1. Henrik Manum, student, NTNU
Extensions of Skogestad’s SIMC tuning rules to oscillatory and unstable processes
Henrik Manum,
student, NTNU

2. Project goals
Extend the SIMC-rules to oscillatory and unstable processes
Reduce the model at hand to a first or second order plus delay model
can use existing SIMC-rules on the reduced model
Derive new rules based on the given model

3. Reminder of the SIMC PID tuning rules
Assume we have a model on one of the following forms:
SIMC-PID controller settings:
Fast and robust

4. Processes covered Stable process with pair of complex poles
Unstable process with single real RHP pole

5. Stable process with pair of complex poles
Divide the processes into three parts
Category A
Pure 2nd order underdamped system
Category B
Damped oscillations, but a clear peak in the frequency domain
Category C
Peak less than steady state gain
Main focus today

6. Category B Resonant peak, asymptotically:
Phase, empirical, from Bode-plot
Conservative for all frequencies
Most likely too complicated,
but will use this as a starting-point.

7. Category B Justification for gain-approximation
Peak in gain for pure 2nd order under-damped process:

8. Category B

9. Category B
So, we use the maximum gain to stay safe in gain, and we use the empirical phase-approximation to get a model on the form
with the approximations given in the previous slides

10. Category B
Direct synthesis of controller for the process (for setpoints)
Pure I-controller

11. Category B
Performance and robustness evaluation of the resulting I-controller
Want to solve this optimization problem for a PI-controller and compare the resulting controller to our I-controller

12. Category B
Naive solution to the optimization problem:

13. Category B
Our I-controller

14. Category B
Our I-controller

15. Category B Pros and cons with this method of controller evaluation
Difficult to find a solution
SIMULINK model often diverges
The problem is most likely non-convex
Good graphical representation of trade-off between IAE and TV
Further work:
Look at method by Kristiansson and Lennartson.
Frequency based approach
Broader range of input-signals
Probably easier to use in practice

16. The remaining processes
Category C: Same procedure as category B, but with I derived a 1st order model with a resulting PI-controller
Categroy A: Pure oscillatory. Based on work done by prof. Skogestad, compared with method from literature
Unstable process: Reviewed work by prof. Skogestad and compared to a method found in literature
PLEASE CONSULT THE REPORT IF YOU HAVE INTEREST

17. Summary
The goal of extending the SIMC rules to oscillatory and unstable processes has not been achieved, but we are closer to the goal than when we started
The author has learned a lot, including:
Frequency analysis
Robustness and performance measures in frequency domain
Properties of linear models in frequency domain in general
Optimization used in practice
Time domain analysis
Experience with Matlab on control problems

18. References SIMC-rules Optimal controller
For more references see the report

19. THE END