How can I design a robust PID controller for a second order plant having parametric uncertainties using h infinity. I tried using 'hinfsyn' function in matlab but it gives a higher order controller. Is it possible to convert it to a PID structure.
I also tried using 'systune' command in matlab to tune PID block in Simulink, there how to decide on TuningGoal.Senstivity class parameters (i.e. maximum sensitivity to disturbance as a function of frequency).
Thank You.
Hinfsyn in Matlab will naturally give you a controller which has the order of the plant (second order) in your case plus the order of all the weighting functions you select. The plus of the method is that the synthesis procedure solves a convex optimization problem. So it is not trivial to reduce the resulting controller to an exact PID structure. Hinf is usually very powerful for MIMO systems, for which you do not care about the structure any more.
Further note, if you want to explicitly want to consider structured uncertainties, i.e. a defined Delta block, you need to consider a mu design.
For systune you can design controllers for which you preselect the structure of your controller in advance (therefore it is sometime called structured Hinf). For example a PID controller. This however results in a non-convex problem and may result in a local minima of your optimization problem.
If you try to reduce the sensitivity as you fo, you basically try be robust against inverse multiplicative input uncertainties at your plant input. Not sure if you can interpret your uncertainties in this form.
Bottom line, if you want to design a pure PID controller with with Hinf, systune would be the way to go as you can define your structure. However there is no method yet for which you can explicitly consider your modeled uncertainties.
Thus what you need to do is, analyze your parametric uncertainties and try to reflect them as so called weighting functions, for example on the plant input. Matlab offers you some tools for that. Generate a range of your uncertain parameters (e.g. ureal, for example frequency and damping in your second order model), then build a second uncertain order system (uss), and then try to generate a filter which covers the uncertainty (for example ucover, https://de.mathworks.com/help/robust/ref/ucover.html). Include the filter in the systune design and optimize the criteria you like (margins, response times, ect.)
Hope that helps!
Dear Aayush Bhadani,
I suggest you to see links and attached file in topic.
-Design of robust PID controllers by plotting of the stability regions - STU
https://www.kirp.chtf.stuba.sk/publication_access.php?id=1263...
-Graphical method for robust PID controllers design - Institute of ...
https://www.kirp.chtf.stuba.sk/publication_access.php?id=1357...
-Control of systems with parametric uncertainties using a robust PI ...
https://www.atpjournal.sk/buxus/docs/casopisy/.../plus84_87.pdf
-Robust PID design for processes with interval parametric uncertainty ...
https://www.researchgate.net/.../313128407_Robust_PID_design_f...
-PID-Structured controller design for interval systems: Application to ...
https://hal.archives-ouvertes.fr/hal-00606522/document
-An automatic tuner with short experiment and ... - LU Research Portal
portal.research.lu.se/portal/files/16435277/soltesz16.pdf
Best regards
Hinfsyn in Matlab will naturally give you a controller which has the order of the plant (second order) in your case plus the order of all the weighting functions you select. The plus of the method is that the synthesis procedure solves a convex optimization problem. So it is not trivial to reduce the resulting controller to an exact PID structure. Hinf is usually very powerful for MIMO systems, for which you do not care about the structure any more.
Further note, if you want to explicitly want to consider structured uncertainties, i.e. a defined Delta block, you need to consider a mu design.
For systune you can design controllers for which you preselect the structure of your controller in advance (therefore it is sometime called structured Hinf). For example a PID controller. This however results in a non-convex problem and may result in a local minima of your optimization problem.
If you try to reduce the sensitivity as you fo, you basically try be robust against inverse multiplicative input uncertainties at your plant input. Not sure if you can interpret your uncertainties in this form.
Bottom line, if you want to design a pure PID controller with with Hinf, systune would be the way to go as you can define your structure. However there is no method yet for which you can explicitly consider your modeled uncertainties.
Thus what you need to do is, analyze your parametric uncertainties and try to reflect them as so called weighting functions, for example on the plant input. Matlab offers you some tools for that. Generate a range of your uncertain parameters (e.g. ureal, for example frequency and damping in your second order model), then build a second uncertain order system (uss), and then try to generate a filter which covers the uncertainty (for example ucover, https://de.mathworks.com/help/robust/ref/ucover.html). Include the filter in the systune design and optimize the criteria you like (margins, response times, ect.)
Hope that helps!
I don't know if you have already tried it, but just to make sure: Matlab has a command named hinfstruct that lets you perform H_inf tuning for fixed-structure, predetermined controllers.
Mathworks provides a PI tuning example here: https://www.mathworks.com/help/robust/examples/fixed-structure-h-infinity-synthesis-with-hinfstruct.html
Best regards!
I recommend the following book: S. Skogestad and I. Postlethwaite: MULTIVARIABLE FEEDBACK CONTROL-Analysis and design. Wiley (1996; 2005). They describe how to robustify a PID controller, also MATLAB code is attached to the examples, or can be downloaded from following link: http://folk.ntnu.no/skoge/book/1st_edition/matlab.html
- Badges
- Science topic