UNIVERSITI MALAYSIA PERLIS
SEMESTER 2 SIDANG AKADEMIK 2011/2012
ERT 210 – Kawalan dan Dinamik Proses / Process Control and Dynamics
PROBLEM BASED LEARNING (PBL)
QUESTIONS FOR GROUP 11, 12, AND 13
Figure Q3 Stirred-tank Blending System
It is desired to control the exit concentration of c3 of the liquid blending system shown in Figure Q3. Using the information given below, do the following:
a. / Develop the dynamic model for this system as functions of time for any given variation in inputs. / [15 M]b. / Perform a degrees of freedom analysis. Identify all input and output variables. / [10 M]
c. / Draw a block diagram for the composition control scheme. (Use the symbols in the figure as much as possible.) / [10 M]
d. / Derive an expression for each transfer function and substitute numerical values. / [20 M]
e. / Determine the overall transfer function of the block diagram. / [10 M]
f. / Test the stability of the transfer function using the Routh stability criterion. / [10 M]
g. / Determine the PID controller parameters for the Ziegler-Nichols (Z-N) settings and Cohen and Coon method. / [15 M]
h. / Suppose that the PI controller has been tuned for the nominal set of operating conditions below. Indicate whether the controller should be retuned for each of the following situations. (Briefly justify your answers.)
(i) The nominal value of c2 changes to = 0.08 lb solute/ft3.
(ii) The span of the composition transmitter is adjusted so that the transmitter output varies from 4 to 20 mA as c3 varies from 3 to 14 lb solute/ft3.
(iii) The zero of the composition transmitter is adjusted so that the transmitter output varies from 4 to 20 mA as c3 varies from 4 to 10 lb solute/ft3. / [10 M]
i. / Use MATLAB/SIMULINK to solve the problems whenever it is appropriate to do so.
Available information:
1. The tank is perfectly mixed.
2. The volumetric flow rate and solute concentration of stream 2, q2 and c2, vary with time, while those of stream 1 are constant.
3. The flow-head relation for the valve on the exit line is given by;
4. The densities of all three streams are identical and do not vary with time.
5. A 2-min time delay is associated with the composition measurement. The transmission output signal varies linearly from 4 to 20 mA as c3 varies from 3 to 9 lb solute/ft3.
6. The pneumatic control valve has negligible dynamics. Its steady-state behaviour is summarized below where pt is the air pressure signal to the control valve from the I/P transduser.
Group 11 / Group 12 / Group 13pt (psi) / q2 (gal/min) / pt (psi) / q2 (gal/min) / pt (psi) / q2 (gal/min)
6 / 20 / 4 / 15 / 5 / 20
9 / 15 / 8 / 10 / 10 / 15
12 / 10 / 16 / 5 / 15 / 10
7. An electronic, direct-acting, PI controller is used.
8. The current-to-pressure transduser has negligible dynamics and a gain of 0.3 psi/mA.
9. The nominal operating conditions are:
Group 11 / Group 12 / Group 13ρ (lb/ft3) / 75 / 80 / 90
(gal/min) / 10 / 15 / 20
(gal/min) / 15 / 20 / 25
(lb of solute/ft3) / 5 / 7 / 9
(lb of solute/ft3) / 7 / 9 / 11
CV (gal/min/(ft)1/2) / 12.5 / 15.5 / 20.5
D (tank diameter) (ft) / 4 / 5 / 6
-END OF QUESTIONS-
QUESTIONS FOR GROUP 14 AND 15
Figure Q4 Jacketed Vessel
The jacketed vessel in Figure Q8 is used to heat a liquid by means of condensing steam.
Using the information given below, do the following:
a. / Develop the dynamic model for this system as functions of time for any given variation in inputs. / [15 M]b. / Perform a degrees of freedom analysis. Identify all input and output variables. / [10 M]
c. / Draw a block diagram for the composition control scheme. (Use the symbols in the figure as much as possible.) / [10 M]
d. / Derive an expression for each transfer function and substitute numerical values. / [20 M]
e. / Determine the overall transfer function of the block diagram. / [15 M]
f. / Test the stability of the transfer function using the Routh stability criterion. / [15 M]
g. / Determine the PID controller parameters for the Ziegler-Nichols (Z-N) settings and Cohen and Coon method. / [15 M]
h. / Use MATLAB/SIMULINK to solve the problems whenever it is appropriate to do so.
(a) Process
(i) The volume of liquid within the tank may vary, thus changing the area available for heat transfer.
(ii) Heat losses are negligible.
(iii) The tank contents are well mixed. Steam condensate is removed from the jacket by steam trap as soon as it has formed.
(iv) Thermal capacitances of the tank and jacket walls are negligible.
(v) The steam condensation pressure Ps is set by a control valve and is not necessarily constant.
(vi) The overall heat transfer coefficient U for this system is constant.
(vii) Flow rates qF and q are independently set by external valves and may vary.
(b) Transfer Line
(i) Pump volume can be neglected.
(ii) Transmitter dynamics are negligible.
(iii) The transfer line dimensions are as follows.
Group 14 / Group 15Length (m) / 25 / 30
Inner diameter (m) / 0.6 / 0.7
(c) Temperature Transmitter Data
(i) The transmitter data are as follows.
Group 14 / Group 15T (oC) / Tm (mA) / T (oC) / Tm (mA)
10.00 / 4 / 10.00 / 5
30 / 20 / 30 / 25
(d) Step test
A step test was performed to develop a FOPTD model. The results of the step test are as follows.
Time / Input / Output / Time / Input / Output2 / 13.89 / 20 / 13 / 17.89 / 25.77
3 / 15.06 / 20.65 / 14 / 17.92 / 25.84
4 / 15.89 / 21.79 / 15 / 17.95 / 25.88
5 / 16.49 / 22.83 / 16 / 17.96 / 25.92
6 / 16.91 / 23.68 / 17 / 17.97 / 25.94
7 / 17.22 / 24.32 / 18 / 17.98 / 25.96
8 / 17.44 / 24.79 / 19 / 17.99 / 25.97
9 / 17.6 / 25.13 / 20 / 17.99 / 25.98
10 / 17.71 / 25.38 / 50 / 17.99 / 25.98
11 / 17.8 / 25.55 / 60 / 17.99 / 25.98
12 / 17.85 / 25.68 / 70 / 18.00 / 26.00
(e) I/P Transducer Data
(i) The I/P transducer data are as follows.
Group 14 / Group 15p (mA) / pv (psig) / p (mA) / pv (psig)
4 / 3 / 5 / 4
20 / 15 / 25 / 20
(f) Control valve
(i) An equal percentage valve is used, which has the following relation:
Group 14 /Group 15 /
For a step change in input pressure, the valve requires approximately 1min to move to its new position.
-END OF QUESTIONS-
SEM2, 2011/2012 RAHIMAH@ UniMAP