Exam CH3043 "Process Dynamics and Control "

Thursday January 9*̂ 2014,14:00 - 17:00

Instructions

• Write clearly! iVIake sure your name and student number is on each page you hand in.

• All mobile phones should be turned off and are not allowed on the table.

• The test is open-book: You may use the course book "Process Dynamics and Control" by Seborg et al. during the exam. Separate papers with notes or lecture slides are not allowed.

• You may use a pocket calculator.

• Read all questions first. Give all relevant calculations, derivations, etc.

• The exam consists of 4 main questions with equal weight. Note that some questions are divided into two parts that should be solved independently from each other.

• Please start writ ing on a new sheet of paper when starting with question Good luck!

Question 1

Two constant-volume stirred tanks connected in series (Figure 1), are fed by a single stream of a binary solution with constant volumetric flow rate, F. The feed composition Q can vary with time (assume that density is constant and no reactions occur).

F.Q , _ J 1

F.Q ,

• wl

Figure 1: Flow diagram for questions l a and lb

a. Develop a dynamic model for this process that can be used to calculate the concentrations exiting Tank 1 (C,) and Tank 2 (C2).

b. IVIake a degree of freedom analysis for your model, indicating the input(s), output(s), parameters etc.

c. Suppose a recycle stream is used to return some multiple of the inlet f low (rF) from the exit stream of Tank 2 to Tank 1. Write out the new model, and determine the degrees of freedom in this case.

F.Q

I 1 Figure 2: Flow diagram for questions Ic and Id

d. Under which condition(s) can the process shown in Figure 2 be simplified as a single stirred

tank?

Question 2

The following transfer function is not wri t ten in a standard form:

. . . 2 ( 5 + 0.5)

(s + 2)(2s + DfiSs

a. Rearrange it in a standard gain/time-constant form, and determine the gain, poles and zeros.

b. Replace the time-delay term by a 1/1 Padé approximation and repeat question 2a.

Another process has the following block diagram

(0.1s + ly 4s2 -1- 2s + 1

Figure 3: Block diagram for questions 2c-2e.

c. Will the process exhibit overshoot for a step change in w ? Explain/demonstrate why or why not.

d. What will be the approximate maximum value of 3̂ for K = KiKi = 1 and a step change Uis) =

3 / 5 ?

e. Approximately when will the maximum value occur.

Question 3

Part 1 : Consider a SISO process with the following transfer function:

a. If G is to be controlled by PID control, tune the PID controller using the Direct Synthesis approach.

Include the desired closed-loop time constant (T^) as a parameter where necessary.

b. Suppose that the PID tuning as calculated under question 3a is implemented, but that the real

process gain is not equal to 1. For what values of the real process gain will the closed-loop system be

stable for any positive value of the desired closed-loop time constant? Justify your answer with a

calculation.

Part 2: For a different case, a block diagram that represents the closed-loop configuration of a system is shown

in Figure 4. The variables in the diagram represent the Laplace transforms of deviation variables.

Figure 4: Block diagram for question 3 (Part 2 only).

The process transfer function is given by:

300

120,s + l

Furthermore, assume:

= = 1

The controller is a PI controller with a gain of = 6.67 x 10"l The integral t ime of the controller is half the value which would give a critically damped response of controlled variable 7 t o a unit step input of the disturbance D within the closed-loop system.

c. Derive an expression for the closed-loop transfer function for disturbance changes (Y(s)/D(s)) at

constant set point for the system described by the block diagram.

d. Calculate the integral t ime of the controller.

Question 4

Part 1:

A conventional multi-loop control scheme consisting of two PI controllers (MIMO) is considered to control the production composition at the top (XD) and bottom (XB) of a distillation column. The manipulated variables are the reflux f low rate (/•) and the reboiler steam flow rate (s). Steady-state conditions are given in Table 1.

Table 1: Steady-state conditions for question 4 (Part 1 only)

r 5 XD XB

Run (kg/min) (kg/min)

1 50 22 0.98 0.03 2 75 22 0.96 0.04 3 ICQ 22 0.94 0.05 4 75 20 0.95 0.05 5 75 24 0.97 0.03

a. Use the data in Table 1 to calculate the RGA and determine the recommended pairing between the

controlled and manipulated variables.

b. Does this recommended pairing seem appropriate from dynamic considerations? Justify your

answer using engineering judgement.

c. Design a static decoupler for the recommended pairing.

Part 2: For a different case, vapor is condensed and collected in a reflux drum at the top of a distillation column. The reflux f low rate is controlled by a flow controller. The product composition is controlled by using the set point of the reflux f low controller as manipulated variable in a feedbacl< control loop (see Figure 5).

d. The composition control loop is an example of an extended controller. What is the common name

of this type of extended controller?

e. A simpler scheme can be obtained by eliminating FT and FC from Figure 5 and by connecting the

output of QC directly to the control valve. Explain why the extended scheme shown in Figure 5 can

give a significantly better dynamic response compared to this simpler scheme.

Figure 5: Flowsheet for question 4 (Part 2 only)