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It is desired to control the exit temperature T2 of the heat exchanger by adjusting the steam flow rate ws. Unmeasured disturbances occur in inlet
It is desired to control the exit temperature T2 of the heat exchanger by adjusting the steam flow rate ws. Unmeasured disturbances occur in inlet temperature T1. The dynamic behavior of the heat exchanger can be approximated by the transfer functions Ws(s)T2(s)=12s+12.5e2sT1(s)T2(s)=5s+11.3e3skg/sCdimensionless where the time constants and time delays have units of seconds. The control valve has the following steady-state characteristic ws=0.5p4 where p is the controller output expressed in mA. At the nominal operating condition, p=12mA. After a sudden change in the controller output, ws reaches a new steady-state value in 25s (assumed to take five time constants). The temperature transmitter has time constant 1s and is designed so that its output signal varies linearly from 4 to 20mA as T2 varies from 50C to 90C. A. Draw a block diagram. B. Write a characteristic equation. C. If a proportional-only feedback controller is used, what is Kcm ? What is the frequency of the resulting oscillation when Kc=Kcm ? Use the direct-substitution method and nonlinear solver (Matlab, Excel). D. Estimate Kcm using the Routh test. E. Determine the offset for Kc=40. It is desired to control the exit temperature T2 of the heat exchanger by adjusting the steam flow rate ws. Unmeasured disturbances occur in inlet temperature T1. The dynamic behavior of the heat exchanger can be approximated by the transfer functions Ws(s)T2(s)=12s+12.5e2sT1(s)T2(s)=5s+11.3e3skg/sCdimensionless where the time constants and time delays have units of seconds. The control valve has the following steady-state characteristic ws=0.5p4 where p is the controller output expressed in mA. At the nominal operating condition, p=12mA. After a sudden change in the controller output, ws reaches a new steady-state value in 25s (assumed to take five time constants). The temperature transmitter has time constant 1s and is designed so that its output signal varies linearly from 4 to 20mA as T2 varies from 50C to 90C. A. Draw a block diagram. B. Write a characteristic equation. C. If a proportional-only feedback controller is used, what is Kcm ? What is the frequency of the resulting oscillation when Kc=Kcm ? Use the direct-substitution method and nonlinear solver (Matlab, Excel). D. Estimate Kcm using the Routh test. E. Determine the offset for Kc=40
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