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

ProcessOutput

ManipulatedVariable

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

LI

FFC

steam

FI

LI

steam

FI

FFCFB

Σ

Feedback control

Feedforward control

Combined feedforward-feedback control

LI

FB

BoilerFeed control

steam

FI

EXAMPLES

Design Procedures (Block diagram Method)

GL(s)

Load transfer function

GF(s)

Load

Manipulated Variable

Gp(s)

Process

X2

C

Output

L

M∑

FF

Controller

Derivation

function transfer process ,(2)

function transfer load),()1(:need

or

0)(

Hence ).( allfor 0)( want We

)()(

)()()()()(

)()()()()(

sG

sG

sG

sGsG

sGsGsG

sLsC

sLsGsGsG

sLsGsGsLsG

sMsGsLsGsC

P

L

P

LF

FPL

FPL

FPL

PL

Examples

Example 1 Let Gp(s)=Kp/τps+1, GL(s)=KL/τLs+1

Then, GF(s)=-(KL/Kp)(τps+1)/(τLs+1)

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

Example 2 Let Gp(s)=Kpe-Dps/τps+1, GL(s)=KLe-DLs/τLs+1

Then, GF(s)=-(KL/Kp)(τps+1)/(τLs+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 This has three adjustable constants, K, τ1, τ2

Tuning K, K is selected so that for a persistent disturbance, there is no steady state error in output.

Adjustingτ1, τ2 can be obtained from transfer functions. Fine tune τ1, τ2 such that for a step disturbance, the response is somewhat symmetrical about the set point.

1

1)(

2

1

s

sKsGF

Example: A simulated disturbed plant

Waste water treatment

Disturbed flow rate

BOD

Chemicals

(CV)

DV

MV

Simulated Block Disgram

1

1 2 3s s s Disturbed flow rate

+

3

1

1s Chemicals

Feedforward v.s. Feedback Control

0 5 10 15 20 25 30-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

FB

FF

Example: Distillation Column

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

In practice

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

setset

set

xy

xzFD

)(

Design of Feedforward Control Using Material and Energy Balances Consider the hear exchanger

Energy Balance yields Q=WC(T2-T1)=Wsλ

Where λ=hear of vaporization Ws=WC(T2-T1)/λ

This equation tells us the current stream demand based on (1) current flow rate, W, (2) current inlet temperature, T1, (3) desired value of outlet temperature T2.

Steam

T2w, T1

Condensate

Ws

Control Law and Design

Implementation:

Note no dynamics are incorporated

Σ

K

X

measured Tset

Gain

measured Ws

w

T1- +

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

PCPT

TC

Illustrative Example: Steam Jacket - Continued Energy Balance of the Tank:

Energy Balance of Jacket:

Material Balance of the Jacket

LossHeat TThAdt

dTV J

dt

nPd

R

V

Rn

VP

dt

d

dt

dT sJJ

s

JJJ /

condensatendt

dnin

s

Illustrative Example: Steam Jacket - Continued Assume:

Where X=valve position

21110

1

13130

1

)(

sssX

sP

sssP

sT

J

J

Block Diagram

Feed back Controller

Steam Valve

Stirred Tank

Tset

Steam supply

pressureValve

position

Jacket

steam pressure primary

Tank

Temp.secondary

Primary Controller

Jacket Pressure Controller

Steam Valve

Stirred Tank

Tset secondary

Jacket

pressure

supply pressure

Tank

Temp.

Secondary loop

Primary loop

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

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

ControlValve Motor

Desired

position

Secondary loop

Valve position

Air Pressure to Valve Motor

Application 2. Cascade Flow LoopOutput From

Primary Controller “ no cascade “

Output From

Primary ControllerFC

FT

Fset

DP

“ cascade “

GC2 GC1 GP1 GP2Σ

Primarycontroller

Secondarycontroller

Secondaryprocess

primaryprocess

cm2e2

mset

Secondary loop

Primary loop

cset

211

112

1 CPC

PC

set

GGG

GG

m

m

GC2 GCL GP2Σmset m2

ccset

22

22

1 PCLC

PCLC

set GGG

GGG

c

c

Gc 12ΣΣ)110()1(

12 SS )13)(130(

1

SS

+

-Primary

+

-

GC2

Secondary

G2(S) G3(S)

2

32

121

12

G

GG

c

For a cascade system(open-loop)

Without cascade control

32GGc

θcθ

Illustrative Example: Steam Jacket – Continued – Cascade Case

Wu = 0.53

Mag = 20*log10(AR) = -30 (dB)

AR = 0.0316

6228.311

AR

Ku

Illustrative Example: Steam Jacket – Continued – No Cascade Case

Wu = 0.25

Mag = 20*log10(AR) = 0 (dB)

AR = 1

11

AR

Ku

Illustrative Example: Steam Jacket – Continued – No Cascade Case

Ku = 1;wu = 0.25;Pu = 2*Pi / wu = 25.1327

Kc = Ku/1.7 = 0.5882

Taui = Pu / 2 = 12.5664

Taud = Pu /8 = 3.1416

Illustrative Example: Steam Jacket – Continued – Cascade Case

Ku = 20;wu = 0.53;Pu = 2*Pi / wu = 12

Kc = Ku/1.7 = 11.8

Taui = Pu / 2 = 6

2-3 Selective Control Systems Override Control Auctioneering Control Ratio Control

Change from one controlled (CV) or manipulated variables (MV) to another

LT LC LSS

PC

Normalloop

water

steam

1. Override Control – Example Boiler Control

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

motor

SC

HSS

PC FC

Gas out

Gas in

Normal loop

Example: Compressor Surge Control

High Pressure Line

Low Pressure Line

PC

PC

HSS

Example: Steam Distribution System

Length of reactor

Tem

perate

T1

T2

Hot spot

2. Auctioneering Control Systems

Temperature profiles in a tubular reactor

TT TTTTTT

HSS

Cooling flow

Auctioneering Control Systems

TC

Temperature Control

Steam

T2

Bypass

Exchanger

TC

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

Boiler 2 Steam Header

Boiler 2

Boiler 2

PC

Example: Steam Header: Pressure Control

FT

Driver

FT

A Wild stream

Controlled StreamB

FB

ε Gc

Desired

Ratio

FA

3. Ratio Control – Type of feedforward control

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

Disadvantage:Ratio may go To erratic

A Wild stream

FT

Desired Ratio

Multiplier

ε FC

FT

Controlled streamFB

FA

Another implementation of Ratio Control

+

-