CHAPTER 7: THE FEEDBACK LOOP Disturbance Response = IAE = - - PowerPoint PPT Presentation

CHAPTER 7: THE FEEDBACK LOOP Disturbance Response

5 10 15 20 25 30 35 40 45 50

• 0.2

0.2 0.4 0.6 0.8 Time 5 10 15 20 25 30 35 40 45 50

• 1.5
• 1
• 0.5

Time

= IAE = |SP(t)-CV(t)| dt

Maximum CV deviation from set point

⌠ ⌡

∞

CHAPTER 7: THE FEEDBACK LOOP

• To reduce the variability in the CV,

we increase the variability in the MV.

• We must design plant with MV’s

that can be adjusted at low cost.

100 200 300 400 500 600 700 800 900 1000

• 20
• 10

10 20 Time Controlled Variable 100 200 300 400 500 600 700 800 900 1000

• 20
• 10

10 20 Time Manipulated Variable

CHAPTER 7: THE FEEDBACK LOOP Class exercise: For each of the performance measures below, determine a good value, i.e., large/small, positive/negative, etc.

• Offset
• IAE
• Decay ratio
• Rise time
• Settling time
• MV overshoot
• Maximum CV

deviation

• CV variance
• MV variance

Can we achieve good values for all at the same time? What are the tradeoffs?

Class exercise: Comment on the quality of control for the four responses below.

20 40 60 80 100 120

• 0.5

0.5 1 1.5 S-LOOP plots deviation variables (IAE = 17.5417) Time Controlled Variable 20 40 60 80 100 120

• 0.5

0.5 1 1.5 2 Time Manipulated Variable

A

20 40 60 80 100 120

• 1

1 2 3 S-LOOP plots deviation variables (IAE = 43.9891) Time Controlled Variable 20 40 60 80 100 120

• 1

1 2 3 4 Time Manipulated Variable

B

20 40 60 80 100 120

• 0.5

0.5 1 1.5 S-LOOP plots deviation variables (IAE = 34.2753) Time Controlled Variable 20 40 60 80 100 120

• 0.5

0.5 1 Time Manipulated Variable

C

20 40 60 80 100 120

• 0.5

0.5 1 1.5 S-LOOP plots deviation variables (IAE = 24.0376) Time Controlled Variable 20 40 60 80 100 120

• 0.5

0.5 1 1.5 Time Manipulated Variable

D

Class exercise: Comment on the quality of control for the four responses below.

20 40 60 80 100 120

• 0.5

0.5 1 1.5 S-LOOP plots deviation variables (IAE = 17.5417) Time Controlled Variable 20 40 60 80 100 120

• 0.5

0.5 1 1.5 2 Time Manipulated Variable

A

20 40 60 80 100 120

• 1

1 2 3 S-LOOP plots deviation variables (IAE = 43.9891) Time Controlled Variable 20 40 60 80 100 120

• 1

1 2 3 4 Time Manipulated Variable

B

20 40 60 80 100 120

• 0.5

0.5 1 1.5 S-LOOP plots deviation variables (IAE = 34.2753) Time Controlled Variable 20 40 60 80 100 120

• 0.5

0.5 1 Time Manipulated Variable

C

20 40 60 80 100 120

• 0.5

0.5 1 1.5 S-LOOP plots deviation variables (IAE = 24.0376) Time Controlled Variable 20 40 60 80 100 120

• 0.5

0.5 1 1.5 Time Manipulated Variable

D

Too oscillatory Generally acceptable Too slow Gets close quickly; Gets to set point slowly

CHAPTER 7: THE FEEDBACK LOOP We can apply feedback via many approaches 1, No control - The variable responds to all inputs, it “drifts”.

• 2. Manual - A person observes measurements and

introduces changes to compensate, adjustment depends upon the person.

• 3. On-Off - The manipulated variable has only two

states, this results in oscillations in the system.

• 4. Continuous, automated - This is a modulating control

that has corrections related to the error from desired.

• 5. Emergency - This approach takes extreme action

(shutdown) when a dangerous situation occurs.

CHAPTER 7: THE FEEDBACK LOOP, WORKSHOP 1

The control valve is used to

introduce a variable resistance to flow.

• What is the body of the valve?
• Describe three bodies and what

factors are important in selecting.

• What is the actuator?
• What power source is used? What

happens when the power source fails?

CHAPTER 7: THE FEEDBACK LOOP, WORKSHOP 2

Recommend the correct failure position (open or closed) for each of the circled control valves.

FT 1 FT 2 PT 1 PI 1 AT 1 TI 1 TI 2 TI 3 TI 4 PI 2 PI 3 PI 4 TI 5 TI 6 TI 7 TI 8 TI 9 FI 3 TI 10 TI 11 PI 5 PI 6

air fuel feed product

CHAPTER 8: THE PID CONTROLLER

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

• Understand the strengths and weaknesses
• f the three modes of the PID
• Determine the model of a feedback system

using block diagram algebra

• Establish general properties of PID

feedback from the closed-loop model

Outline of the lesson.

• General Features and history of PID
• Model of the Process and controller - the

Block Diagram

• The Three Modes with features
• Proportional
• Integral
• Derivative
• Typical dynamic behavior

CHAPTER 8: THE PID CONTROLLER

CHAPTER 8: THE PID CONTROLLER

PROPERTIES THAT WE SEEK IN A CONTROLLER

• Good Performance - feedback

measures from Chapter 7

• Wide applicability - adjustable

parameters

• Timely calculations - avoid

convergence loops

• Switch to/from manual -

bumplessly

• Extensible - enhanced easily

TC

v1 v2

CHAPTER 8: THE PID CONTROLLER

SOME BACKGROUND IN THE CONTROLLER

TC

v1 v2

• Developed in the 1940’s, remains

workhorse of practice

• Not “optimal”, based on good

properties of each mode

• Programmed in digital control

equipment

• ONE controlled variable (CV) and

ONE manipulated variable (MV). Many PID’s used in a plant.

CHAPTER 8: THE PID CONTROLLER

PROCESS Proportional Integral Derivative + +

• sensor

CV = Controlled variable SP = Set point E Final element Process variable MV = controller

• utput

Note: Error = E ≡ SP - CV

Three “modes”: Three ways of using the time-varying behavior of the measured variable

CHAPTER 8: THE PID CONTROLLER

GENERAL CLOSED-LOOP MODEL BASED ON BLOCK DIAGRAM Gd(s) GP(s) Gv(s) GC(s) GS(s) D(s) CV(s) CVm(s) SP(s) E(s) MV(s) + + +

• Transfer functions

GC(s) = controller Gv(s) = valve + GP(s) = feedback process GS(s) = sensor Gd(s) = disturbance process Variables CV(s) = controlled variable CVm(s) = measured value of CV(s) D(s) = disturbance E(s) = error MV(s) = manipulated variable SP(s) = set point

CHAPTER 8: THE PID CONTROLLER

Gd(s) GP(s) Gv(s) GC(s) GS(s) D(s) CV(s) CVm(s) SP(s) E(s) MV(s) + + +

• Where are the models for the transmission, and signal

conversion?

• What is the difference between CV(s) and CVm(s)?
• What is the difference between GP(s) and Gd(s)?
• How do we measure the variable whose line is

indicated by the red circle?

• Which variables are determined by a person, which by

computer? Let’s audit

• ur

understanding

CHAPTER 8: THE PID CONTROLLER

Gd(s) GP(s) Gv(s) GC(s) GS(s) D(s) CV(s) CVm(s) SP(s) E(s) MV(s) + + +

• Set point response

Disturbance Response

) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( s G s G s G s G s G s G s G s SP s CV

S c v p c v p

+ = 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( s G s G s G s G s G s D s CV

S c v p d

+ = 1

• Which elements in the control system affect

system stability?

• Which elements affect dynamic response?

PROCESS Proportional Integral Derivative + +

• CV

SP E MV Note: Error = E ≡ SP - CV

CHAPTER 8: THE PID CONTROLLER, The Proportional Mode

p c

I t E K t MV + = ) ( ) ( : domain Time

C C

K s E s MV s G = = ) ( ) ( ) ( : function Transfer

KC = controller gain “correction proportional to error.”

How does this differ from the process gain, Kp?

PROCESS Proportional Integral Derivative + +

• CV

SP E MV Note: Error = E ≡ SP - CV

CHAPTER 8: THE PID CONTROLLER, The Proportional Mode

p c

I t E K t MV + = ) ( ) ( : domain Time

KC = controller gain “correction proportional to error.”

How does this differ from the process gain, Kp? Kp depends upon the process (e.g., reactor volume, flows, temperatures, etc.) KC is a number we select; it is used in the computer each time the controller equation is calculated

PROCESS Proportional Integral Derivative + +

• CV

SP E MV Note: Error = E ≡ SP - CV

CHAPTER 8: THE PID CONTROLLER, The Proportional Mode

p c

I t E K t MV + = ) ( ) ( : domain Time

PROCESS Proportional Integral Derivative + +

• CV

SP E MV Note: Error = E ≡ SP - CV

CHAPTER 8: THE PID CONTROLLER, The Proportional Mode Key feature of closed-loop performance with P-only Final value after disturbance:

1 1 ≠ + ∆ = + ∆ =

→ ∞ → p c d p c d s t

K K K D K K K s D s t CV lim ) (

• We do not achieve zero offset; don’t return to set point!
• How can we get very close by changing a controller

parameter?

• Any possible problems with suggestion?