AERATOR MIXING STATION

Transcription

1 AERATOR MIXING STATION Green Team: Marc Labrie Matt Baltimore Michael Newman Michael Sherrit University of Tennessee at Chattanooga April 13, 211 ENGR 328L

2 OVERVIEW System Overview SSOC Analysis Step Response Analysis FOPDT Modeling FOPDT Analysis Sine and Relay Experiments Root Locus model Proportional-only Controller Experiment Proportional Integral Controller Design Conclusions

3 SCHEMATIC AND BLOCK DIAGRAM OF THE SYSTEM Speed Controller Speed Recording Controller Speed Transmitter

4 EXPERIMENTAL DATA ANALYSIS 75 rpm 6 rpm 75+/- 12 rpm

5 STEADY STATE OPERATING CURVE Operating Ranges -25% lower 25-5% lower mid 5-75% upper mid 75-1% upper

6 CONCLUSION Linear in the operating range of -1% corresponding to an output of -174RPM Small uncertainty

7 STEP RESPONSE EXPERIMENTAL DATA UP

8 STEP RESPONSE DATA UP CONTINUED To=.1sec (Black Lines) Tau=.4s (Green Lines)

9 RESULTS

10 CONTINUED.12 Step Response Dead Time, t (Dead Time).1.8 Time (s) %-25% Up %-25% Down 25%-5% Up 25%-5% Down 5%-75% Up 5%-75%Down 75%-1% Up 75%-1% Down

11 CONTINUED

12 Step Response 5% to 95% Output(RPM) Input Value(%) Output (%) Input (%) Dc = 1549 RPM Dm = 9 K= 17.2 RPM/% t =.1 s τ =.7 s MWN 4/17/ Time (s)

13 Step Response 95% to 5% MWN 4/17/11 Output(RPM) Input Value(%) Output (RPM) Dc = 1545 RPM Dm = 9 K= 17.2 RPM/% t =.1 s τ =.6 s Input (%) Time (s)

14 FOPDT THEORY FOPDT Transfer Function For step functions the Manipulated variable m(t) and the Output c(t) are:

15 Model Output

16 Step Response Model 5%-95% Output(RPM) 9 14 Output (Model) 8 12 Input Value(%) 7 Output (RPM) MWN 4/17/11 Input (Model) K= 17.3 RPM/% t =.1 s τ =.7 s Input (%) Time (s)

17 Step Response Model 5% to 95% MWN 4/17/ Output (%) K= 17.4 RPM/% t =.1 s τ =.6 s Input (%) 6 4 Output(RPM) Output (Model) Input Value(%) 1 Input (Model) Time (s)

18 Gain, K (RPM/%) Up Experimental Up Model Down Experimental Down Model K (RPM/%) % 25-5% 5-75% 75-1% 5%-95% Input

19 Dead Time, to(sec) Up Experimental Up Model Down Experimental Down Model K (RPM/%) % 25-5% 5-75% 75-1% 5%-95% Input

20 Time Constant, τ(sec) Up Experimental Up Model Down Experimental Down Model K (RPM/%) % 25-5% 5-75% 75-1% Input

21 CONCLUSIONS K and t from the model and graphical method closely agreed while there was a larger difference in tau for the two methods.

22 SINE RESPONSE Power Input Speed (RPM)

23 Frequency Response (f=.5 Hz) 13 8 Output (RPM) Ar = ±.3 PA = -38 ± Time (s) Output(RPM) Input Value(%) MWN 3/1/ Input (%)

24 Amplitude Ratio % range AR A Frequency (Hz) Frequency (Hz) PA (degrees) MSS 2/27/211 K = 17.1 RPM/% τ =.15 s t =.17 s fu = 3.4 Hz Kcu =.37 %/RPM Order = 2 Phase Angle MSS 2/26/211

25 Amplitude Ratio.1.1 Frequency (Hz) 1 1 MWN MSS 1 Experimental (5%-74%) Model (5%-74%) Experimental (75%-99%) 1 Amplitude Ratio Model (75%-99%).1.1 Frequency (Hz) 1 1 MWN MSS Phase Angle Experimental (5%-74%) Model (5%-74%) Experimental (75%-99%) Model (75%-99%) 75-1% range K= 17.1 RPM/% t=.8s tau=.17s 5-75% range K= 17.3 RPM/% t=.9s tau=.16s Phase Angle

26 Gain, K (RPM/%) Experimental Model K (RPM/%) % - 74% 75% - 99% Input (%)

27 Dead Time, t (s) Experimental Model t (s) % - 74% 75% - 99% Input (%)

28 Time Constant, τ (s).2 Experimental Model.15 Tau (s).1.5 5% - 74% 75% - 99% Input (%)

29 SINE WAVE.1HZ sine output 5% baseline 45% amplitude 18 1 output rpm Output(RPM) Input Value(%) input% Sine wave of whole axis experimental model K to.1.13 ta u time

30 5-1% Relay Response Trial Input (%) Output (RPM) Time (s)

31 2 K (RPM/%) K (RPM/%) Frequency Response Relay Response

32 .5 Tau, τ (sec) Tau (s) Frequency Response Relay Response

33 .12 Dead Time, to (sec).1.8 t (sec) Frequency Response Relay Response

34 CONCLUSION Overall, the frequency experiment more closely agrees with what was found for K, t, and tau in previous experiments than those from the relay experiment.

35 TRANSFER FUNCTION The transfer function for an FOPDT system is After substituting Pade s approximation and simplifying, the transfer function becomes

36 TRANSFER FUNCTION (CONT D) The transfer function for a proportional feedback controller is For an FOPDT system with proportional control, the OLTF is And the characteristic equation becomes 1 + OLTF =

37 ROOT LOCUS MODEL 5-75% 4 MWN 3/27/11 Kc 1/1 Kc 1/4 3 2 K cu IMAGINARY AXIS Kcd Kc 1/ Kcu=.26 %/RPM Kc 1/4 =.17 %/RPM Kc 1/1 =.13 %/RPM Kc 1/5 =.36 %/RPM Kcd=.17 %/RPM REAL AXIS

38 KCU COMPARISON Kcu (%/RPM) MSS 3/27/11 Root locus Relay Frequency -25% 25-5% 5-75% 75-1%

39 FU COMPARISON Fu (Hz) Root locus Relay Frequency MSS 3/27/ % 25-5% 5-75% 75-1%

40 SYSTEM CONTROLLER RANGE GREEN TEAM ROOT LOCUS PLOT MWN 3/27/11 Kc 1/1 Kc 1/ K cu IMAGINARY AXIS Kc 1/ Under damped Region Kcd -1 Over-damped Region Kcu =.28 %/RPM Kc 1/4 =.18 %/RPM Kc 1/1 =.14 %/RPM Kc 1/5 =.61 %/RPM Kcd =.18 %/RPM REAL AXIS

41 CONTROLLER GAIN EXPERIMENT FOR THE ULTIMATE GAIN Experimental Kcu MSS Output (RPM) Set-P=165RPM M bar=95% Step=-25RPM AR=.52 Offset=34RPM Overshoot=6.% Settling time=n/a Kc=.3%/RPM Output(RPM) SET-P(RPM) Input Value(%) 6 4 Input (%) OFFSET Time (s)

42 CONTROLLER GAIN EXPERIMENT FOR ¼ DECAY Experimental 1/4 Decay Set-P=165RPM M bar=95% Step=-25RPM MSS Output (RPM) AR=.24 Offset=6RPM Overshoot=3.8% Settling time=1.2s Kc=.16%/RPM Output(RPM) SET-P(RPM) Input Value(%) Input (%) 144 OFFSET Time (s)

43 CONTROLLER GAIN EXPERIMENT FOR 1/1 DECAY Exeperimental 1/1 Decay Set-P=165RPM M bar=95% Step=-25RPM MSS Output (RPM) AR=.6 Offset=82RPM Overshoot=1.7% Settling time=1s Kc=.1%/RPM OFFSET Output(RPM) SET-P(RPM) Input Value(%) Input (%) Time (s)

44 CONTROLLER GAIN EXPERIMENT FOR 1/5 DECAY Experimental 1/5 Decay MSS Output (RPM) Set-P=165RPM M bar=95% Step=-25RPM Offset=11RPM Overshoot=.48% Settling time=.5s Kc=.7%/RPM Output(RPM) SET-P(RPM) Input Value(%) OFFSET Input (%) Time (s)

45 CONTROLLER GAIN EXPERIMENT FOR CRITICAL DAMPING Experimental Kcd Set-P=165RPM M bar=95% Step=-25RPM MSS Output (RPM) Offset=165RPM Overshoot=% Settling time=.5s Kc=.2%/RPM OFFSET Output(RPM) SET-P(RPM) Input Value(%) Input (%) Time (s)

46 -25% REGION EXPERIMENT Decay for 12.5% and 1 rpm step up output rom 2 15 Output(RPM) 15 1 input % 1 SET-P(RPM) 5 Input Value(%) ML Team Green team Kc=.5 Step up= 1rpm time

47 KC=.1

48 KC RESULTS AND COMPARISON Kcu =.28 %/RPM Kc 1/4 =.18 %/RPM Kc 1/1 =.14 %/RPM Kc 1/5 =.61 %/RPM Kcd =.18 %/RPM

49 Kcu Across All Regions AR=.5 Offset = 113RPM Overshoot= 8% Settling time=n/a Kc=.29%/RPM Output (RPM) 1 8 MWN 4/17/11 6 Input (%) Input Value(%) Time (s) Kcu=.28 %/RPM Set Pt = 345 RPM Step = 12 RPM Output(RPM) SET-P(RPM) 2

50 PROPORTIONAL INTEGRAL CONTROLLER

51 τ I = 3.33t Tau I =.3 (5%-75%) REAL Kqd =.16 Kcu =.24 3 Kcd =.22 K5 =.55 K1 =.12 fu = 4. Hz IMAGINARY MWN 4/16/11 K = 17.4 RPM/% τ =.16 s t =.9 s -2-3

52 Tau I = 1 (5%-75%) REAL MWN 4/16/11 Kcd.18 K5 =.52 K = 17.4 RPM/% τ =.16 s t =.9 s K1 =.13 Kqd =.17 Kcu =.25 fu = 4.3 Hz IMAGINARY

53 Tau I =.7 (5%-75%) REAL K5 =.12 Kcd =.7 MWN 4/16/11 K1 =.36 Kqd =.57 Kcu =.11 fu = 2.4 Hz IMAGINARY

54 Lower τ I Values %-25% (Tau I =.8) 25%-5% (Tau I =.83) 5%-75% (Tau I =.7) 75%-1% (Tau I =.68).12.1 %/RPM Kcd Kc5 Kc1 Kqd Kcu

55 Middle τ I Values.3.25 %-25% (Tau I =.3) 25%-5% (Tau I =.33) 5%-75% (Tau I =.3) 75%-1% (Tau I =.27).2 %/RPM Kcd Kc5 Kc1 Kqd Kcu

56 Large τ I Values.35.3 %-25% (Tau I = 1.3) 25%-5% (Tau I = 1.3) 5%-75% (Tau I = 1) 75%-1% (Tau I = 1.8).25.2 %/RPM Kcd Kc5 Kc1 Kqd Kcu

57 CONCLUSIONS The SSOC shows a linear correlation between input power and speed. The operating range of the system is -1% corresponding to an output range of -174 RPM. The gain (K) of the system calculated is equal to the slope of the SSOC and experimental vs. model results match closely.

58 CONCLUSIONS CONTINUED From the experimental Bode plot the order is 2. The sine response model shows the best estimate of the FOPDT parameters Best FOPDT Estimate K (RPM/%) 17.3 τ (sec).2 t (sec).1

59 CONCLUSIONS CONTINUED The Kcu of about.3 %/RPM from the Root Locus model agreed with what was found from previous experiments. The ultimate frequency (Fu) from the Root Locus model did not agree with what was found from previous experiments. Experimental results allow for controller gain recommendations to customers. Recommended Controller Gains and corresponding Tau I values found in the table below. Response Tau I =.8 Tau I =.3 Tau I = 1 Value Value Symbol (%/rpm) Response Symbol (%/rpm) Response Symbol Value (%/rpm) Critical Kcd.6 Critical Kcd.28 Critical Kcd.21 1/5 Kc5.13 1/5 Kc5.6 1/5 Kc5.58 1/1 Kc1.41 1/1 Kc1.13 1/1 Kc1.14 1/4 Kqd.63 1/4 Kqd.17 1/4 Kqd.19 Ultimate Kcu.126 Ultimate Kcu.25 Ultimate Kcu.27

60 WHAT WE CAN GIVE THE CUSTOMER WITH A PROPORTIONAL-INTEGRAL CONTROLLER Quarter Decay: Kc=.17 %/RPM, Tau I = Output (RPM) Input (%) MWN 4/18/11 Output(RPM) SET-P(RPM) Input Value(%) Time (s)

61 ASSUMPTION No offset Least reset windup Fastest to reach set point Least oscillation

62 PI Controller Set Pt. = 11 RPM ΔSet Pt. = 25 RPM Tau I =.3 s Kc =.55 %/RPM K5 From P Controller MWN 4/22/ Output (RPM) Input (%) Output(RPM) SET-P(RPM) Input Value(%) Axis Title

63 ALL REGIONS INCLUDED Optimized Proportional Integral Controller Output(RPM) SET-P(RPM) Input Value(%) output rpm ML Team Green Kc=.55 TI=.3 Set point = 1 to innput % Time (s)

64 CONCLUSIONS Proportional Integral controller has best output curve PI has no offset Best values for Proportional TI=.3 or higher Kc=.55 %/rpm Kc is for 1/5 th decay in proportional and acts with little overshoot