Chapter 7, Topics 3235

1
Chapter 7, Topics 32-35

• PID Controller Tuning, pt. 1

2
Topic 32 Controller Tuning and Performance
Assessment

• Involves selection of the proper values of Kc,
  tI, and tD.
• Affects control performance.
• Affects controller reliability.
• Controller tuning is often a compromise between
  performance and reliability.

3
Tuning Criteria, pt. 1

• Minimize Deviations from Setpoint
• Let the process measurement (PM) wander, just
  dont let it wander very far.
• Attain Good Setpoint Tracking
• Try to get the PM to follow any setpoint changes
  with minimal over- or under-shoot.
• Avoid excessive variation in manipulated
  variables (not PM)
• Try to keep the process under reasonable control
  with minimal valve movements.

4
Tuning Criteria, pt. 2

• Maintain Process Stability During Major
  Disturbances
• Try to keep the process operating under extreme
  conditions. (At DOW, controllers were for normal
  operating conditions, and operators were trained
  to handle major disturbances.)
• Eliminate Offset
• Try to keep the PM on setpoint no matter what.

5
Tuning Criteria - Summary

• The various tuning criteria are to a large extent
  mutually exclusive you cant have it all and
  have to choose what you want to accomplish with
  your controller.

6
QAD Quarter-Amplitude Damping

• It is fairly common to try to tune controllers to
  get a 14 decay ratio (second peak 1/4th the
  amplitude of the first.)
• This is called Quarter-Amplitude Damping, or QAD

A ratio of 13 is also common.
7
Tuning Criteria - Restated

• Specific criteria
• Decay ratio (e.g., QAD)
• Minimize settling time
• General criteria
• Minimize variability
• Remain stable for the worst disturbance upset
  (i.e., reliability)
• Avoid excessive variation in the manipulated
  variable

8
Decay Ratio forNon-Symmetric Oscillations
9
Performance Assessment

• Performance statistics (IAE, ISE, etc.) which can
  be used in simulation studies.
• Standard deviation from setpoint which is a
  measure of the variability in the controlled
  variable.
• SPC charts which plot product composition
  analysis along with its upper and lower limits.

Text calls it deviation from setpoint but
formula is for standard deviation.
10
Performance Assessment Statistics

• IAE Integral Absolute Error
• ITAE Integral Time Absolute Error
• ISE Integral Square Error
• ITSE Integral Time Square Error

These are used to assess process performance, not
to tune controllers but they might help you see
that a controller needs to be retuned.
11
Example of an SPC Chart
Can be used to see which controller is working
better.
12
Topic 33 P-Only Control

• KC is the only adjustable coefficient (tuning
  parameter) in the controller equation for a
  P-only controller
• Want to see how increasing KC impacts the
  dynamics of a closed-loop (controlled) process.

13
P-only Control

• For an open-loop overdamped process as Kc is
  increased the process dynamics goes through the
  following sequence of behavior
• overdamped
• critically damped
• oscillatory
• ringing
• sustained oscillations
• unstable oscillations

A first-order process without deadtime will not
go unstable.
14
Dynamic Changes as Kc is Increased for a FOPDT
Process
Offset
FOPDT First Order Process with Dead Time
P-Only Controller ? Offset
15
Root Locus Diagram(Kc increases a to g)
16
Effect of Kc on Closed-Loop z
Increasing KC increases closed-loop oscillation.
17
Effect of Kc on Closed-Loop tp
Increasing KC shortens closed-loop process
response time.
18
P-only Controller Applied to First-Order Process
without Deadtime

• Without deadtime, the system will not become
  unstable regardless of how large Kc is.
• First-order process model does not consider
  combined actuator/process/sensor system.
• Therefore, first-order process model without
  deadtime is not a realistic model of a process
  under feedback control.

This assumes that at least two parts of the
actuator/process/sensor system are of similar
slow time scales. If one part is much slower
than the other two, a first-order process model
(based on the slow response) may be OK.
19
Topic 34 PI-Control

• Want to see how increasing KC and decreasing tI
  (i.e., stronger integral action) impacts the
  dynamics of a closed-loop (controlled) process.

20
PI Control

• As Kc is increased or tI is decreased (i.e., more
  aggressive control), the closed-loop dynamics
  goes through the same sequence of changes as the
  P-only controller
• Overdamped
• Critically damped
• Oscillatory
• Ringing
• Sustained oscillations
• Unstable oscillations.

21
Effect of Variations in Kc
Increasing KC
Effect of Variations in tI
Decreasing tI
22
Analysis of the Effect of Kc and tI

• When there is too little proportional action or
  too little integral action, it is easy to
  identify.
• But it is difficult to differentiate between too
  much proportional action and too much integral
  action because both lead to ringing.

23
Response of a Properly Tuned PI Controller
Controller Output
Controlled Variable
The Lag should be small, but present.
?
24
Response of a PI Controller with Too Much
Proportional Action
The Lag is almost gone (too much P-action)
?
25
Response of a PI Controller with Too Much
Integral Action
The Lag is excessive too much I-action (tI too
small)
?
26
Topic 35 PID Control

• Want to see how increasing KC, decreasing tI
  (i.e., stronger integral control), and increasing
  tD impacts the dynamics of a closed-loop
  (controlled) process.

27
PID Control

• Kc and tI have the same general effect as
  observed for PI control.
• Derivative action tends to reduce the oscillatory
  nature of the response and results in faster
  settling for systems with larger deadtime to time
  constant ratios.

28
Comparison between PI and PIDfor a Low qp/tp
Ratio
?p/tp Ratio is ratio of deadtime to process time
constant large ratio means sluggish process
(this example is not very sluggish)
29
Comparison between PI and PID for a Higher qp/tp
Ratio
This is a more sluggish process (so D-action
accomplishes more)
30
An Example ofToo Much Derivative Action
Process measurement on caffeine
31
Effect of tD on Closed-Loop z