CHAPTER 12: PRACTICAL ISSUES Feedback Controller - P, I and D - - PowerPoint PPT Presentation

CHAPTER 12: PRACTICAL ISSUES

Feedback Controller - P, I and D Proportional - The proportional mode can be formulated with various engineering units. Several common methods are used in commercial systems. They do not change the performance of the controller. Scaled variables - Many digital (and all analog) systems represent variables in scaled (dimensionless) form.

range scaled

CV CV CV CV CV CV CV CV

min min max min

− = − − =

range scaled

CV E CV CV CV CV SP SP E = − − − − =

min max min min

) ( ) (

range scaled

MV MV MV MV MV MV MV MV

min min max min

− = − − =

CHAPTER 12: PRACTICAL ISSUES

Feedback Controller - P, I and D

I dt t CV d T dt CV t E T CV t E PB MV t MV

t d r I r r

+           − +       =

∫

r

CV ) ( ' ) ' ( 1 ) ( 100 ) (

PB K

s c

100 ) ( =

This is the Proportional Band. In some software, the engineer must input PB.

CHAPTER 12: PRACTICAL ISSUES

Feedback Controller - P, I and D

I R

T T 1 =

This is the Reset Time. In some software, the engineer must input TR.

I dt t CV d T dt t E T t E K t MV

t d R c

+       − + =

∫

) ( ' ) ' ( ) ( ) (

CHAPTER 12: PRACTICAL ISSUES

Feedback Controller - P, I and D

I dt t CV d T dt t E T t E K t MV

t d R c

+       − + =

∫

) ( ' ) ' ( ) ( ) (

Reset Windup - The integral is persistent, it doesn’t stop until the error is zero. But, if the final element (valve) has reached its maximum or minimum, the integral should “stop”; if it doesn’t, the calculated value could increase in magnitude towards infinity. This is called reset windup and must be prevented.

CHAPTER 12: PRACTICAL ISSUES

Feedback Controller - P, I and D

Behavior without anti-reset-windup: The controller output continues to change (winds up). It takes some time to return to a value where the controller output affects the valve. Behavior with anti-reset-windup: The controller output stops at the boundary (doesn’t wind up). The increase in the controller output immediately affects the valve when needed

• Windup. The controller output

exceeds the range of the valve movement.

No windup!

CHAPTER 12: PRACTICAL ISSUES

Feedback Controller - P, I and D Anti-reset-windup - Several approaches are used. One simple approach is demonstrated here.

iteration next the during MV as use for stored and d implemente is MV ) 2 ( ) (

1

• N

N min max 1 2 1 1

MV MV MV MV MV MV MV CV CV CV t T E T t E E K MV

N N N N N N N N d N I N N c N

≥ ≤ ∆ + =       + − ∆ − ∆ + − = ∆

− − − −

Anti-reset-windup modification

CHAPTER 12: PRACTICAL ISSUES

Feedback Controller - P, I and D Derivative Filter - If we filter the measurement, we “slow” all controller modes. An option exists to filter

• nly the derivative mode.

1 + s T s T

d d

α

α usually is specified as 0.1, which gives a filter of 10% of the derivative time.

CHAPTER 12: PRACTICAL ISSUES

Output processing Bumpless transfer - When the controller is switched from manual (off) to automatic (on), the final element (valve) should start from its initial value.

min max

; ; ) ( ) ( ; MV MV MV MV CV CV CV CV MV MV MV END CV CV CV t T E T t E E K MV CV SP E E E CV CV CV SP E MV N IF

N N N N N N N N N N N N d N I N N c N N N N N N N N N N N N

≥ ≤ = = ∆ + =       + − ∆ − ∆ + − = ∆ − = = = − = = ∆ = =

− − − − − − − − − 1 1 2 1 2 1 1 1 1

2 1 ELSE MV element final to

• utput

Current

N

Special calculation for initialization

CHAPTER 14: CASCADE CONTROL

When I complete this chapter, I want to be able to do the following.

• Identify situations for which cascade is a

good control enhancement

• Design cascade control using the five

design rules

• Apply the tuning procedure to cascade

control

Outline of the lesson.

• A process challenge - improve

performance

• Cascade design rules
• Good features and application

guidelines

• Several process examples
• Analogy to management principle

CHAPTER 14: CASCADE CONTROL

TC 2 T 1 F 1 F 2 T 3 L 1

feed product heating stream

CHAPTER 14: CASCADE CONTROL

Discuss this stirred tank heat exchanger. PID controller

CHAPTER 14: CASCADE CONTROL

TC 2 T 1 F 1 F 2 T 3 L 1

feed heating stream

Disturbance = heating pressure Control performance not acceptable!

Pressure disturbance

20 40 60 80 100 120 140 160 180 200 72 73 74 75 76 IAE = 147.9971 ISE = 285.4111 temperature

minimum Class exercise: What do we do? TC

CHAPTER 14: CASCADE CONTROL

TC 2 T 1 F 1 F 2 T 3 L 1

feed product heating stream

Let’s think about the process behavior.

• Causal relationship

from P disturbance to T (without control)

• What measurable

effect always occurs when P changes? v (valve) → ??? → Q → TC P (heating oil)

P

TC 2 T 1 F 1 F 2 T 3 L 1

feed product heating stream

CHAPTER 14: CASCADE CONTROL

Sketch a Proposal here. PID controller

TC 2 T 1 F 1 FC 2 T 3 L 1

feed product heating stream

CHAPTER 14: CASCADE CONTROL

Key variables for the two PID controllers.

SP1 from person SP2 = MV1 F2=CV2 v=MV2 T2=CV1

A New Control Structure!!

primary secondary

CHAPTER 14: CASCADE CONTROL

Control Performance Comparison for CST Heater Single-Loop Cascade

20 40 60 80 100 120 140 160 180 200 72 73 74 75 76 IAE = 147.9971 ISE = 285.4111 temperature 50 100 150 200 72 73 74 75 76 IAE = 11.5025 ISE = 1.6655

Much better performance! WHY?

CHAPTER 14: CASCADE CONTROL

Each controller is a PID!

Class exercise

computer plant

T 2 F 2

computer person

T2SP

2 2 2 2 2 2 2 2

1 2 2 MV v I ' dt E ) T ( E ) K ( MV F F E

F t F F I F F c sp F

= +         + = − =

∫

1 2 2 2 2 2 1 2

2 1 2 2 MV F I ' dt E ) T ( E ) K ( MV T T E

SP T t T T I T T c sp T

= +         + = − =

∫

CHAPTER 14: CASCADE CONTROL

TC 2 T 1 F 1 FC 2 T 3 L 1 feed product heating stream SP1 for person SP2 = MV1 CV2 MV2 CV1

What have we gained and lost using cascade control? For each case, is cascade better, same, worse than single-loop feedback (TC2 → v)?

• A disturbance in heating medium inlet pressure
• A disturbance in heating medium inlet temperature
• A disturbance in feed flow rate
• A change to the TC set point

CHAPTER 14: CASCADE CONTROL

TC 2 T 1 F 1 FC 2 T 3 L 1 feed product heating stream SP1 for person SP2 = MV1 CV2 MV2 CV1

What have we gained and lost using cascade control? For each case, is cascade better, same, worse than single-loop feedback (TC2 → v)?

• A disturbance in heating medium inlet pressure
• A disturbance in heating medium inlet temperature
• A disturbance in feed flow rate
• A change to the TC set point

Cascade better Both the same Both the same Both the same

CHAPTER 14: CASCADE CONTROL

CASCADE DESIGN CRITERIA Cascade is desired when 1. Single-loop performance unacceptable 2. A measured variable is available A secondary variable must 3. Indicate the occurrence of an important disturbance 4. Have a causal relationship from valve to secondary (cause → effect) 5. Have a faster response than the primary Very important

CHAPTER 14: CASCADE CONTROL

ADVANTAGES OF CASCADE CONTROL

• Large improvement in performance when the

secondary is much faster than primary

• Simple technology with PID algorithms
• Use of feedback at all levels. Primary has zero offset

for “step-like” disturbances.

• Plant operating personnel find cascades easy to
• perate. Open a cascade at one level, and all

controllers above are inactive.

CHAPTER 14: CASCADE CONTROL

A cascade is a hierarchy, with decisions transmitted from upper to lower levels. No communication flows up the hierarchy.

• What are advantages of a

hierarchy?

• What information should be

transmitted up the hierarchy?

• What information should flow

from secondary to primary in a cascade?

CHAPTER 14: CASCADE CONTROL

Does cascade apply to instrumentation? Yes, a valve positioner is a secondary that reduces effects of friction!!

TC 2 T 1 F 1 T 3 L 1 feed product heating stream

Valve positioner: Measures the stem position and adjusts the air pressure to (closely) achieve the desired

• position. This is located

at the valve.