Love it Brian, thank you! I think there is a mistake at 9:44 where you say (and draw) the locus of the a root locus starting at the zeros and travelling to the poles. I thought that it is the other way around? The locus begins at the poles and travels to zeros? Otherwise excellent as usual!
I will be learning from these videos to understand control as we have just started learning classical control this semester. Thank you so much for the videos.
Listening to your lectures makes me wonder about the future of >$200USD engineering mathematics textbooks... Maybe they have their place for the time being, but still...
I would rather pay you the $1000 cost of my controls class instead of my university. Especially during Covid-19 distance learning. This is just better quality.
Thanks for your video, but I have a question about that. If the system is a first order system with no finite zero instead of a second order system which in the video, so there exist 1 infinite zero. After mapping all those spots to z-domain, the order of the numerator and denominator should be the same, because there are one pole and one infinite zero. So my question is that should I ignore the only one (z+1) term in numerator to make sure the order of denominator is geater than that of numerator?
Excellen video! Could you recommend me any book on Discrete Control. I'm student at the university and I'm looking for straightforward book on this topic.Unfortunately in your Playlist there aren't all topics that we would have in this term.
Are you sure the dynamics of an LTI system cannot be exactly determined by the pole zero locations? You can have the same poles of a system but different eigenvectors and have a different response.
Great lecture, just one question: how do I convert a pure integrator? There is a multiplication of the sampling time that I don't know how to justify ... Thanks!!
Hi Brian, since s = a + bj, if we map a zero at s=infinity to z=-1, are we assuming that a=0 and b goes infinity? If so, why do we take this assumption? When we say s=infinity, do we mean that a goes infinity or b or both?
This is a question to which I don't have a satisfying answer! I tried to quickly find a good proof of it and came across this interesting discussion, www.researchgate.net/post/Prove_that_if_a_systems_transfer_function_is_not_proper_order_of_numerator_greater_than_order_of_denominator_then_the_system_is_not_causal2. I don't have a good mathematical explanation, but I do have an intuitive one for why you can't have more zeros than poles that I use for myself so I can sleep at night. I'll see if I can type it out here succinctly. Think of the magnitude plot on a Bode plot. Let's say there are no poles or zeros at the origin. Starting from the left most part of the graph, as you increase in frequency the magnitude line is horizontal until you hit the first pole or zero. If it's a zero you turn the line up 20 dB per decade, if it's a pole you turn the line down 20 dB per decade. Now each future zero you encounter you turn up an additional 20 dB/dec and each future pole you turn down and additional 20 dB/dec. So if there are 2 poles and no zeros, you end up with a magnitude plot that continues down at 40 dB/dec as the input frequency gets faster and faster. However, if there are 2 zeros and 1 pole (not proper), then the magnitude plot continues increasing at 20 dB/dec as the input frequency gets faster and faster. In this case, very high frequency inputs would produce outrageously high amplitude outputs. Any time you have more zeros than poles, the amplitude of the output signal will tend toward infinity as the input frequency increases. This is fine in the world of math, but real life systems don't behave like this. With a real life system, as you increase the input frequency higher and higher, eventually the output amplitude would not grow, but would drop back to almost nothing. Imagine if shaking the end of a spring at a frequency of several gighertz - even if the amplitude of the input is a tiny fraction of a millimeter - and having the other end of the spring oscillate at several gigihertz over several kilometers. Or more to the point, imagine an analog differentiator doing the same (that's closer to a non-proper system since it's trying to be s/1), tiny input voltages at high frequency and outrageously huge output voltages at those same high frequencies. In reality, there is always one or more high frequency poles in any real system that keep that amplitude from increasing to infinity. So our real life differentiator might actually have the transfer function (s + 1) / (2e-6s^2 + 0.003s + 1). This keeps it strictly proper, but also keeps it acting like a differentiator at relatively low frequencies. This was wordy, I hope it makes sense and helped a bit. Cheers!
Another way to think about it is to obtain a partial fraction representation of a nonproper rational function. Then since you have a higher degree polynomial it is possible to have a partial fraction expansion such that some terms are necessarily polynomial of 's'. Otherwise you wouldn't have a nonproper function in the first place. That allows us to conclude that the system acts like a pure derivative 's'. This is where things get a bit hairy. In the input/output view of systems such that systems are like signal processors this cannot happen since the derivative gives us the information about the future at least locally. But this is not a time invariant system. Assume two input sequences and when time t=1sec. one increases to 2 and the other one decreases to 0. The system cannot have an idea about this unless this already happened but it hasn't happened so something has to give. This is roughly the sketch why causality and the relative degree of the polynomials matter. But there is an alternative theory that does not enjoy this view and that is the late Jan C. Willems' behavioral approach. In this approach, we don't treat systems as mapping from input to outputs but define their behaviors. For a classic example, if you connect two tanks with a pipe you have to assume that something is the input and the other tank is receiving that input as an external excitation whereas in reality they define a behavior together. Similarly an mechanical system defines a behavior such that Newton's laws apply. But in the signal based approach dictates that F = ms^2. Thus we treat force as an external input and look at the position. The other way also should be perfectly fine but then as I mentioned above this leads to a double differentiator which we don't enjoy. Note that signal based approach is not wrong. It just has limitations as a framework. Without going into deeper reasoning, we can just conclude that in the input/output setting things make sense only if we have proper system descriptions. There is a body of work over the so-called "descriptor systems". But that's another story thatis also related to this discussion :) I guess there is indeed no simple answer.
is it like how a inductor have a output signal that is shifted to the left of the input signal? So it seems like the inductor generate a signal before the actual signal was input to the system. And the transfer function of inductor is Ls which has more zero than poles.
Hi Brian, can you tell us how you come up with the zeros at -1? I thought we just had to choose a high number or something, because it is saying infinity. Kind regards!
How do you transform 1/s with this method? for a PID controller its transfer function is ( K * (s-a)(s-b) / s) and so evaluating the gain k at s=0 gives an indefinition
I think you'd need an indirect method. Since 1 / s is unstable, the DC gain is not defined. You can close the loop to turn it into a regular first order filter, transform it to the discrete version, and do some algebra to find the open-loop transfer function
![Digital Circus Episode 4 [TRAILER]](http://i.ytimg.com/vi/abZtsmMUbJo/mqdefault.jpg)
You are awesome Brian! My teacher and my books often forget to talk about "obvious" things. I'm happy to have your videos, they helped me ALOT.
best teacher ever in the history...................
Please, keep making videos, dont leave us!
you are the best teacher in the world
Love it Brian, thank you! I think there is a mistake at 9:44 where you say (and draw) the locus of the a root locus starting at the zeros and travelling to the poles. I thought that it is the other way around? The locus begins at the poles and travels to zeros? Otherwise excellent as usual!
yeah, that confused the shit out of me for a moment.
9:45 root locus for k>0 starts at poles, and travels to zeroes.
am i right ?
I want to make enough money to support the work of creators like Brian. Alas right now I am a broke college student.
Your work is really important.
I am from Iraq and I am wordless thank you so much so so much
Thanks man! But what about state space man ?! No videos for it ...and please don't leave us again for along time , we really missed you!
State space! I know, I know :) One day. My free-time to make videos ebbs and flows ... right now, I have some time. Cheers!
Brian Douglas thanks a lot bro! You are the best
I will be learning from these videos to understand control as we have just started learning classical control this semester. Thank you so much for the videos.
It is great that you always present the "big picture" and how the subject relates to it. Keep up the good work! Looking forward for your next video.
Oh my finally a new video. Loving them.
Nice to hear from you again!
incredible, I appreciated the concept of Matched method
Hope to see new discrete control video soon !
This series is excellent !
This guy is a legend. 100× better than my university professor. Wow.
Eagerly waiting for the video on Bilinear Transform !! Great Work Brian !
exam in literally 1h, that part caused me so much confusion : 100% understood after 5mn of video
Listening to your lectures makes me wonder about the future of >$200USD engineering mathematics textbooks... Maybe they have their place for the time being, but still...
I like it
Waiting for this lecture....thanks Brian
Really appreciate your work! Thanks a lot
Thanks!
I would rather pay you the $1000 cost of my controls class instead of my university.
Especially during Covid-19 distance learning. This is just better quality.
Great video. 💯 I hope you make some videos on state space analysis.
Thanks for your video, but I have a question about that. If the system is a first order system with no finite zero instead of a second order system which in the video, so there exist 1 infinite zero. After mapping all those spots to z-domain, the order of the numerator and denominator should be the same, because there are one pole and one infinite zero. So my question is that should I ignore the only one (z+1) term in numerator to make sure the order of denominator is geater than that of numerator?
Thank you.I love control system
Excellen video!
Could you recommend me any book on Discrete Control. I'm student at the university and I'm looking for straightforward book on this topic.Unfortunately in your Playlist there aren't all topics that we would have in this term.
I LIKE IT... RESPECTED SIR, YOUR LECTURES ARE INTERESTING AND WANT SOME LECTN ON DISCRETE REDUCTION METHOD
thanks very much.
10:00, How did you get the niquist frequency?
Are you sure the dynamics of an LTI system cannot be exactly determined by the pole zero locations? You can have the same poles of a system but different eigenvectors and have a different response.
What about precogs? hahaha good one!
Great lecture, just one question: how do I convert a pure integrator? There is a multiplication of the sampling time that I don't know how to justify ... Thanks!!
Hi Brian, since s = a + bj, if we map a zero at s=infinity to z=-1, are we assuming that a=0 and b goes infinity? If so, why do we take this assumption? When we say s=infinity, do we mean that a goes infinity or b or both?
What does the number of poles and zeros have to do with the system being strictly causal?
This is a question to which I don't have a satisfying answer! I tried to quickly find a good proof of it and came across this interesting discussion, www.researchgate.net/post/Prove_that_if_a_systems_transfer_function_is_not_proper_order_of_numerator_greater_than_order_of_denominator_then_the_system_is_not_causal2. I don't have a good mathematical explanation, but I do have an intuitive one for why you can't have more zeros than poles that I use for myself so I can sleep at night. I'll see if I can type it out here succinctly. Think of the magnitude plot on a Bode plot. Let's say there are no poles or zeros at the origin. Starting from the left most part of the graph, as you increase in frequency the magnitude line is horizontal until you hit the first pole or zero. If it's a zero you turn the line up 20 dB per decade, if it's a pole you turn the line down 20 dB per decade. Now each future zero you encounter you turn up an additional 20 dB/dec and each future pole you turn down and additional 20 dB/dec. So if there are 2 poles and no zeros, you end up with a magnitude plot that continues down at 40 dB/dec as the input frequency gets faster and faster. However, if there are 2 zeros and 1 pole (not proper), then the magnitude plot continues increasing at 20 dB/dec as the input frequency gets faster and faster. In this case, very high frequency inputs would produce outrageously high amplitude outputs. Any time you have more zeros than poles, the amplitude of the output signal will tend toward infinity as the input frequency increases. This is fine in the world of math, but real life systems don't behave like this. With a real life system, as you increase the input frequency higher and higher, eventually the output amplitude would not grow, but would drop back to almost nothing. Imagine if shaking the end of a spring at a frequency of several gighertz - even if the amplitude of the input is a tiny fraction of a millimeter - and having the other end of the spring oscillate at several gigihertz over several kilometers. Or more to the point, imagine an analog differentiator doing the same (that's closer to a non-proper system since it's trying to be s/1), tiny input voltages at high frequency and outrageously huge output voltages at those same high frequencies. In reality, there is always one or more high frequency poles in any real system that keep that amplitude from increasing to infinity. So our real life differentiator might actually have the transfer function (s + 1) / (2e-6s^2 + 0.003s + 1). This keeps it strictly proper, but also keeps it acting like a differentiator at relatively low frequencies.
This was wordy, I hope it makes sense and helped a bit. Cheers!
Another way to think about it is to obtain a partial fraction representation of a nonproper rational function. Then since you have a higher degree polynomial it is possible to have a partial fraction expansion such that some terms are necessarily polynomial of 's'. Otherwise you wouldn't have a nonproper function in the first place. That allows us to conclude that the system acts like a pure derivative 's'. This is where things get a bit hairy. In the input/output view of systems such that systems are like signal processors this cannot happen since the derivative gives us the information about the future at least locally. But this is not a time invariant system. Assume two input sequences and when time t=1sec. one increases to 2 and the other one decreases to 0. The system cannot have an idea about this unless this already happened but it hasn't happened so something has to give.
This is roughly the sketch why causality and the relative degree of the polynomials matter. But there is an alternative theory that does not enjoy this view and that is the late Jan C. Willems' behavioral approach. In this approach, we don't treat systems as mapping from input to outputs but define their behaviors. For a classic example, if you connect two tanks with a pipe you have to assume that something is the input and the other tank is receiving that input as an external excitation whereas in reality they define a behavior together. Similarly an mechanical system defines a behavior such that Newton's laws apply. But in the signal based approach dictates that F = ms^2. Thus we treat force as an external input and look at the position. The other way also should be perfectly fine but then as I mentioned above this leads to a double differentiator which we don't enjoy.
Note that signal based approach is not wrong. It just has limitations as a framework. Without going into deeper reasoning, we can just conclude that in the input/output setting things make sense only if we have proper system descriptions. There is a body of work over the so-called "descriptor systems". But that's another story thatis also related to this discussion :) I guess there is indeed no simple answer.
is it like how a inductor have a output signal that is shifted to the left of the input signal? So it seems like the inductor generate a signal before the actual signal was input to the system. And the transfer function of inductor is Ls which has more zero than poles.
Wow it's been along time...PEACE
After being gone for so long, it's really nice to see people still sticking around and waiting for something new. Cheers!
Brian Douglas We are your notification squad man...We have clicked the damn Bell icon! =D
I have been sticking around since 2013 :)
Mandar Phadnis yeah
Teacher: careful guys, this method can be difficult to learn
Me: haha Brian goes brrrrr
great video! thanks!
Hi Brian, can you tell us how you come up with the zeros at -1? I thought we just had to choose a high number or something, because it is saying infinity.
Kind regards!
My understanding is to make s=jfs/2=jpi/T , then z=e^(Ts)=e^(jpi)=-1
amazing videos!!!
How do you transform 1/s with this method? for a PID controller its transfer function is ( K * (s-a)(s-b) / s) and so evaluating the gain k at s=0 gives an indefinition
I think you'd need an indirect method. Since 1 / s is unstable, the DC gain is not defined. You can close the loop to turn it into a regular first order filter, transform it to the discrete version, and do some algebra to find the open-loop transfer function
Yeahhhhhhh. I love you man
I love you
I thought it was called "Casual system" the whole time....