Unformatted text preview: 8.6 For PI control
t 1 e(t ) + e(t*)dt * p (t ) = p + K c I 0 t 1 p (t ) = K c e(t ) + e(t*)dt * I 0 Since e(t) = ysp ym and ym= 2 Then e(t)= -2
t 1 2 p (t ) = K c - 2 + (-2)dt * = K c - 2 - I 0 I t Initial response = - 2 Kc Slope of early response = - - 2 Kc = 6 2K c I Kc = -3 I = 5 min - 2K c = 1.2 min-1 I 1234567898 9.1 a) Flowrate pneumatic transmitter: 15 psig - 3 psig qm(psig)= (q gpm - 0 gpm) + 3 psig 400 gpm-0 gpm psig = 0.03 q (gpm) + 3 psig gpm Pressure current transmitter: 20 mA - 4 mA Pm(mA)= ( p in.Hg - 10 in.Hg) + 4 mA 30 in.Hg - 10 in.Hg mA = 0.8 p (in.Hg) - 4 mA in.Hg Level voltage transmitter: 5 VDC - 1 VDC hm(VDC)= (h(m) - 0.5m) + 1 VDC 20 m - 0.5 m VDC = 0.205 h(m) + 0.897 VDC m Concentration transmitter: 10 VDC - 1 VDC Cm(VDC)= (C (g/L)-2 g/L)+1 VDC 20 g/L - 2 g/L VDC = 0.5 C (g/L) g/L b) The gains, zeros and spans are: Solution Manual for Process Dynamics and Control, 2nd edition, Copyright 2004 by Dale E. Seborg, Thomas F. Edgar and Duncan A. Mellichamp 9-1 GAIN ZERO SPAN PNEUMATIC 0.03psig/gpm 0gal/min 400gal/min VOLTAGE CURRENT VOLTAGE 0.8mA/in.Hg 0.205 VDC/m 0.5VDC/g/L 10 in.Hg 0.5m 2g/L 20 in.Hg 19.5m 18g/L *The gain is a constant quantity 9.2 a) The safest conditions are achieved by the lowest temperatures and pressures in the flash vessel. VALVE 1.- Fail close VALVE 2.- Fail open VALVE 3.- Fail open VALVE 4.- Fail open VALVE 5.- Fail close Setting valve 1 as fail close prevents more heat from going to flash drum and setting valve 3 as fail open to allow the steam chest to drain. Setting valve 3 as fail open prevents pressure build up in the vessel. Valve 4 should be fail-open to evacuate the system and help keep pressure low. Valve 5 should be fail-close to prevent any additional pressure build-up. ...
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