Closed Loop System Analysis

EP 314:
Process Dynamics and Controls
(May – Aug, 2015)
Mohd Fauzi bin Zanil

EP 314:
Process Dynamics and Controls
(May – Aug, 2015)
Mohd Fauzi bin Zanil

3f. Closed Loop System- Closed loop System Analysis

No
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Topic
No class
3d and e. Closed Loop System: Z-N & C-C controller design
method
Midterm (20%)
3f. Closed Loop System: Closed loop System Analysis
Tutorial 3
ShortQuiz3
4a. Frequency Response: Modelling in Frequency Domain
4b. Frequency Response: Bode diagram
4c. Frequency Response: PID controller design
Tutorial 4
ShortQuiz4
5a. Stability & System Analysis: Introduction
5b. Stability & System Analysis: Routh's test
5b. Stability & System Analysis: Controller Design
Test (10%)
5c. Stability & System Analysis: Criteria of Good Control
Tutorial 5
ShortQuiz5
6a. Introduction to Advanced Control System
6b. Introduction to Advanced Control System
Revission
Final Assignment Submission (10% from Laboratory )
No class

Week
7

Date
16/06/2015
18/06/2015
23/06/2015

8

25/06/2015

30/06/2015
9

10
11

02/07/2015
07/07/2015
09/07/2015
14/07/2015
16/07/2015
21/07/2015

12
23/07/2015
13
14

28/07/2015
30/07/2015
04/08/2015
06/08/2015

Course Learning Outcome (CLO)

Upon the completion of this course,
students will be able to:
• CLO1: Formulate the transfer function.
• CLO2: Evaluate the closed loop block diagram.
• CLO3: Analyze the stability of system.
• CLO4: Design a conventional controller.
• CLO5: Justify and present the best control.

Revision: Development of Control System
Develop the negative unity feedback control system block diagram for the
system shown below.

𝐺𝑣 𝑠

𝑇𝑅′

𝑈

𝑇𝑚′

𝑇′ 𝑠 =

𝑤
′
𝑇𝑖𝑛
𝑉𝑠 + 𝑤

1
𝜌𝐶𝑝
𝑠 +
𝑄ℎ′ 𝑠
𝑉𝑠 + 𝑤

Typical control system used to study the effect of
controller modes on set-point change
𝑅 = 1/𝑠

Typical control system used to study the effect of
controller modes on load change
𝑈 = 1/𝑠

Proportional Control for Set Point
Change (Servo)
Overall transfer function

This may be rearranged in the form of a firstorder lag to give
Where

Proportional Control for Set Point
Change (Servo) cont.…
For unit step change in TR

Inverse Laplace Transform

for

Proportional Control for Set Point
Change (Servo) cont.…

Figure: Unit-step response for set-point change (P controller)

Proportional Control for Load Change
(Regulator)

• This may be arranged in the first-order system; thus
Where
For unit step change in Ti
Taking inverse Laplace we get
for

Proportional Control for Load Change
(Regulator) cont.…

Figure: Unit-step response for load change (P controller)

Proportional-Integral Control for
Load Change
Overall transfer function for load change is

rearrange this gives

Since the denominator contains a quadratic expression, TF may
be written in standard form of 2nd-order system

Proportional-Integral Control for
Load Change cont.…

For step change in load,

Using inverse Laplace, let

Proportional-Integral Control for
Load Change cont.…

Figure: Unit-step response for load change (PI controller)

Proportional-Integral Control for
Set-Point Change
• Transfer function of system shown

This equation maybe reduced to standard form
Note:
τ1 and ζ are the
same as before

Introduce a step change,

Proportional-Integral Control for
Set-Point Change cont.…

Using Laplace inverse for

Proportional-Integral Control for
Set-Point Change cont.…

Example: Proportional-integral
control of stirred-tank heater

Figure: Stirred-tank set point tracking with PI
control (τ1 = 2 min)

Figure: Stirred-tank set point tracking with PI
control (Kc = 20)

Proportional Control of System
with Measurement Lag

Figure: Control system with measurement lag

Proportional Control of System
with Measurement Lag cont.…
Transfer function is
where
For set-point change in T’R , for

Proportional Control of System
with Measurement Lag cont.…

Figure: Effect of controller gain and measuring lag on system response for unit-step change in set point

Challenge
Determine the offset for Proportional-Integral Control
system with measurement lag. Given, 𝑇′𝑅 (𝑠) = 1/𝑠

𝑘𝑐

1
1+
𝑇𝐼 𝑠