ PI Controller) Rs + E s Gc M s 1 GC ( s ) K c 1 I s KL L s 1 KP P s 1 + + C s K1 K V s K 2 KL KP 1* K T K1 K T C s ( s ) M ( s ) ( s ) i s 1 i s 1 M ( s ) s 1 s 1 L P dC (t ) C (t ) K T i (t ) K1 K T M (t ) dt energy balance on tank w/o control K M (t ) K C E (t ) C E (t )dt I PI controller equation E (t ) R(t ) C (t ) 2 Stirred Tank Heater dC (t ) C (t ) KT i (t ) K1 KT M (t ) dt K M (t ) K C E (t ) C E (t )dt I (w/ PI Controller) dC (t ) 1 K KK C (t ) T i (t ) 1 T M (t ) dt Let: errsum E (t )dt d errsum E (t ) dt d errsum R(t ) C (t ) dt M (t ) K C R(t ) C (t ) KC I errsum 3 ODE Solver (POLYMATH; MATLAB; MATHCAD; etc) C t 0 @ t 0 dC (t ) 1 K KK C (t ) T i (t ) 1 T M (t ) dt d errsum R(t ) C (t ) dt M (t ) K C R(t ) C (t ) 5 min K T 0.5 %oTO C errsum 0 @ t 0 KC I errsum Polymath code: step= if (t<1) then (0) else (1) Ti = 0 + step * 10 TO K1 KT 0.8 %%CO R(t ) 0 K C 1.3 %%CO TO I 10 min 4 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) 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? Ti = 0 + step * 10 # step change disturbance Kc = 1.3 # %CO/%TO tauI = 10 # min t(0) = 0 t(f) = 100 # min 5 CBE 491 / 433 Model of Stirred Tank Heater Goal: set up models to simulate and see effect of tuning parameters • 1st principles (Chaps 3 – 6); • transfer functions (just looked at this a bit) • process simulators (AspenPlus Dynamics; CBE 450/550 class) 6 Stirred Tank Heater i s (transfer function simulator) Rs + E s Gc GC ( s ) M s 0.5 5 s 1 0.8 5 s 1 + + C s M (s) 1 1.31 E (s) 10 s 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%? 7 CBE 491 / 433 Model of Stirred Tank Heater Goal: set up models to simulate and see effect of tuning parameters • 1st principles (Chaps 3 – 6); • transfer functions (just looked at this a bit) • process simulators (AspenPlus Dynamics; CBE 450/550 class) 8 SAVE your Polymath and Loop Pro Developer Models !! 9