AERATOR MIXING STATION
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1 AERATOR MIXING STATION Steady State, Step Response Analysis, Sine and Relay Analysis, Root Locus Green Team: Marc Labrie Matt Baltimore Michael Newman Michael Sherrit University of Tennessee at Chattanooga March 29, 2011 ENGR 3280L
2 OVERVIEW System Overview SSOC Analysis Step Response Analysis FOPDT Modeling FOPDT Analysis Sine Analysis Relay Analysis Root Locus plot Conclusions
3 SYSTEM DIAGRAM
4 SCHEMATIC OF THE SYSTEM Speed Recording Controller Speed Transmitter Speed Controller
5 EXPERIMENTAL DATA ANALYSIS 75 rpm 6 rpm 75+/- 12 rpm
6 STEADY STATE OPERATING CURVE Operating Ranges 0-25% lower 25-50% lower mid 50-75% upper mid % upper
7
8 STEP RESPONSE EXPERIMENTAL DATA UP
9 STEP RESPONSE DATA UP CONTINUED To=.1sec (Black Lines) Tau=.4s (Green Lines)
10 STEP RESPONSE DATA DOWN
11 STEP RESPONSE DATA UP CONTINUED To=.1s (Black Lines) Tau=.4s (Green Lines)
12 RESULTS
13 CONTINUED 0.12 Step Response Dead Time, t0 (Dead Time) Time (s) %-25% Up 0%-25% Down 25%-50% Up 25%-50% Down 50%-75% Up 50%-75%Down 75%-100% Up 75%-100% Down
14 CONTINUED
15 FOPDT THEORY FOPDT Transfer Function For step functions the Manipulated variable m(t) and the Output c(t) are:
16 Model Output
17 Model Output
18 FOPDT MODEL Model Equation System Output c(t) can be modeled by changing K,τ,to, and td. Parameters for 25-50% Step up td (s) A (%) K (RPM/%) to (s) τ(s) Inbl. (%) Outbl. (RPM) Parameters for 25-50% Step-down td (s) A (%) K (RPM/%) to (s) τ(s) Inbl. (%) Outbl. (RPM)
19 Gain, K (RPM/%) Up Experimental Up Model Down Experimental Down Model K (RPM/%) % 25-50% 50-75% %
20 Dead Time (sec) Up Experimental Up Model Down Experimental Down Model Time (sec) % 25-50% 50-75% %
21 Time Constant, τ(sec) Up Experimental Up Model Down Experimental Down Model Time (s) % 25-50% 50-75% %
22
23 SINE RESPONSE Input Speed (RPM)
24 Frequency Response (f=0.5) Output (RPM) Ar = ± 0.03 PA = -38 ± Time (s) Output(RPM) Input Value(%) MWN 3/01/ Input (%)
25 Amplitude Ratio (RPM/%) K = 17.6 RPM/% τ= 0.17 s t 0 = 0.3 s fu = 3.2 Hz Kcu= 0.4 RPM/% Order = 2 Amplitude Ratio (Ar) A Frequency (Hz) MWN 3/01/ Phase Angle (degrees) MWN 3/01/2011 Phase Angle (PA) Frequency (Hz)
26 Sine Response Theory
27 Amplitude Ratio Frequency (Hz) Experimental MWN Model 3/02/2011 K = 17.4 RPM/% τ= 0.2 s t 0 = 0.1 s 10 Amplitude Ratio(RPM/%) 1 Phase Angle Frequency (Hz) Experimental Model MWN 3/02/ Phase Angle (degrees)
28 Gain, K (RPM/%) Experimental Model K (RPM/%) % - 74% 75% - 99% Input (%)
29 Dead Time, t 0 (s) 0.35 Experimental Model t 0 (s) % - 74% 75% - 99% Input (%)
30 Time Constant, τ (s) Experimental Model Tau (s) % - 74% 75% - 99% Input (%)
31 Ultimate Frequency, fu (Hz) Experimental fu (Hz) % - 74% 75% - 99% Input (%)
32 Ultimate Controller Gain, K cu (%/RPM) Experimental K cu (%/RPM) % - 74% 75% - 99% Input (%)
33 50-100% Relay Response Trial Input (%) Output (RPM) Time (s)
34 20 K (RPM/%) Frequency Response Relay Response
35 0.5 τ (sec) Frequency Response Relay Response
36 0.12 to (sec) Frequency Response Relay Response
37
38 TRANSFER FUNCTION The transfer function for an FOPDT system is After substituting Pade s approximation and simplifying, the transfer function becomes
39 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 = 0
40 ROOT LOCUS MODEL ROOT LOCUS PLOT IMAGINARY AXIS REAL AXIS -20
41 KCU COMPARISON Kcu MSS 3/27/11 Root locus Relay Frequency % 25-50% 50-75% %
42 FU COMPARISON Fu Root locus 6 5 MSS 3/27/11 Relay Frequency % 25-50% 50-75% %
43 USEFUL KCU RANGE GREEN TEAM ROOT LOCUS PLOT MWN 3/27/11 Kc 1/ K cu IMAGINARY AXIS Over-damped Region Kc 1/500 Kc 1/10 Kcd REAL AXIS Underdamped Region Kcu= 0.29 RPM/% Kc 1/4 = 0.19 RPM/% Kc 1/10 = 0.14 RPM/% Kc 1/500 = 0.06 RPM/% Kcd= 0.02 RPM/%
44
45 CONCLUSIONS The SSOC shows a linear correlation between input power and voltage The operating range of the system is 0-100% The gain (K) of the system calculated is equal to the slope of the SSOC and experimental vs. model results match closely. The to (dead time) was consistent throughout the experiments
46 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) 0.2 t 0 (sec) 0.1
47 CONCLUSIONS CONTINUED The Kcu from the Root Locus model agreed with what was found from previous experiments. The Fu from the Root Locus model did not agree with what was found from previous experiments. The useful range of Kcu for the speed system varies between 0.06 RPM/% and 0.29 RPM/%.
AERATOR MIXING STATION
AERATOR MIXING STATION Green Team: Marc Labrie Matt Baltimore Michael Newman Michael Sherrit University of Tennessee at Chattanooga April 13, 211 ENGR 328L OVERVIEW System Overview SSOC Analysis Step Response
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