Pressure System Essay Example

Pressure System Essay A Pressure system with two resistances Consider a pressure system with tank of volume V and varying pressure P at constant temperature. Fl is inlet flow through resistance RI with source pressure Pl. F2 is output flow through resistance R2 and flowing out at pressure P2. As the flows into and out of the tank are both influenced by the tank pressure, both flow resistances affect the time constant. A typical control problem would be to manipulate one flow rate (either in or out) to maintain a desired drum pressure. Variables: Controlled variable: P Manipulated variable: F2 Disturbance variable: Fl Here we develop a model that describes how the tank pressure varies with the inlet and outlet flow rates. Making a mass balance, Accumulation in the tank = Input flow rate (Fl) Output flow rate (F2) Flows (Ohms law is I = Driving Force Resistance dp dt RIR2 V (Rl+R2) RI +R2 RI R2 ( RI +R2) + ( Rl+R2) rp dP+p = KI Pl+K2P2 Where Kl= (Eq. l) VRI R2 Taking Laplace transform of equation (Eq. l) ps P(S) + P(S) = KI PI'(S) + K2P2(S) P(S) (1+ IPS) = KI PI'(S) + K2 P2(S) 1+1 s + KI P2(S) (Eq. 2) Equation 2 can be represented in a block diagram as below: rps+l rp S+l A Block Diagram of a pressure system with two resistances Assume: RI = 2 rntn,t-n3; R2 v=5rn3 2+4 20 3 6. 6676mtn l. Processing Without Control Where K ? 4 = 0. 667; Assuming step change from 2 m3/min to 3 m3/min in the disturbance variable: S(3S+1) Disturbance response without Control 0. 8 0. 4 0. 2 10 50 time (min) II. Proportional Integral Control for the Disturbance Changes Process: We will write a custom essay sample on Pressure System specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Pressure System specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Pressure System specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Process Transfer function: Gp(s) = Disturbance Transfer function: Gd(s) = I-I(S) Pressure Sensor-Transmitter (Analyzer): Gm(s) = Km m s+l but negligible dynamics > > > Gm(s) = Km Pm(s) = Gm(s)Pa(s) Block diagram for the pressure sensor-tramsmitter pa(S) m S+l Pm(s) Controller (PI controller): GC(S) = ) pa(S) = Control Valve: GV(S) = KV Pt'(S) o. S+l ; but negligible dynamics r > > > Comparator: E(s) = P sp (s) P m (s) P sp (s) = K m P sp (s) Block diagram for the entire process: Rd(S Psp(s) P sp (s) KC(I + ) pa(S) KIP PLI(S) Where: Y=controlled variable U=manipulated variable D=disturbance variable (also referred to as load variable) P=controller output E=error signal Ym=measured value of Y Ysp=set point sp=internal set point (used by the controller) Yu=change in Y due to U Yd=change in Y due to D Gc=controller transfer function GFtransfer function for final control element (including K , if required) IP Gp=process transfer function Gd=disturbance transfer function