Answer Happy

Feedback control system to control the composition of the output stream in a stirred tank blending process is shown in Figure 11.1, page 176 of Textbook (as shown below). X1 X2 w2 wi TH Pt 1/P 4 IP w xm AT AC *, V 1 1sp Figure 11.1 Composition control system for a stirred-tank blending process. Mass fraction x of the output stream is the controlled variable, flow rate w 2 of the input stream is the manipulated variable and mass fraction x 1 of the other input stream is the disturbance variable. The following data are available: Volume and density are constant. V=3.2 m3, p= 900 kg/m 3 The process is operating at steady state with w 1=500 kg/min, w 2= 300 kg/min, x 1= 0.4, X 2= 0.8 Gm= Km = 16 mA/(mass fraction), Gy= K v = 20 kg/min mA The process transfer function G p= X'(s)/W 2'(s) = K 1/(TS+1) where I = Vp/w and K 1 =(1-x)/w The transfer function relative to the disturbance variable G d = X'(s)/X 1'(s) = K 2 /(TS+1) where K2 =W1/W A PI controller is used with K c=3 and 1 = 1 min The set point for the exit mass fraction x is set at the initial steady state value. (a) If the disturbance variable x 1 is suddenly decreased to 0.2 from the initial steady state value of 0.4, derive an expression for the response of outlet composition x to this step change [Expression). (b) Calculate the composition of the exit stream (x) 1 minutes after the change. [X-1min] (c) Calculate the composition of the exit stream (x) 2 minutes after the change. [x-2min] (d) What is the composition x when a new steady state is reached? [New-SS] (e) What is the offset? [OFFSET]