1. Chemical Process Controls: PID control, part II Tuning
By Peter Woolf
University of Michigan Michigan Chemical Process Dynamics and Controls Open Textbook version 1.0
Creative commons

2. Heater Example from last class
F, Tin
F, T
Goal: Heat the output stream to a desired set point temperature, Tset
Assumptions:
All liquid in lines and tank, thus Fin=Fout=F
Flow is constant
Fluid does not boil
No reactions
Tank is well stirred
Heater has no lag
Heater has finite range
Question: How do we choose PID control parameters?

3. Case: Heated CSTR
Starting at 120, and
Tset=130. Tfeed=100.
(see PID.example.xls)

4. Case: Heated CSTR
Starting at 120, and
Tset=130. Tfeed=100.
(see PID.example.xls)
Here we use a smaller
 to show integrator
windup

5. Case: Heated CSTR
Starting at 120, and
Tset=130. Tfeed=100.
(see PID.example.xls)
Here  and Kc are
smaller.
What happened??

6. Case: Heated CSTR
Starting at 120, and
Tset=130. Tfeed=100.
(see PID.example.xls)
Here  and Kc are
even smaller.
What happened??

7. Possible Tuning Strategies
Perturb system, see what happens and use this response to choose PID parameters
Adjust PID parameters until something bad happens and then back off
Numerical optimization based on data

8. Reaction Curve Tuning (=Open Loop)
Based on a First Order Plus Dead Time (FOPDT) process model assumption
time
First order process delayed response
to signal v

9. Example from http://www.controlguru.com
• Change set point
from 39 to 42% CO
Observe delay (0.8)
Observe max slope
of response at T=27
Slope=
Kmax= output change/
Input change=k1/k2
Max slope
Units? %?
Relative to what?
Example from

10. i d
Aside: intuition
If slope is high (Kmax big) then want a small gain (Kc), as the system is sensitive
If large dead time, then want a small gain because response is delayed, thus aggressive control could be dangerous.
Large dead time also reduces the effect of integration, but increases derivative. Integration can cause oscillations, and with a large delay could be a problem. Derivative can still work with time delay, in most cases.

11. i d
Advantages of open loop tuning:
• fast: the experiment takes just one run
• does not introduce oscillations: Oscillations can be could be dangerous in a large plant, so best avoided.
• Can be done before controller is installed
Disadvantages of open loop tuning:
• can be inaccurate: does not take into account control dynamics or dynamics of other processes
• can be difficult to implement: max slope is not always easy to find.
• Terms can be ambiguous

12. Closed Loop Tuning i d
Zeigler-Nichols (Z-N) Tuning parameters for closed loop i d

13. Closed Loop Tuning Advantages of closed loop tuning 1)Easy experiment
2)Incorporates in closed loop dynamics
Disadvantages of closed loop tuning
1)this experiment can be slow
2)Oscillations could be dangerous in some cases, or if not at least wasteful

14. Model Based Tuning
FOPDT is okay for a first approximation, but we know what the process is doing.
Given a model and normal operating data, we can create a good model of the process.
PID parameters can then be optimally selected based on this model using regression!

15. Model Based Tuning Set points
Predicted model response for a given Kc, i, and d.
temp
time
Goal: Use solver to find optimal values of Kc, i, and d that minimize

16. Model Based Tuning Advantages of model based tuning
1) Incorporates in knowledge about the physical system
2)Incorporates in closed loop dynamics
3) Incorporates in physical limitations in valves and sensors
4) Includes inherent noise in system
Disadvantages of model based tuning
1) Requires a good model that takes time to produce
2) Requires significant data describing a range of operating behaviors
3) Optimization for large systems can be difficult.
4) Overkill for simple systems that are FOPD like

17. Light bulb control system a little bit of real data…

18. FLOW
Light bulb
(=heater)
Temperature sensors
Fan
(=pump)
Purge
valve
inlet

19. Note: valves don’t always look like valves!
open
closed

20. Thermocouple
RTD

21. Sample Response Curve (closed loop)
temp
Time (sec)

22. Closed loop tuning? Difficult to define as we have
(1) Limited control action, thus Ku tops out quickly.
(2) The oscillation frequency is only somewhat stable.
temp
Time (sec)

23. Different PID tuning parameters
Small i, large Kc
All derivative
control
Open recycle
temp
Change set point
Time (sec)

24. Parameterize the model based on historical data
Model based tuning?
Create a model
Parameterize the model based on historical data
If fit is poor, adjust model in step 1 and repeat.
Fit PID tuning parameters to optimize performance.
temp
Time (sec)

25. Model based tuning?
Create a model
Parameterize the model based on historical data
If fit is poor, adjust model in step 1 and repeat.
Fit PID tuning parameters to optimize performance.
F, Tin
F, T
What if this did not fit?
What might be a better model?

26. One idea… 4 CSTRs, each with different functions.
thermocouple
TC2
heater
TC1
RTD
Flow in due
to pressure
balance
Flow due to
recycle
(Look to your reactors text for many more examples of such lumped models of multiple CSTRs)

27. Take Home Messages
PID tuning parameters can be estimated from data using a variety of methods
PID tuning can be difficult and time consuming
Complex physical processes can often be broken down into smaller, more familiar systems