Team Green John Barker John Beverly Keith Skiles UTC ENGR Steady State and Step Response Performance Speed Control System

Outline  System Background –Description, SSOC, Step Response  FOPDT Model  Model Theory  Results  Conclusions

Aerator Mixer Speed Control System

Block Diagram of System

Time Response (Gain)

Time Response (Dead Time)

Time Response (Time Constant)

Step Response Values and Errors K (RPM/%)t0 (s) τ (s) Average Std. Dev

Laplace Domain FOPDT Model  System Transfer Function  G(s) = Ke / τ s+1 –Parameters t 0 =Dead Time t 0 =Dead Time K = System Gain K = System Gain τ = Time Constant τ = Time Constant -t0s-t0s

FOPDT Model  Model Equation in Time Domain – C(t) = A*u(t-t d -t 0 )*K*(1-e ) -( t-td-t0 )

Results

Time Response (Gain)

Time Response (Dead Time)

Time Response (Time Constant)

Overall Results Experimental Results: Steady State Gain : K= 17.1RPM/% ± 0.10 Dead Time : t 0 = 0.06s ± Time Constant : τ = 0.19s ± Model Results: Steady State Gain : K= 17.4RPM/% Dead Time : t 0 = 0.1s Time Constant : τ = 0.23s

Conclusions  Operating Range RPM  K = 17.4 RPM/%  t 0 = 0.1s  τ = 0.23s

Red Team -Pressure- Steady State Operating And Step Response Dennis To Cory Richardson Jamison Linden 6/28/2015, UTC, ENGR-329

Contents  Background Description, SSOC, Step Response  FOPDT Model  Model Theory  Results  Conclusions

Background  System  Input  Output  SSOC  Operating Range

System Figure 1. Schematic diagram of the Dunlap Plant Spray-Paint Booths

Block Diagram Figure 2. Block diagram of paint Booth System

SSOC Operating Range for Output Operating Range for Input

Operating Range  Input operating range (45%-90%)  Output operating range ( cm-H2O)

Theory  Transfer Function  Parameters

Transfer Function Transfer Function m(s) Input c(s) Output 1 0   s Ke st  K=Gain=∆c/∆m=(cm-H2O)/% to=Dead Time τ=Time Constant (use 0.632∆c) Uncertainties (max-min)*(t/n)

Parameters LowerUpper Middle

Results  Experimental (Step-up, Step-down)  Time Response (Gain)  Time Response (Dead Time)  Time Response (Time Constant)

Experimental (Step-up)

Experimental (Step-down)

Time Response (Gain)

Time Response (Dead Time)

Time Response (Time Constant)

FOPDT Model  Model Equation  C(t) = A*u(t-t d -t 0 )*K*(1-e -((t-t d -t 0 )/tau) ) Parameters  t d =15 sec.  A = 15 %  K =.21 cm-H 2 O /%  t 0 = 0.52 sec.  tau = 1.8 sec.  inbl= 60%  outbl=2 cm-H 2 O

Model Time Response (Gain)

Model Time Response (Dead Time)

Model Time Response (Time Constant)

Results  EXPERIMENTAL PARAMETERS INCREASING STEADY STATE GAINK cm-H2O/% DEAD TIMEto0.5 s TIME CONSTANTt1.7 s  EXPERIMENTAL PARAMETERS DECREASING STEADY STATE GAINK cm-H2O /% DEAD TIMEto0.5 s TIME CONSTANTt1.7 s

Conclusions  Input operating range  Output operating range  (K) goes up as the input % is increased ( cm-H2O/%)  (t o) stays constant (0.5sec)  ( ) stays constant (1.7sec)

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

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

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

Flow System Setup

Block Diagram

Steady State Operation

SSOC

Step Response: 70%-85%

FOPDT Model  Transfer Function

FOPDT Model  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)