Yellow Team Pressure Control System Proportional Control: Model and Experiment

Transcription

1 Yellow Team Pressure Control System Proportional Control: Model and Experiment Team Members: Jason Hixson Laura Amini Mike Bradley UTC ENGR 8 Nov. th, Outline Bakground System Diagram Operating Range SSOC Graph Theory General Step Response Graph FOPDT Parameters Transfer Funtion Frequeny Response Graph Bode Plots and Modeling Closed Loop Transfer Funtion (CLTF) Results Root Lous Plots Damping Effets on Output Controller Gains Controller Operating urves for regions Proportional Control Model and Experimental Graphs Disturbanes for different values of K Conlusions and Reommendation

2 Pressure System PS PS Bakground Pressure Sensor Computer PRC 9 PCZ 9 Damper # Damper # Blower PT 9 Pressure Transduer nput Manipulated Variable. Rated power to blower motor. Measured as perent. Output Controlled Variable. Paint spray booth pressure. Measured in entimeters of water (m- H).

3 Operating Range (SSOC). 8. Region Output (m-ho)... Region Region nput (%) -7 FOPDT Model. (t) (m H O). Graphial FOPDT Solver. FOPDT 7 9

4 Output (m HO) Frequeny Engineering Response Example (Region ) ΔC=.7 m HO ΔM= % AR=. m HO/% PA= Bode Plots Region %-7% FOPDT Parameters Amplitude Ratio (m H/%).. /Ku=. Ku=7 %/m H m=- Fu=.... Frequeny (yles/se). K Tau t Phase Angle ( ) Fu= Frequeny (yles/se)

5 Output Response Root Lous Find roots of the denominator. Plot Real vs. maginary ROOT LOCUS PLOT REGON : -7% K = K QD = K CU "ultimate" = fu = Y π MAGNARY AXS K = K CD "ritial" = - - REAL AXS -

6 ROOT LOCUS PLOT REGON : 7-8% K QD = K CU "ultimate" = 7 K = fu = Y π MAGNARY AXS K = K CD "ritial" = - - REAL AXS - ROOT LOCUS PLOT REGON : 8-9% K QD = K CU "ultimate" = 8 K = fu = Y π MAGNARY AXS K = K CD "ritial" = REAL AXS -

7 Ultimate Frequenies Ultimate Frequenies Root Lous Bode Plot Regions Region Region Region Root Lous... Bode Plot..8 Controller Gain Responses

8 SSOC + Operating Curves - Region - -7% ritially damped overdamped Output m HO 8 Quarter deay /th deay /th deay Ultimate deay /th Δr = m-ho offset = nput (%) Region 7-8% 8 /th deay ritially damped overdamped Output m HO Quarter deay /th deay Ultimate deay /th Deay Δr = m-ho offset = nput (%)

9 Region 8-9% Quarter deay /th deay /th deay ritially damped overdamped 8 Ultimate deay Output m HO /th Deay Δr = m-ho Offset = nput (%) Region -7% / th Deay Experimental Model Experimental RESPONSE K Deay Ratio Offset... OUTPUT/SET PONT.. Model TME

10 Deay Ratio Offset Region 7-8% Model.. / th Deay Experimental.. RESPONSE K Experimental. OUTPUT/SET PONT. Model TME Region K Deay Ratio Offset 8-9% / th Deay Model Experimental Experimental RESPONSE 8. OUTPUT/SET PONT Model TME

11 Greetings, There were things that the ustomer has asked me about your presentation today. -- You showed an experimental response at K = in region in whih you said Offset =. This alls for a "Nope." The offset seems to be zero beause you were using an inorret value for m-bar. believe that offset follows the formula of deltar*(-kk/(+kk)). Chek it out. -- n showing a omparison of Region Ultimate deay showed a frequeny of the experiment that was about. Hz. That's drastially different from your results shown on Slide. ran an experiment and got a little higher frequeny. Also, an't tell that your Output funtion settled down to the initial set point before you hanged the set point. think some mention of and desription of the different frequenies would have been good. believe the ustomer would like to have these things orreted in the next presentation. Look at some notes made on 8 --> Yellow --> Yellow-Team-wk-rev-.pdf JMH

12 Region K Deay Ratio Offset -7% / th Deay Model Experimental.... Experimental RESPONSE. OUTPUT/SET PONT.. Model TME Region K Deay Ratio Offset 7-8% Quarter Deay Model Experimental.... RESPONSE Experimental. OUTPUT/SET PONT.. Model TME

13 K Deay Ratio Offset Region -7% Model -- Ultimate Deay Experimental. -- RESPONSE OUTPUT/SET PONT Experimental Model TME Disturbanes Pressure System PS PS Pressure Sensor Computer PRC 9 Creates Disturbanes PCZ 9 Damper # Damper # Blower PT 9 Pressure Transduer

14 Region Critial Deay Dampers Open Dampers Closed input (%) output (m-ho) time (s) Region / th Deay Dampers Open Dampers Closed nput (%) Output (m-ho) Time (s)

15 Region Quarter Deay Dampers Open Dampers Closed 9. 8 nput (%) 7.. Output (m-h) time (s) Proportional ntegral Design K m( t) = m + K e( t) + e( t) dt τ Charateristi Equation ( τ * τ * t )s (* τ + *K o + ( τ * t C o *K * τ - K + * τ * τ - K K * τ * t )s C *K * t )s + *(K o C o C + *K) = Root Lous K C

16 K=. τ=.7 t =. τ =.8 REAL K C QD = K CU = 8 K C = fu=. K C = K CR = MAGNARY K=. τ=.7 t =. τ =. REAL K C = K C = K CR =9. K CU =8 K C QD =8 fu= MAGNARY

17 K=. τ=.7 t =. τ =. REAL K C QD = K CU = K C =.8 K C =. K CR =. fu= MAGNARY. Region Engineering Critial Deay τ =.8s K =.9% / m H Output (m H)...

18 7 Region Engineering Ultimate Deay τ =.8s K = % / m H Output (m H) Output (m H)..... Region Engineering τ =.8s K C K = % / m H

19 . τ =.s Region Engineering K C K = % / m H Output (m H).... Region Engineering τ =.s K C K =.% / m H Output (m H)... 8

20 Experiment D = (

21 . Engineering Region Critial Deay Output (m H). τ =.s K = 9.% / m H. SettlingTime = 8se τ =.8s. K =.9% / m H SettlingTime = 7se Output (m H)..... τ =.8s K = % / m H Overshoot = 7% SettlingTime = 9se Engineering Region K C τ K =.s = % / m H Overshoot = 8% SettlingTime = se

22 Output (m H)..... τ =.s K = % / m H K C Overshoot = % SettlingTime = se Engineering Region =.s K C = % / m H Overshoot = 8% SettlingTime = se τ K. Region Engineering τ =. s K C K = % / m H Output (m H)...

23 . Region Engineering τ =.s K = % / m H Output (m H)... Engineering Region Output (m H).... τ =.s K = % / m H Overshoot = % SettlingTime = se τ K =.s = % / m H Overshoot = % SettlingTime = se

24 /th Region T =. τ =.s K C K = 8% / m H nput (%) nput (%) /th Region T =. τ =.s K = % / m H

25 nput (%) /th Region T =. τ =.s K = 8% / m H /th Region T = τ =.s K = % / m H Overshoot = % SettlingTime = se nput (%) τ =.s K = 8% / m H Overshoot = % SettlingTime = se τ =.s K = 8% / m H Overshoot = % SettlingTime = se 8 8

26 Output (m H).... Dampers & Open Engineering Disturbane Response 7 Damper Closes Damper Closes Reset Windup

27 Region Conlusions / th Deay K = %/m-h τ =.se. Output (m H).. 8 Region Conlusions K = %/m-h τ =.9se. Output (m H).. 8

28 Region Conlusions K = %/m-h τ =.se 9 8. Output (m H) Appliation of Controller Gain in Experimental Modeling Bath Distillation nformation.... Reflux Ratio 8. Controller Gain = %/ C Reflux Model Atual Reflux Time (minutes)

29 Bath Distillation nformation... Reflux Ratio. Controller Gain = 9 %/ C Reflux Model Atual Reflux.. 8 Time (minutes)