It is well known that every controller, when optimized in a proper way, will yield good results. Under such circumstances, how should I compare the relative performance of two different controllers that can help me ascertain the superiority of one controller over the other. How can I reduce the bias in tuning so as to genuinely claim the superiority of one over the other ?
If you have applied your controllers to a physical system, you can compare the performance of your controllers at the level of the response time of the controlled system, its accuracy to reach the desired profile and its stability. On the other side, if you want to implement the control algorithms, you should choose the one that is suitable to the development target (memory size, algorithm complexity).
Thank you for your reply Emna. What I want to know is what is the basis for comparison of controllers. Suppose one controller is performing better than the other in terms of set-point tracking and disturbance rejection then what is the benchmark for a reasonable comparison between the two ??
That is quite complex.
I will say that you must define a common performance indicator for both controllers.
For example reference tracking bandwidth then tune both control strategies to fullfil the common requirement.
And make the comparison around the other performance indicators.
We have done that in this paper, take a look.
Article Embedded model control, performance limits: A case study
You may find time (frequency) response of a system using the two controllers. Then measure and compare the time (frequency) domain specifications of both. The comparison shows which is better.
But that is dependent on the tuning of the specific controller. If I tune a particular controller good enough then I can make it perform better than the other but that doesn't mean that the control strategy is better. How can I guarantee that the best performance achieved by a particular controller will always be better than the best performance achieved by the other one ?
You can compute and compare the Hinf norm of the of the closed-loop system, linearized around the operating point, with each controller. I assume that you design a linear controller. The one having smaller norm would have a better worst case performance.
You may also use error criterion like Mean Square Error which gives a single value for the entire response or similar error indices or combinations of them.
You may study control strategies like disturbance rejection, robustness etc
Hi Biswajit,
Thank you for asking me to join this discussion. By an large, I would tend to agree with the view hinted by Andres in his reply.
For one thing, comparison for a real life problem can be specific to requirements of the problem itself !!
Then given a specific problem, a realistic rephrase for the question of comparative performance will be something like:
By a best possible design by method "A", performance criterion "x" achieves a value x1; while by a best possible design by method "B" the same criterion has a value x2.
Of course, design methods differ, and have always been the subject of research, but performance criteria have generally ended up being one or the other combo of the following (I have tried to list these in some sort of decreasing order of importance, if I may phrase it so !):
(Whew ! What a list !!) Hope that helped...
-Sanjay
Dear Sir, thank you for the reply.
How can I ascertain that I have used the best possible design? Suppose, I am tuning the parameters of a controller to satisfy certain criterion then how will I be able to say 'for sure' that this is the best achievable performance for this controller. Can convexification of the problem help ?
Hi Biswajit,
(You seem to have posted this last one while I was "completing" my previous reply !!)
Convexification may help - not in all cases !!
-Sanjay
Sir,
Can you please specify the cases when convexification will not be helpful. That may help me avoid the pitfalls !!!
Thanks
Not sure if a firm answer exists to this last one ! Rather problem specific, I may say !!
Dear Biswajit,
In my humble opinion, there is no method to determine that Controller A is "absolutely" better than Controller B.
However, we can define a scope for 'performance': What is 'good' w.r.t. your application? Are you looking for quick response? Good 'worst-case scenario' performance? better SP tracking/ Disturbance rejection? Robustness? Less computation?
Define your scope. Once done, the comments above are good for start, just select the ones that are more relevant to your notion of 'good control performance.
Hope it helps.
This depends on what you want to achieve, do you want fast control? then compare based on rise time. do you want good stability, then compare settling time. are you concerned about long term effects then compare ITAE. etc
Hi, you can compare using integral square error criterion, like a method analyzing dynamic error behavior.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Control Theory
- Control Systems