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). X2 102 PH P I/P AT AC XV Figure 11.1 Composition control system for a stirred-tank blending process = 1 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 m?p=900 kg/m3 The process is operating at steady state with w 1=500 kg/min, w 2E 300 kg/min, X 1= 0.4, X 2= 0.8 Gm-Km = 16 mA/(mass fraction). Gv=Ky = 20 kg/min ma The process transfer function p=X'(s)/W 25) = K 1/(t+1) G where T = Vp/w and K 1 =(1-x)/W The transfer function relative to the disturbance variable Go - X'(s)/X 1'(s) = K 2/(T5+1) where K 2 =W1/W A PI controller is used with K =3 and T = 1 min The set point for the exit mass fraction x is set at the initial steady state value. (a) If the disturbance variable xq 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. IX-2min] (0) What is the composition x when a new steady state is reached? [New-ss] (e) What is the offset? (OFFSET]