Flow Rate Control System “Step Response Modeling” February 15, 2006 U.T.C. Engineering 329

Yellow Team b Jimy George b Jeff Lawrence b Taylor Murphy b Jennifer Potter

Outline b System Background Description, SSOC, Step ResponseDescription, SSOC, Step Response b FOPDT Theory b Model Theory b Results b Conclusions

Flow System Setup

Block Diagram

Steady State Operation

SSOC

Step Response: 70%-85%

FOPDT Model b Transfer Function

FOPDT Model b Model Equation Excel Parameters –t d = Time step occurs –A = Height of Step –inbl = Initial Input –outbl= Initial Steady Value

Experimental and Model Results K (lb/min/%) =0.26 Tau (sec) =0.46 t0 (sec) =0.42

Experimental and Model Results…cont K (lb/min/%) = 0.27 Tau (sec) = 0.47 t0 (sec) = 0.47

Results

Results … cont

MODEL PARAMETERS DECREASING STEADY STATE GAINK2.5 V/% DEAD TIMEt o 0 s TIME CONSTANT  0.6 s / 1.2 s / 2.4 s EXPERIMENTAL PARAMETERS DECREASING STEADY STATE GAINK2.5 V/% DEAD TIMEt o 0 s TIME CONSTANT  0.2 s OVERALL RESULTS MODEL PARAMETERS STEADY STATE GAIN,K =0.25 lb/min/% DEAD TIME,t o = 0.45 s TIME CONSTANT,  0.48 s EXPERIMENTAL PARAMETERS STEADY STATE GAIN,K =0.25 lb/min/% DEAD TIME,t o = 0.39 s TIME CONSTANT,  0.51 s OVERALL RESULTS

b Experimental Error Standard Deviations STEADY STATE GAIN,K = ± 0.01(lb/min/%) DEAD TIME,t o = ± 0.08 (sec) TIME CONSTANT,  ± 0.03 (sec) MODEL Error Standard Deviation STEADY STATE GAIN,K = ± 0.01 (lb/min/%) DEAD TIME,t o = ± 0.02 (sec) TIME CONSTANT,  ± 0.04 (sec)