## The root locus is useless

## The root locus is useless

(OP)

The root locus does not provide a closed loop transfer function.

The root locus is only good for find where the poles will be as ONLY a proportional gain is changed.

What systems use only a proportional gain? Only mechanical systems like a speed governor or some spring based hydraulic devices.

Teaching root locus is almost useless. There are many threads on YouTube that show how to calculate the root locus and various related items.

I once asked a college instructor why he taught the root locus. The answer is that is is part of the curriculum that was always taught.

I think learning root locus it is a waste of time.

What is important is knowing where the break away point is. After that the rest is useless.

Root locus could be useful to mechanical designers that need to make sure their speed governors or spring type hydraulic control devices will work.

However, after 30+ years of control I have yet to see where any mechanical engineer knows how to calculate an open loop transfer function.

Look at the videos on YouTube. They all assume one knows an open loop transfer function to work with. This is definitely NOT the case in real life.

The root locus is useless unless one first has an open loop transfer function. The root locus is useless when using modern controllers capable of PI, PD, PID or leadlag closed loop control.

I submit that colleges and universities are wasting students time and money learning about the root locus. There are better things to learn that make learning the root locus obsolete.

This is my finger in the eye of those who continue to waste time and money teaching root locus.

Don't bother to object unless you have a very good argument for root locus.

The root locus is only good for find where the poles will be as ONLY a proportional gain is changed.

What systems use only a proportional gain? Only mechanical systems like a speed governor or some spring based hydraulic devices.

Teaching root locus is almost useless. There are many threads on YouTube that show how to calculate the root locus and various related items.

I once asked a college instructor why he taught the root locus. The answer is that is is part of the curriculum that was always taught.

I think learning root locus it is a waste of time.

What is important is knowing where the break away point is. After that the rest is useless.

Root locus could be useful to mechanical designers that need to make sure their speed governors or spring type hydraulic control devices will work.

However, after 30+ years of control I have yet to see where any mechanical engineer knows how to calculate an open loop transfer function.

Look at the videos on YouTube. They all assume one knows an open loop transfer function to work with. This is definitely NOT the case in real life.

The root locus is useless unless one first has an open loop transfer function. The root locus is useless when using modern controllers capable of PI, PD, PID or leadlag closed loop control.

I submit that colleges and universities are wasting students time and money learning about the root locus. There are better things to learn that make learning the root locus obsolete.

This is my finger in the eye of those who continue to waste time and money teaching root locus.

Don't bother to object unless you have a very good argument for root locus.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: The root locus is useless

I'll grant you that, it is not a useful method in plant automation given the complexity of the real-world.

## RE: The root locus is useless

What do you do when you need a PI or PID controller?

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: The root locus is useless

If you've never taught controls, you may not see the value in root locus analysis. I've taught controls for years (and also worked as a controls engineer in industry for over 22 years), and I think root locus analysis is a great teaching tool, though I'm not a fan of root locus controller design as presented by most textbooks. I like root locus analysis for teaching because root-locus plots allow students to see the connection between closed-loop pole locations in the s-plane and the closed-loop time domain behavior of a system to simple inputs like impulses and steps. As the closed-loop pole location is varied by changing a parameter (and you are incorrect to say that the parameter has to be a proportional gain, it can be any parameter if you know how to recast the characteristic equation appropriately), students can see how the closed-loop time domain response changes. I've noticed students find it much more difficult to relate Bode, Nyquist, or Nichols frequency-domain plot shapes to time-domain behavior.

I agree with your statement that an open-loop transfer function is necessary and that most people don't know how to find one, that's why I taught my students both modeling using physical principles (which we only used for very simple systems I refer to as toys, and I would never suggest these methods for a real system that hadn't already been modeled for some other reason) and some system identification techniques we used on real systems for coming up with transfer functions before we even started talking about feedback controller algorithm selection/design. (I happen to know you personally, Peter, and I know how much importance you place on system identification. I think I recall you saying once that 90% of the effort in good controller design is solving the system identification problem.)

After getting non-minimum phase open-loop transfer functions using one of those methods, I showed my students root locus plots using software, but didn't teach them how to draw it. I think that's a waste of time since computers can do it so easily. I did talk about some of the basic steps of root locus plotting to try to give them an intuitive feel for what the root locus plot would look like for a given open-loop transfer function, but I no longer ask them to plot one by hand.

I showed them (using a computer), for systems with second-order dominant closed-loop poles, how:

- Closed-loop poles on the real axis give an overdamped response.
- Widely-separated closed-loop poles on the real axis give a response dominated by the pole closest to origin.
- Complex closed-loop poles near the real axis give a response with little overshoot, and those with the same spectral radius closer to the quadrature (I refuse to say imaginary) axis give more overshoot. In other words, I showed them how the damping factor affects overshoot.
- Moving complex closed-loop poles up and down near the quadrature axis with the same real component affect the damped oscillation frequency.
- Moving complex closed-loop poles left and right with the same damped oscillation frequency, i.e., changing the real component, affects the speed of decay of the damped sinusoid's envelope.

All of these things can give students an intuitive feel for how real and quadrature components of closed-loop poles affect the time-domain step response behavior. I taught them formulas they could use with second-order dominant systems to calculate closed-loop pole locations that were functions of rise time, settling time, overshoot, damped frequency, etc., so they would know where to put their closed-loop second-order poles to achieve a certain time-domain response. I then showed them how adding poles and zeros via a controller changes the shape of the root locus so if they knew where they wanted their closed-loop poles, they could try to shape the locus so it passes through those points to achieve the desired closed-loop time domain response. That helps them when they may later learn about pole placement theory in state-space feedback control systems.Root locus analysis is also good for examining the effects of adding controller poles and zeros on closed-loop stability. I showed how adding controller poles shifts the root locus toward the right-half plane, typically reducing stability margins, and adding controller zeros shifts the root locus back toward the left-half plane, typically increasing stability margins. I also used root locus analysis to show students why trying to cancel right-half plane poles with right-half plane controller zeros is a bad idea and may result in closed-loop poles trapped in the right-half of the s-plane if the cancellation isn't perfect, leading to a system that is unstable no matter what else you try with your controller.

I disagree that the "root locus is useless when using modern controllers capable of PI, PD, PID or leadlag [sic] closed loop control." I taught students how real systems typically have at least three poles (one in the actuator, one in the plant, and one in the sensor), so most root locus plots have branches moving into the right half of the s-plane, meaning most systems can be made unstable by too much proportional gain (or other parameter as appropriate). This was a great lead-in when teaching PID tuning via the Ziegler-Nichols closed-loop tuning method to show that most systems will oscillate if you increase the gain too much. (Don't worry, I also tell them there are many other (some better) heuristic tuning methods than those developed by Ziegler and Nichols. I'm actually not a big fan of the Z-N formulas since they overshoot and oscillate too much for my tastes, but I have to give them credit for being the first to develop heuristic tuning methods, and they are in pretty much every textbook. The tuning gains calculated by Z-N were a place for students to start when I had them tune a real system - but I emphasized they're usually tweaked after seeing the system behavior in response.) I also showed them how PID variations affect stability using the root locus plot, and that the causal PID formula could be shown in the s-plane by two zeros and two poles (one an integrator and one a high frequency low-pass filter pole).

I happen to think that root locus analysis should remain a part of teaching control system design. I don't disagree that other methods have value also, but I think they should be taught in addition to, not instead of, root locus analysis.

xnuke

"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand,

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## RE: The root locus is useless

Single loop systems or simple cascade loops without transport delays, you won't need such tools

## RE: The root locus is useless

Even if it is never used in the actual design of control laws (and I never use it myself), I think students are better grounded for having been exposed to its concepts.

At the American Controls Conference circa 1990, various awards were being handed out. Most recipients got a smattering of applause. But when Evans (very old at that time, and due to a stroke wheelchair-bound and without speech) got a "lifetime award" for his root locus technique, the whole room immediately stood up and cheered him for several minutes.

Curt Wilson

Omron Delta Tau

## RE: The root locus is useless

My reasons are probably similar to Curt Wilson's since we both make motion controllers where customer expect perfect results, not just stable results.

Both Curt and I have customers that need to know how to tune a motion system. From making the first open loop moves to a tuned system in as short a time as possible ( auto tuning ) does not require root locus. This is why you would have a very difficult time convincing me root locus is useful in real applications.

I don't think much of Z-N either for the same reasons stated by x-nuke. Z-N is not applicable to motion, force or torque control applications.

The reason why I made this thread is that there was another relatively recent thread about root locus and I was wondering who uses that when there are auto tuning software packages or it is easy enough to write your own using Scilab or Matlab.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: The root locus is useless

You will agree that such tools are always handy when you need them,:)

First used root locus methods in '66 but did not resort to them again until '15 when dealing with an eight-order system, it permitted considerable insight

## RE: The root locus is useless

Symbolic math provides better solutions. The solutions are better because they are perfect plus they truly provide insight.

How did you identify an 8th order system? As I said above, I have NEVER seen transfer function for a mechanical system. At least until we or our customers ran the auto tuning program.

Maybe some day on a regular basis at a university. I have given presentations at a couple or taught one period classes on invitation from college instructors.

I prefer symbolic math like what can be done on Mathematica. It is easy to compute the pole locations as a function of gains but I think that is backwards. Gains should be calculated from the pole locations.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: The root locus is useless

you are dealing with a specific, well defined class of controls. Root-locus methods are not commonly used outside of the first controls class, but they can be useful at times.

## RE: The root locus is useless

https://www.amazon.com/Control-System-Design-Guide...

Root Locus is not discussed. I believe that it was Richard Fineman who said, "First comes the understanding, then comes the math."

## RE: The root locus is useless

What about temperature control? Dead time plays a significant role there. How does root locus handle dead time?

If what you teach isn't useful outside the class room then why bother?

That is why root locus is useless. Who uses root locus after college NOW? I can understand back in the dark ages that root locus may be useful but not now. With Mathematica or Mathcad I can compute the gains as a function of the closed loop poles or calculate the closed loop poles and zeros as a function of gains. What should be done is calculate the gains as a function of the pole locations. If one is clever they can place the closed loop zero locations too so that the bandwidth is extended without causing over shoot. Root locus doesn't show how to do that. If one is clever one can calculate forward path gains to provide a notch filter or other desirable attributes.

Pole and zero placement rules. The rest is just a waste of time. Relent guys. Pole and zero placement is much more intuitive than

1+2+3+4...=-1/12. Look it up.

I do not need to know root locus to tune a system. I can do the math toot locus math but there are only 3 things that control people really need to know.

1 System identification. Without system identification nothing else matters.

2 Pole placement and after that zero placement.

3. Observer control or Kalman filter control but none of these are viable without #1.

If I were an instructor I would place an emphasis on the 3 things I mentioned above and being able to write the differential equations for the system they are trying to control. Why? Because I can write non-linear differential equation and if I understand the non-differential non-linear equation I can still control the system perfectly. This will require adjusting the gains on-the-fly. This means one must have some way of calculating the gains as the state changes.. Root locus doesn't provide that.

Real control engineers use differential equations. Too many text books use matrix math. After doing a little matrix math any understanding gets lost in the blender. All one has is numbers.

Yes, I would be one hard a$$ instructor but my students would either fail or have insight that the students today do not.

But one doesn't come without the other.

Lord Kelvin “When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarely, in your thoughts advanced to the stage of science.”

I take that first part to mean when you can identify the system you are trying to control.

If you have ever written an auto tuning program you know that root locus isn't needed. Neither is understanding root locus needed. One must only know that placing the closed loop poles in a certain location will provide a certain type of response so place the poles in a location that will provide the response you want.

Placing the poles on or near the negative real axis in the s-plane is a good start.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: The root locus is useless

"1 System identification. Without system identification nothing else matters."

hmmm,

When dealing with contol systems outside the scope of the problems you have described, there are times you will resort root-locus methods, but you will not need them in the system design phase or in operating plants.

Definition of the system dynamics begins years before the basis for design is prepared. What ypu have described is certainly the case in the design commissioning phase of the work, but that is the final phases of any project...

## RE: The root locus is useless

One can, however, assess its utility by whether people are still writing peer-reviewed journal articles, and there are still a substantial number of IEEE journal articles with "root locus" in their abstracts. Now, admittedly, most authors of IEEE articles are academic, and admittedly, most of the abstracts I looked at were simply comparing their latest and greatest control scheme against the results of root-loci methods.

Nevertheless, it seems that root locus does still have a place, in the tool box, even if the primary methods use something else, since having a reliable canonical approach as a reference guide is still useful.

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

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## RE: The root locus is useless

Never

If you don't need root locus in the design phase or in operating plants then when do you need root locus?

??? This is my big complaint. I have NEVER seen an open loop transfer function provided with the machine so how can you use root locus?

Many people buy a software package like Expertune or Control Station to tune their systems. The person using these auto tuning programs doesn't need root locus. The person writing these programs does use root locus.

Here is my rant.

Look at this video.

https://youtu.be/wCyhRqEG6U4

This is the last of 8 videos this guy makes on root locus. Like all the other videos he does a very good job of thoroughly covering this topic but after 8 videos he still doesn't have a control system that works.

There is my counter video. I used the same open loop system in the video above.

https://www.youtube.com/watch?v=uYhz3TuTkfM

I can control that system. I can place the poles just about anywhere to get the response I want.

I make the point that none of the video is worth a hoot until one can do system identification. I have videos on system identification too.

One thing you may notice is that I tend to use symbolic math and differential equations MUCH more than others. Laplace transforms and state space have their place but real control engineers should use differential equations.

If you can write the differential equations then you really understand the system. If you can write the differential equations then you fear no non-linearity. If I were a college professor I wouldn't give a passing grade to students that couldn't write the differential equations for a system. I can't see where root locus tops being able to write the differential equation or system of differential equations.

Yes IRstuff, I am still using Mathcad 13.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: The root locus is useless

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers