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Analysis of System DynamicsChapter 10 (Seborg 3 rd Ed)

Chapter 8(Donald 3rd

Ed)

By

Marwan M. Shamel

August 2013

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1) Block Diagrams, revision and applications

2) Dynamic Behavior of Closed-Loop Control Systems

3) Control bands

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Lecture Outlines

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Block Diagram

Example

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Block Diagram

Example

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Block Diagram

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Block Diagram

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Revise the following topic in Chemical

process Modelling (CHE3513)

Solution of non linear (linearisation)differential equations

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1) Feedback/closed system will be in focus

2) Based on block diagram analysis, a useful

simplification and process application will be

done

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Dynamic Behavior of Closed-Loop ControlSystems

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Work in group to propose a feedback controller to the following processes

a) liquid level in a tank

b) Distillate Reflex Ratio

c) High pressure Steam flow in a 10 steam pipe

d) Temperature control for Stirred tank reactor

Include in your discussion

1) Controller

2) Level measuring element

3) The process

4) The final control element

5) Identify the items in the process (disturbance, manipulated variable, and

instruments) C P

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Class Exercise (15 minutes)

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Identify the items in the process (disturbance, manipulated variable, and instruments)

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Dynamic Behavior of Closed-Loop Control Systems

Example: A stirred-tank blending system

)(1

)(1

)( '22'

11' sW

s K

s X s K

s X

Composition control for stirred-tank blending process

x2 1, x1 = 1.0

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Dynamic Behavior of Closed-Loop Control Systems

)(1

)(1

)( '22'

11' sW

s K

s X s K

s X

constantareK andK , 21where

11 2

1, , and (11-2)

wV x K K

w w w

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Identify symbols and blocks

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The symbol denotes the internal set-point compositionexpressed as an equivalent electrical current signal. is

related to the actual composition set point by thecomposition sensor-transmitter gain K m:

sp x t sp x t

sp x t

(11-7) sp m sp x t K x t

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Current-to-Pressure (I/P) Transducer

The transducer transfer function merely consists of a steady-stategain K

IP :

(11-9)t IP P s

K P s

Control ValveAs discussed in Section 9.2, control valves are usually designed sothat the flow rate through the valve is a nearly linear function ofthe signal to the valve actuator. Therefore, a first-order transfer

function is an adequate model

2 (11-10) 1

v

t v

W s K P s s

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I/Pconvertor

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Composition Sensor-Transmitter (Analyzer)

We assume that the dynamic behavior of the composition sensor-transmitter can be approximated by a first-order transfer function,

but m is small so it can be neglected.

mm

X s K

X sController

Suppose that an electronic proportional plus integral controller isused.

11 (11-4)

c

I

P s K

E s s

where and E ( s) are the Laplace transforms of the controlleroutput and the error signal e(t ). K c is dimensionless.

P s p t

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Control Bands

Integral Control:

s

K )s(G)s(E

sK

)s(PtdteK

PI

CC

I

Ct

0I

C

no offset

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Proportional ControlC C K sG )( With offset

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adjust K c and I to obtain satisfactory response

PI Control:

no offset

PID Control: (pure PID)

s

K sG I

C C 11)(

s

s1

1K )s(G DI

CC

No offset, adjust K c, I , D to obtain satisfactory result(requires solving for roots of 4 th order characteristicequation).

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Ideal first order systemExample (from Process Dynamics and Control, Seborg et al . )

A stirred-tank blending process described below is operating with w 1 =600 kg/min, w 2 = 2 kg/min, x 1 = 0.05 and x 2 = 1 (note w is the massflowrate and x the mass fraction). The liquid volume and density areconstant with V = 2 m 3 and = 900 kg/m 3. Find

The initial steady state value of the exit composition, x(0) The exit composition to a step increase in inlet concentration x

1 from 0.05 to

0.075. Take the initial steady state from part (a) Find the approximate exit composition response to a sudden change in w 2 from 2 kg/min to 1 kg/min. Take the initial steady state from part (b).

w1, x1 w2, x2

w, x

The system has constant volume (V) and constant density ( r ), so the following

can be derived: