Closed Loop System Analysis

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EP 314:

Process Dynamics and ControlsMay Aug, 2015)

Mohd Fauzi bin Zanil


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EP 314:

Process Dynamics and ControlsMay Aug, 2015)

Mohd Fauzi bin Zanil

3f. Closed Loop System- Closed loop System Analysis


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No Topic Week Date

13 No class 16/06/2015

143d and e. Closed Loop System: Z-N & C-C controller design

method18/06/2015

15 Midterm (20%) 23/06/2015

163f. Closed Loop System: Closed loop System Analysis

Tutorial 325/06/2015

17ShortQuiz3

4a. Frequency Response: Modelling in Frequency Domain

18 4b. Frequency Response: Bode diagram 30/06/2015

194c. Frequency Response: PID controller design

Tutorial 402/07/2015

20ShortQuiz4

5a. Stability & System Analysis: Introduction07/07/2015

21 5b. Stability & System Analysis: Routh's test 09/07/2015

22 5b. Stability & System Analysis: Controller Design 14/07/2015

23 Test (10%) 16/07/2015

24 5c. Stability & System Analysis: Criteria of Good ControlTutorial 5

21/07/2015

25ShortQuiz5

6a. Introduction to Advanced Control System23/07/2015

26 6b. Introduction to Advanced Control System 28/07/2015

27 Revission 30/07/2015

28 Final Assignment Submission (10% from Laboratory) 04/08/2015

29 No class 06/08/2015

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12

13

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7

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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.


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Revision: Development of Control System

Develop the negative unity feedback control system block diagram for thesystem shown below.

=

+

+

1

+


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Typical control system used to study the effect of

controller modes on set-point change

= 1/


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Typical control system used to study the effect of

controller modes on load change = 1/


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Proportional Control for Set Point

Change (Servo)

Overall transfer function

This may be rearranged in the form of a first-

order lag to give

Where


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Change (Servo) cont.

For unit step change in TR

Inverse Laplace Transform

for


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Change (Servo) cont.

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


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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


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Proportional Control for Load Change

(Regulator) cont.

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


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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


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Load Change cont.

For step change in load,

Using inverse Laplace, let


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Load Change cont.

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


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Set-Point Change

Transfer function of system shown

This equation maybe reduced to standard form

Introduce a step change,

Note:

1 and are the

same as before


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Set-Point Change cont.

Using Laplace inverse for


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Set-Point Change cont.


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Example: Proportional-integral

control of stirred-tank heater

Figure: Stirred-tank set point tracking with PI

control (1 = 2 min)

Figure: Stirred-tank set point tracking with PI

control (Kc = 20)


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Proportional Control of System

with Measurement Lag

Figure: Control system with measurement lag


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with Measurement Lag cont.

Transfer function is

whereFor set-point change in TR , for


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with Measurement Lag cont.

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


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Challenge

Determine the offset for Proportional-Integral Control

system with measurement lag. Given, () = 1/

1 + 1

Closed Loop System Analysis

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