Chapter 2

Traditional Advanced Control Approaches – Feedforward, Cascade and Selected Control

2-1 Feed Forward Control (FFC)

 Block Diagram  Design of FFC controllers  Examples  Applications

Why Feedforward ?

 Advantages of Feedback Control   Corrective action is independent of sources of disturbances No knowledge of process (process model) is required  Versatile and robust  Disadvantages    No corrective action until disturbance has affected the output. Perfect control is impossible.

Nothing can be done about known process disturbance If disturbances occur at a frequency comparable to the settling time of the process. Then process may never settle down.

Feedforward Control

Feedforward Controller

Disturbance Process Output Manipulated Variable

Feedforward Control

 Advantages   Corrective action is taken as soon as disturbances arrives.

Controlled variable need not be measured.

 Does not affect the stability of the processes  Disadvantages    Load variable must be measured A process model is required Errors in modeling can result in poor control

EXAMPLES Boiler Feed control LI FI steam FB Feedback control LI FI steam FI LI FB FFC Σ FFC steam Feedforward control Combined feedforward-feedback control

 Design Procedures (Block diagram Method)

Load transfer function Load

G

L

(s)

L FF Controller G F (s) Process M Manipulated Variable G p (s) X 2 ∑ C Outp ut

Derivation

C

(

s

) 

G L

(

s

)

L

(

s

) 

G P

(

s

)

M

(

s

)   

G L G L

(

s s

)  

L

 (

s G

)

P



G

 

P G

(

F s

( )

G s

)

F



L

( (

s

)

s

)

L

(

s

) We want

G L



G P C

(

s

)  

G



F

0 for all

L

(

s

).

Hence (

s

)  0 or

G F

 

G L G P

    need : ( 1 ) (2)

G L G P

(

s s

), load transfer function , process transfer function

Examples

 Example 1    Let

G p (s)=K p /τ p s+1

,

G L (s)=K L /τ L s+1

Then

, G F (s)=-(K L /K p )(τ p s+1)/(τ L s+1)

Therefore, feedforward controller is a “lead-lag” unit.

 Example 2   Let

G p (s)=K p e -Dps /τ p s+1

,

G L (s)=K L e -DLs /τ L s+1

Then

, G F (s)=-(K L /K p )(τ p s+1)/(τ L s+1)e (-DL+DP)s

 If

-DL+DP

is positive, then this controller is unrealizable. However, an approximation would be to neglect the delay terms, and readjusting the time constants. In this case, perfect FF compensation is impossible.

Tuning feedforward controllers

    Let

G F

(

s

) 

K

  1

s s

  1 1 2 This has three adjustable constants, K, τ 1 , τ 2 Tuning K, K is selected so that for a persistent disturbance, there is no steady state error in output.

Adjustingτ 1 , τ 2 can be obtained from transfer functions. Fine tune τ 1 , τ 2 such that for a step disturbance, the response is somewhat symmetrical about the set point.

Example: A simulated disturbed plant

Disturbed flow rate DV Waste water treatment Chemicals MV BOD (CV)

Simulated Block Disgram

Disturbed flow rate



s

 1 

s

 1 2 

s

 3 

Chemicals



s

1  1  3

+

Feedforward v.s. Feedback Control

0.15

0.1

0.05

0 -0.05

-0.1

-0.15

-0.2

0

FB

5

FF

10 15 30 20 25

Example: Distillation Column

  Example: Distillation Column    Mass Balance: F=D+B Fz=Dy+Bx D=F(z-x)/(y-x) In practice

D



F

(

z y set

 

x set

)

x set

 For example: If light key increase in feed, increase distillate rate.

 Design of Feedforward Control Using Material and Energy Balances W s Consider the hear exchanger Steam w, T 1 T 2 Condensate   Energy Balance yields

Q=WC(T 2 -T 1 )=W s

λ Where λ=hear of vaporization

W s =WC(T 2 -T 1 )/

λ  This equation tells us the current stream demand based on (1) current flow rate, W, (2) current inlet temperature,

T 1

, (3) desired value of outlet temperature

T 2

.

Control Law and Design

 Implementation: measured T1 Σ + Tset K Gain  measured X w Note no dynamics are incorporated Ws

When to use Feedforward ?

 Feedback control is unsatisfactory  Disturbance can be measured and compensated for  Frequency of disturbance variations are comparable to frequency of oscillation of the system  Output variable cannot be measured.

 There are large time delays in the system

2-2 Cascade Control

 Block Diagram  Design Considerations  Applications

Illustrative Example : Steam Jacket

TC PT PC

Illustrative Example: Steam Jacket Continued  Energy Balance of the Tank: 

V dT dt



hA



T J



T

  Heat Loss  Energy Balance of Jacket:

dT J dt



d dt

 

P J V J n s R

  

V J R d



P J

/

n s



dt

 Material Balance of the Jacket

dn s dt



n in



condensate

Illustrative Example: Steam Jacket Continued  Assume:

T P J P J X

(  

s s s

  )      30 10

s s

  1 1  1 1 

s

3

s

  1  2 1   Where X=valve position

Block Diagram T set Feed back Controller Valve position Steam supply pressure Steam Valve secondary Jacket steam pressure Stirred Tank primary Tank Temp.

T set Primary Controller secondary Jacket Pressure Controller pressure Steam Valve supply Secondary loop Primary loop Jacket pressure Stirred Tank Tank Temp.

Principal Advantages and Disadvantages  Advantages   Disturbances in the secondary loop are corrected by secondary controllers Response of the secondary loop is improved, thus increasing the speed of response of the primary loop  Gain variations in secondary loop are compensated by secondary loop  Disadvantages    Increased cost of instrumentation Need to tune two loops instead of one Secondary variable must be measured

Design Considerations

   Secondary loop must be fast responding otherwise system will not settle  Time constant in the secondary loop must be smaller than primary loop Since secondary loop is fast, proportional action alone is sufficient, offset is not a problem in secondary loop Only disturbances within the secondary loop are compensated by the secondary loop. Hence, cascading improves the response to these disturbances

Applications: 1. Valve Position Control Desired position  Control Air Pressure to Valve Motor Valve Motor Valve position Secondary loop   Valve motion is affected by friction and pressure drop in the line. Friction causes dead band. High pressure drop also causes hysteresis in the valve response Useful in most loops except flow and pressure

Application 2. Cascade Flow Loop Output From Primary Controller “ no cascade “ Output From Primary Controller FT DP FC F set “ cascade “

c set Σ c set Σ Primary controller G C2 m set Secondary controller G C1 e 2 Secondary process G P1 m 2 primary process G P2 Secondary loop

m

2

m set

Primary loop  1

G C



G

1

C G

1

P G

1

P

1 

G C

2 G P2 G C2 m set G CL

c c set

 1

G C



G

2

C G CL

2

G G CL P G

2

P

2 m 2 c c

+ Σ Gc Primary

θ c

+ Σ G C2 12 Secondary G 2 (S) (

S

1  1 ) 2 ( 10

S

 1 ) G 3 (S) ( 30

S

1  1 )( 3

S

 1 )

θ

For a cascade system (open-loop)  

c

 12 1

G

2

G

3  12

G

2 Without cascade control  

c



G

2

G

3

Illustrative Example: Steam Jacket – Continued – Cascade Case  W u = 0.53

  Mag = 20*log 10 (AR) = -30 (dB) AR = 0.0316



K u

 1

AR

 31 .

6228

Illustrative Example: Steam Jacket – Continued – No Cascade Case  W u = 0.25

  Mag = 20*log 10 (AR) = 0 (dB) AR = 1 

K u

 1

AR

 1

Illustrative Example: Steam Jacket – Continued – No Cascade Case     K u  = 1;w K c = K u u = 0.25;P u = 2*Pi / w /1.7 = 0.5882

u  Tau i = P u / 2 = 12.5664  Tau d = P u /8 = 3.1416

= 25.1327

Illustrative Example: Steam Jacket – Continued – Cascade Case    K u  = 20;w K c = K u u = 0.53;P /1.7 = 11.8

u  Tau i = P u / 2 = 6 = 2*Pi / w u = 12

2-3 Selective Control Systems

 Override Control  Auctioneering Control  Ratio Control  Change from one controlled (CV) or manipulated variables (MV) to another

1. Override Control – Example Boiler Control

steam PC water LT LC LSS Normal loop

LSS: Low Selective Switch – Output a lower of two inputs Prevents: 1. Level from going too low, 2. Pressure from exceeding limit (lower)

motor

Example: Compressor Surge Control

Normal loop HSS SC Gas in PC FC Gas out

Example: Steam Distribution System

High Pressure Line PC HSS PC Low Pressure Line

2. Auctioneering Control Systems

Hot spot T 1 T 2 Length of reactor

Temperature profiles in a tubular reactor

Auctioneering Control Systems

TT TT TT TT Cooling flow

TC

HSS

Temperature Control

Split Range Control: More than one manipulated variable is adjusted by the controller

TC Bypass Exchanger T 2 Steam

Example: Steam Header: Pressure Control

Boiler 2 Boiler 2 Boiler 2 Steam Header PC

A

3. Ratio Control – Type of feedforward control

Wild stream F A FT Desired Ratio

Disadvantage: Ratio may go To erratic

Driver ε G c B FT F B Controlled Stream

However, one stream in proportion to another. Use if the ratio must be measured and displayed

A

Another implementation of Ratio Control

Wild stream FT F A Multiplier Desired Ratio

-

ε

+

FC FT F B Controlled stream