What Are Non-Minimum Phase Systems? | Control Systems in Practice
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- Опубліковано 8 гру 2019
- Check out the other videos in the series:
Part 1 - What Does a Controls Engineer Do? • What Control Systems E...
Part 2 - What Is Gain Scheduling? • What Is Gain Schedulin...
Part 3 - What Is Feedforward Control? • What Is Feedforward Co...
Part 4 - Why Time Delay Matters • Why Time Delay Matters...
Part 5 - A Better Way to Think About a Notch Filter • A Better Way to Think ...
We like to categorize transfer functions into groups and label them because it helps us understand how a particular system will behave simply by knowing the group that it’s part of. We gain some insight into the system if we know, for example, that we’re dealing with a type 1, second order transfer function. In a similar way, we can glean some additional information about how our system will behave if we know whether it’s a minimum phase or non-minimum phase system. So, in this video, we’re going to talk about what minimum phase means, what causes a non-minimum phase system, and how that impacts the system behavior.
Check out these other links:
- Inverted pendulum example: bit.ly/35WBdDm
- The MATLAB Tech Talk video on time delay that I reference in the video is here: • Why Time Delay Matters...
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i get excited when i hear. "I'm Brian and welcome to a matlab tech Talk"
I love this guy. He can use simple answers to clear up my doubts on the control system.
Great stuff Brian. Glad to see Matlab picked you up after all the great work on your own channel. Terrific explanation as usual!
Clear and concise. MathWorks will benefit from your work.
Well done!
I would like to add another point or solution however. In the conclusion 13:25 one method to correct is to have a slow controller, but at the cost of response speed. I propose a faster method.
Instead slow the set point, namely pay attention to the derivative. At 9:10 indeed you say that the derivative gives the jolt in the opposite direction. This is because the -du/dt term is going to have a larger negative part than the 2u(t) term for a reference of a step or pulse. Considering that it has an infinite derivative at the step start no constant input gain is going to offset that, in fact it will make it worse. So by having a curved set point like a steep first order trajectory, you can give the derivative finite value that is possibly lower than its lower order zero terms. However if you go to the second order reference that first order derivative if going to.
This does come at a cost of 'lag', in that the reference itself will reach the steady state later, but in my experience all systems do so anyway since they themselves have don't reach the reference in zero time.
Hence if you tweak the reference to have one order more than the highest transfer function zero, you will have a faster response in total, have a system that is still stable (considering you didn't change the poles necessarily) and have a smaller error overall (since the systems follows the trajectory closer, even if you have an arbitrarily small 'lag' at first).
Thanks,Brian for all the knowledge you are sharing.
Brian, you are doing a great job - please keep up with it!
Wow! Just.. wow! You should write a book or something, I love these explanations. These Matlab talks and your channel are of infinite value to control engineers. Seriously, you have helped me grasp concepts that I have struggled with for years. I'm commenting on this specific video but ALL you videos are pure gold. Thank you
This is the official matalab channel
@@PankajSingh-dc2qpblack then, this was on Brian Douglas Channel. It appears than Matlab bought some of its videos
A video about the Smith Predictor would be awesome. Really useful stuff for systems with transport delay.
Good suggestion! I'll add it to the list of future topics. Thanks!
Rear wheels steering is also a RHZ system.
Awesome channel and lecture!
Very Good Lecture
Great video, very informative.
At 13:30 the inverse numerator control method is shown, and i know rhat in theory it looks good but in practice is not at all a solution.
I think something can be said about these systems being non-linear in a non-trivial way. Use of LTI tf and linear control methods kind of leave elegant solutions to these problems at the door.
The underlying dynamics of the system are hidden by a gross locally linear approximation of the gradient space of the dynamics where we decide to look.
I would asume that would also be the cause for the right left right control action on the pendulum cart example. At equilibrium, the cobtrol action in a linear space just says go right, then as the pendulum falls the wrong way it corrects it and winds up in a configuration where going right again actually solves the problem.
Of course in a non-linear case the path to the desired state is not simply a straight line "go right" scenario. You can come up with much more elegant state space trajectories from point A to B that wont stutter when they dont act like it is linear. Predictive control was mentioned, but even that is seriously overkill. Imo
Anyways, RHZeros are something i didnt understand, and led me to put a project on the shelve for a while, but by coincidence i cam accross this video so im back to working on that project!
Hi, Brian your videos about control theory is great, I hope you will talk about MPC controller
Thank you Brian. Your lectures are so useful. Would you ever do one about sliding control?
Giuseppe Perfetto that’s on the list of future topics for sure.
Just perfect.
Amazing video
Thanks
You helped me
Maximum phase is sometimes used to describe have all poles in the RHS.
I think G_delay and G_RHP_zero are close to eachother because (-s+1) is the fist taylor aporximation of the e^-s
gives me a 53.7x better intuitive understanding than the lectures. Much appreciated!
I think it is very non-intuitive, it is claculated and reasoned.
About 9:35, what if you want to write the RHP zero as a s - 2 instead of -s+2, wouldn't this make the derivative positive? How would the explanation work then?
s-2 and -s+2 aren't the same. Sure they have the same zero, but they differ by a gain of -1.
I was thinking the same. But it makes sense. We want to keep the u term positive. If you just plot the step response in MATLAB you will clearly see that the s-2 term will make the step response settle at -ve value
What are unbounded controllers and unbounded controller commands, and what are some examples of that?
I always though trying to cancel RHP poles or zeros was a bad idea because you can never really “cancel” it (especially in a physical system), but rather they’ll just be very close to each-other, resulting in instability (the root locus will connect the pole and zero). It’s basically guaranteeing a closed-loop pole in the RHP.
Are these two ideas related? If so, how?
You are right in that there are multiple problems with trying to cancel RHP poles or zeros like this. As you mention, the real physical pole or zero might move over time or you might not have estimated its location perfectly and so it won't be canceled out exactly. But let's say that we could perfectly cancel the pole/zero and the output of the plant looks great. Even then, there is a problem. Take the open loop system at 13:00. If we commanded that system with a step input, the RHP pole/zero would cancel and the output would look fine. However, if you just looked at the output of the controller, you'd see it building in the negative direction unbounded. That is, it takes an unbounded negative direction signal to drive the RHP zero plant in the right direction from the get-go (no wrong direction bump at all). You can see that this is the case by looking at the step response of just the controller, 1/(-s+2). So there are at least two problems with the canceling approach!
Sir I am completely new to Matlab , which video shall I watch first to know the basics?
You can look up this channel to watch whatever you want to know.
Hi brian..
Are u there in linkedin..
Would love to connect with you..am an aspiring control engineer..ur guidance would be invaluable
What about rhp poles how does it affect phase plot @ matlab
you can see this by plotting the bode plot of a RHP pole in MATLAB. First, the phase will start at -180 and increase to -90 at high frequencies.
Right half plane poles make the system unstable. They lead to exponential growth, instead of decay.