class 21 22 - summary

ICE401: PROCESS INSTRUMENTATION

AND CONTROL

Class 21, 22

Summary

Dr. S. Meenatchisundaram

Email: [email protected]

Process Instrumentation and Control (ICE 401)

Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015

Control System Components:



Control Loops:



Advanced Control Loops:



Mathematical Modeling:



We can define hydraulic resistance (R) to flow as follows:

Hydraulic Capacitance (A) can be given as:

Liquid-Level System:

0

Potential hR

Flow q≡ =

( )

( )

V t QuantityA

h t Potential= =

( )

( )

( ) 1i

H s R

Q s RAs=

+ ( )0 ( ) 1

( ) 1i

Q s

Q s RAs=

+0

( )( )

H sQ s

R=




Liquid-Level Systems with Interaction:

Liquid-Level Systems without Interaction:

( )2

2

1 1 2 2 1 1 2 2 2 1

( ) 1

( ) 1

Q s

Q s R C R C s R C R C R C s=

+ + + +

( )2 2

2

1 1 2 2 1 1 2 2 2 1

( )

( ) 1

H s R

Q s R C R C s R C R C R C s=

+ + + +

1

1

( ) 1

( ) 1

Q s

Q s sτ=

+

2 2

1 2

( ) 1

( ) 1 1

H s R

Q s s sτ τ=

+ +




Thermal System:

CSTR:

( ) =

H(s) 1 Cs

s R

R

θ∆ ∆ +

( ) ( )A A Ai i A

d dn C V C F C F rV

dt dt= = − −

( ) ( )/

0

E RTiAAi A A

FdCC C k e C

dt V

−= − −




Pneumatic System:

Hydraulic System:

0 ( ) 1

( ) ( 1)i

P s

P s RCs

∆=

∆ +

( )

( ) 1 1i

A AX s K K

P s RCs sτ= =

+ +

Dead Time, P&I Diagram:



Process dead time (td) is equal to the distance (D) divided by

the velocity (υ) through the discharge pipe, or td = D/υ.

Direct & Reverse Action:



A controller operates with direct action when an increasing

value of the controlled variable causes an increasing value of

the controller output.

Reverse action is the opposite case, where an increase in a

controlled variable causes a decrease in controller output.

Classification of Controller Modes:



Controller Action:



Two-Position Mode:

Neutral Zone:

00%

0100%

p

p

ep

e

<=

>

Controller Action:



Multi-Position Mode:

Floating Control Mode – Single Speed:

Multi Speed:

1

1 1

1

100%

50%

0%

p

p

p

e e

p e e e

e e

>

= − < < < −

F p p

dpK e e

dt= ± > ∆

Fi p pi

dpK e e

dt= ± > ∆

Controller Action:



Proportional Mode:

0p pp K e p= +

100

p

PBK

=

Controller Action:



Integral Mode:

0

( ) (0)

t

I pp t K e dt p= +∫

1=

I

I

TK

Controller Action:



Derivative Mode:

Proportional-Integral Control Mode:

Proportional-Derivate Control Mode:

Proportional-Integral-Derivate Control Mode:

( )p

D

dep t K

dt=

0

( ) (0)

t

P P P I p Ip t K e K K e dt p= + +∫

0( )p

P P P D

dep t K e K K p

dt= + +

0

( ) (0)

t

p

P P P I p P D I

dep t K e K K e dt K K p

dt= + + +∫

Controller Action:



Proportional-Integral

Controller Action:



Proportional-Derivative

Effects of KP, KI and KD:



KP KI

Effects of KP, KI and KD:



KD

Controller Action:



Try:

A PI controller is reverse acting, PB = 20, 12 repeats per

minute. Find (a) the proportional gain, (b) the integral gain,

and (c) the time that the controller output will reach 0% after

a constant error of -1.5% starts. The controller output when

the error occurred was 72%.

Solution: 1005%

p

PBK

= =

( )

12%

% minIK =

−

Controller Action:



class 21 22 - summary

Engineering