Middle East Technical University
09.06.2021
Department of Chemical Engineering
Ch.E. 407 – Process Control (Section 1)
Instructor: Prof. Dr. Canan Özgen
Assistant: Berkan Atman
Tutorial for MT2
1. Tuning constants for PI controller for the following process are to be determined.
𝐺𝑝 (𝑠)𝐺𝑣 (𝑠)𝐺𝑚 (𝑠) =
7.5𝑒 −2.3𝑠
8.5𝑠+1
; 𝐺𝐿 (𝑠) =
100
5𝑠+1
A colleague has calculated several sets of values for the controller gain and integral
time. Determine which of these sets of constants, if any is acceptable and explain why
not.
Tuning
Case A
Case B
Case C
Case D
Kc
12.0
12.0
0.3
0.3
τI
6.0
1.0
6.0
1
2. Consider a process with a transfer function
𝐺𝑝 (𝑠) =
2𝑒 −𝑠
(10𝑠+1)(5𝑠+1)
with 𝐺𝑣 = 𝐺𝑚 = 1
a. Find an approximate FOPDT model using Skogestad’s method.
b. Design
PI
controllers
using
ITAE(set-point),
ITAE(load),
Direct
Synthesis(τc=3) and IMC(τc=0.2τ).
c. Comment on the controllers you design by preparing a table showing all the
controller parameters.
3. The mathematical model for a chemical reactor where an exothermic reactionis taking
place is given below. The temperature in the broth is adjusted to the set point by cooling
water passing through the jacket surrounding the reactor. The control valve is located
on the cooling water line.
−(1 − 0.5𝑒 −10𝑠 )
𝑇′𝑠 =
𝐹 (𝑠) + 0.5𝑒 −10𝑠 𝑇 ′ 𝑖 (𝑠)
(4𝑠 + 1)(5𝑠 + 1) 𝑐𝑤
where T’ and T’i [˚C] are effluent and inlet steam temperatures and F’cw[kg/s] is the
flowrate of cooling water passing through jacket.
Valve TF is:
𝐺𝑣 (𝑠) =
4
𝑘𝑔/𝑠
[
]
0.1𝑠 + 1 𝑝𝑠𝑖
Controller is a P only and the sensor Km= 1 psi/˚C.
Obtain a FOPDT model for process, valve and sensor using Taylor’s expansion method.
Design PI controllers using Z-N method.
4.
5. A step change in the steam pressure to a heat exchanger is made from 20 to 24 psig. The
system outlet response (Figure 1) appears to be approximately second order. Someone
forgot, however, to note the recorder speed. A second test of the system using a
sinusoidal variation of steam pressure to the heat exchanger with an amplitude of 2psig
and frequency of 2 cycles/in yields output temperature variation with amplitude of 4˚.
Determine an approximate transfer function for this system.
Figure 1
6. Identify the transfer function for the Bode plot given below.