Consider the blending system shown in Fig. E12.10. A feedback control system is used to reduce the effect of disturbances in feed composition x1 on the controlled variable, product composition, x. Inlet flow rate w2 can be manipulated. Do the following: (a) Draw a block diagram of the feedback control system. (b) Using the information shown below, derive a transfer function for each block. (c) Simulate the closed-loop response for the PI controller settings given below and a step disturbance of +0.2 in x1. (d) Repeat part (c) for a set-point change of -0.1. Attempt to obtain better closed-loop responses by tuning the PI controller. Which controller settings give the best results? (e) Attempt to obtain improved control by adding derivative action to your best PI controller of part (d). Try several values of derivative time, Tn. Which one gives the best results? (f) Suppose that the sampling line to the composition analyzer becomes partially plugged so that the measurement time delay is now three minutes. Using your best controller settings of part (d), simulate the closed-loop response for the same set-point change and the new time-delay value. Explain X! ll ~ I xz wl t ~ wz I I Cip X w Figure E12.10 your new simulation results. Does the larger time delay have a major effect on control system performance? Process Information The pilot-scale blending tank has an internal diameter of 2 m and a height of 3 m. Inlet flow rate w1 and inlet composition x2 are constant. The nominal steady-state operating conditions are as follows: wl = 650 kg/min w2 = 350 kg/min p = 1 g/cm3 .X1 = 0.2 h = 1.5 m x2 = 0.6 x = 0.34 The overflow line maintains a constant liquid volume in the tank. Instrumentation: The range for all of the electronic signals is 4 to 20 rnA. Current-to-pressure transducer: The liP transducer acts as a linear device with negligible dynamics. The output signal changes from 3 to 15 psi when the input signal changes fullscale from 4 to 20 rnA. Control valve: The behavior of the control valve can be approximated by a first-order transfer function with a time constant of 5 s (i.e., 0.0833 min). A 1.2-psi change in the signal to the control valve produces a 300 kg/min change in w2. Composition measurement: The zero and span of the composition transmitter for the exit composition are 0 and 0.50 (mass fraction), respectively. A one-minute time delay is associated with the measurement. Feedback controller: Initially, consider a standard PI controller tuned using the IMC relations in Table 12.1. Justify your choice of 'Tc

Problem 12.10Consider the blending system shown in Fig. E12.10. A feedback control system is used toreduce the effect of disturbances in feed composition x on the1controlled variable, productcomposition, x. Inlet flow rate w2n be manipulated. Do the following:(a) Draw a block diagram of the feedback control system.(b) Using the information shown below, derive a transfer function for each block.(c) Simulate the closed-loop response for the PI controller settings given below and a stepdisturbance of +0.2 in x1(d) Repeat part (c) for a set-point change of -0.1. Attempt to obtain better closed-loop responsesby tuning the PI controller. Which controller settings give the best results(e) Attempt to obtain improved control by adding derivative action to your best PI controller ofpart (d). Try several values of derivative time, Tn. Which one gives the best results(f) Suppose that the sampling line to the composition analyzer becomes partially plugged so thatthe measurement time delay is now three minutes. Using your best controller settings of part (d),simulate the closed-loop response for the same set-point change and the new time-delay value.Explain your new simulation results. Does the larger time delay have a major effect on controlsystem performanceProcess Information The pilot-scale blending tank has an internal diameter of 2 m and a heightof 3 m. Inlet flow rate w an1 inlet composition x are co2stant. The nominal steady-stateoperating conditions are as follows: w 1 650 kg/min x1= 0.2 h= 1.5 w2 = 350 kg/min x2= 0.6 = 1 g/cmm3 x = 0.34The overflow line maintains a constant liquid volume in the tank.Instrumentation: The range for all of the electronic signals is 4 to 20 mA.Current-to-pressure transducer: The liP transducer acts as a linear device with negligibledynamics. The output signal changes from 3 to 15 psi when the input signal changes full scalefrom 4 to 20 rnA.Control valve: The behavior of the control valve can be approximated by a first-order transferfunction with a time constant of 5 s (i.e., 0.0833 min). A 1.2-psi change in the signal to thecontrol valve produces a 300 kg/min change in w2.Composition measurement: The zero and span of the composition transmitter for the exitcomposition are 0 and 0.50 (mass fraction), respectively. A one-minute time delay is associatedwith the measurement.Feedback controller: Initially, consider a standard PI controller tuned using the IMC relations inTable 12.1. Justify your choice of T\n Step-by-step solution Step 1 of 26 ^(a)Refer Figure E12.10 in the text book.The block diagram of th feedback control system is drawn to maintain the exit composition x at aconstant set point x despsp disturbances in inlet composition, x 1The inlet flow rate is wand the composition of the other inlet stream xis constant. Assume that 1 2x1 is measured not that of x. The feedback control is processed if x is measured. Themanipulated variable the inlet flow rate w 2