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Recently I learned about the topic.

Decades ago, when no computational power was available for engineers, it was surely helpful in some way. But I do not understand what the advantage is nowadays, because with any math-tool I can compute poles for a given closed loop system quickly without the need to have ~10 construction rules for loci in mind. Within seconds I can visualize the results on pole locations when I change a parameter in the control function.

Additionally: it is seems only usable when there is only ONE parameter to be changed. But even in the case of a simple PID controller we have three parameters to be changed simultaneously.

Note: This is not criticism, I just want to understand why the method is usually taught. It seems for me, it is more a "didactical concept" which helps to understand what's the effect of changing a parameter but not really a design tool.

MichaelW
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    Why it is taught in schools, colleges and universities is defined by them and not by EEs. I believe you are inadvertently soliciting opinions basically. – Andy aka Mar 31 '22 at 09:58
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    You misunderstood me: I wanted to figure out what the practical impact of this method is. I'm neither in a position to criticize educational institutions nor an expert to judge on this topic. I just wonder, whether such method is still useful when everybody can calculate poles by other means. 70 years ago it was surely useful, because nobody had access to computers. I have a feeling you are defending something that I have not attacked. – MichaelW Mar 31 '22 at 11:24
  • You said this `I just want to understand why the method is usually taught` hence, you are asking for opinions. – Andy aka Mar 31 '22 at 11:43
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    My question means: "For me it seems that the method must have some relevance in practice, otherwise it wouldn't be taught". My focus is not mainly why it is taught, but what is the practical relevance. I do not understand, why you are going to "manipulate" my question into a wrong direction...if the question is somehow stupid, then let me know, but at the moment I cannot follow what you try to tell me. – MichaelW Mar 31 '22 at 12:26
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    You wrote those words not me. I'm not manipulating anything. The rephrased question in the comment above contradicts the only true question in the body of your question because, you say this: `My focus is not mainly why it is taught`. If you cannot decide what your question is, how can anyone reading your question decide that for you? Note: This is a question and answer site and does not work well trying to guess what you really want to know. – Andy aka Mar 31 '22 at 12:45
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    Site rules: `This question is likely to be answered with opinions rather than facts and citations. It should be updated so it will lead to fact-based answers.` See also [this](https://electronics.stackexchange.com/help/dont-ask) and [How do I ask a good question?](https://electronics.stackexchange.com/help/how-to-ask) – Andy aka Mar 31 '22 at 12:47
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    You answered your own question with the last paragraph. Software is garbage in garbage out. You teach people to understand, not to crunch numbers. – DKNguyen Mar 31 '22 at 13:31
  • By which way did I answer my own question? Is it forbidden here to ask, why there is something? I learned about a method which was new for me. Why shouldn't I ask about its relevance after first understanding it? There was a technical answer, so my question cannot be completely silly. – MichaelW Mar 31 '22 at 13:45
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    "*helps to understand what's the effect of changing a parameter*" That's a practical advantage. – DKNguyen Mar 31 '22 at 13:46

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You might find it interesting to know that the PID controller was around long before root locus. Root locus was so popular when it was first discovered because it was one of the first methods that could be used to actually design a control system without needing to play around with the parameters

Controllers like a PID are what I call trial and error methods where you use a canonical approach and then guess the parameters through trial and error. Although this works in many applications, for others you could end up damaging something, and it actually takes longer than just doing a root locus design in the first place.

You can do the same approach with classical controllers like a gain controller or a lead compensator by guessing the k parameter until you get something you like, but you don’t need to do this if you have the root locus. If you understand the root locus well enough, you can find the exact k value you want that gives you the proper response time and damping very easily.

You can use a computer to plot the root locus and analyze it to find the right gain parameter in seconds without needing to go through trial and error.

Yes root locus is really intended for single input single output designs with one control parameter, but there’s a lot of applications that need this, so I would say it’s still useful.

Your university might teach you how to go through the painstaking process of plotting the root locus for the same reason they teach you how to analyze circuits even when you can use a simulator. It pays to have a fundamental knowledge of how something works when you use it.

Ryan
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