Workshop for Flipped Class
Based on students having completed the Chapter 4 e-Lesson before class
Chapter 4 Part II
Modeling and Analysis for Process Control
Copyright © Thomas Marlin 2016
CHAPTER 4: MODELING AND ANALYSIS FOR PC
Workshop 2. Key features from Transfer function
The transfer function for the series process shown below
was introduced in the lesson. Determine the features in the
table for this system.
1.
Stability
2.
Damping
3.
Order
4.
Final Value for unit
step input
5.
Steady-state Gain
𝑇𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑠)
−0.12
𝐾
=
𝑣(𝑠)
10𝑠 + 1 300𝑠 + 1 250𝑠 + 1 % 𝑜𝑝𝑒𝑛
CHAPTER 4: MODELING AND ANALYSIS FOR PC
Workshop 3a. Key features from Transfer function
The dynamic model for a non-isothermal CSTR is derived
in Appendix C. A specific example has the following
transfer function. Determine the features in the table for
this system.
Exothermic reaction
1.
Stability
T
2.
Damping
3.
Order
4.
Final Value
5.
Steady-state Gain
A
C A ( s)
0.0224
kmole / m 3
 2
Fc ( s ) ( s  1.91s  1.13) m 3 / min
CHAPTER 4: MODELING AND ANALYSIS FOR PC
Workshop 3b. Key features from Transfer function
The dynamic model for a non-isothermal CSTR is derived
in Appendix C. A specific example has the following
transfer function. Determine the features in the table for
this system.
Exothermic reaction
1.
Stability
T
2.
Damping
3.
Order
4.
Final Value
5.
Steady-state Gain
A
C A ( s)
0.114
kmole / m 3
 2
Fc ( s ) ( s  1.23s  1.38) m 3 / min
CHAPTER 4: MODELING AND ANALYSIS FOR PC
Workshop 5. Block Diagram
For each of the following block diagrams, determine an
equivalent block diagram. (There are many correct
answers.)
X1(s)
A.
B.
+
X2(s)
X(s)
G1(s)
Y(s)
+
+
Y(s)
+
-
G2(s)
X3(s)
D.
C.
X2(s)
+
G1(s)
+
X1(s)
Y(s)
X1(s)
X2(s)
+
G1(s)
+
X3(s)
G2(s)
Y(s)
CHAPTER 4: MODELING AND ANALYSIS FOR PC
Workshop 4. Sensor dynamics affecting accuracy
A gas flows through a duct, and its temperature is changing. A thermocouple
sensor is being used to measure the temperature. The sensor is inside a
thermowell to protect it from corrosion (grounded thermocouple, ¼ inch
thermowell diameter). The model of the dynamic response of the measurement
to changes in gas temperature is first-order with a time constant of seconds.
How much error occurs in the magnitude of the temperature variation due to the
thermowell dynamics?
Well insulated
Tgas amplitude 20 degrees C
and period 30 seconds
Direction of flow
Velocity  20 m/s
Time
𝑇𝑚𝑒𝑎𝑠𝑢𝑟𝑒 (𝑠)
1
=
𝑇𝑔𝑎𝑠 (𝑠)
(10𝑠 + 1)
Measured temperature, Tmeasure