Why Padé Approximations Are Great! | Control Systems in Practice

Watch an introduction to Padé approximations. Learn what Padé approximations are and how to calculate them, why they are important, and when to use them-specifically in the context of time delay and control system design.
Learn More:
- Robust Control of an Active Suspension: bit.ly/3xL5LZz
- Tech Talk video: What Is Linear Quadratic Regulator (LQR) Optimal Control? | State Space, Part 4: bit.ly/3OmWaNU
- Tech Talk video: Why Time Delay Matters | Control Systems in Practice, Part 4: bit.ly/3b7Zgap
- Tech Talk video: The Step Response | Control Systems in Practice, Part 9: bit.ly/3tGtbwG
- Time-Delay Systems: Analysis and Design with MATLAB and Simulink: bit.ly/3O3S91l
- Check out this journey on Resourcium to see these references in an organized list: bit.ly/3O5lNTY
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[@dhaneshprabhu72]

That's the best and crisp explanation I can ever get on Pade approximation. Good job MATLAB team

[@viniciusfriasaleite8016]

Great to see another of your videos!

[@Dynamic_Flyer]

Brilliant explanation, particularly the bit on what order Padé approximation to use vs cutoff frequency. I understand it much better now! This is a REALLY important topic because time delays are common in electronic control systems, particularly digital ones. Even a few addition 10’s of ms of delay can wreck the system bandwidth or introduce instability.

[@AJ-et3vf]

Great video. Thank you

[@sandeeprmurthy]

Awesome!

[@thecontrolenggeek786]

Waw as usual awesome..........

[@martijnlely9462]

Can you give an intuitive reason why a time delay has an infinite number of poles?

[@jrgenmyklebust5157]

the taylor expansion of e^x has an infinite sequence of polynomials, hence the time delay has an infinite number of poles

[@rishikeshkulkarni2259]

Thanks for the answer I had the exact same question

[@wellid2087]

Great video! But I wonder how to determine the delay time of a system, after all, all the measuring methods have delay time.

[@maciejmikulski7287]

In the table with Pade Approximations in the cell (m=1, n=3) there is x^2 in the denominator. Is it just a typo or I misunderstood sth? 🤔 BTW, excellent content and aesthetics of the video 👍

[@user-zm9wo3rk5n]

This is a fantastic explanation. Thanks to you, I now have a much better grasp on the padé approximation. TBH idk why we don't teach it this way in school.

[@BrianBDouglas]

Thank you!

[@Debraj1978]

Scilab cannot plot bode with time delay in transfer function. You have to use Pade aproximation, even to plot frequency response.

[@JamesTJoseph]

This is the very reason we get squiggles in the step response plot on models obtained from subspace identification.

[@dimasrizky1413]

What playlist should this video belong to?

[@kwinvdv]

Would the Padé approximation also be useful to construct fraction order controllers?

[@jafetriosduran]

Of course you can, compute the Taylor series of the backwards Euler method for example to approximate the derivative T(x) =(1-z)^a where a is the order and then make it equal to the ratio between two polynomials T(x) = P(x)/Q(x) and there you have an approximation using padé for a discrete fractional derivative operator

[@heroasik5423]

we can easily implement this in excel spread sheet

[@Qaidi_804]

Hello to all COntrol System Experts, I have one question, Can I make Non Linear Controllers using Analog circuits? As for PID Controller, we use Resistors, Capacitors, and Opamp. How to make nonlinear controllers like this?

[@alexlo7708]

Any passive , active device that has property of non-linear in the range such sin , exp for example ,diode , transistor etc.

[@fernandocaballero5102]

Fuckin amazing!

[@jjpp1993]

the question should be why would anyone choose to use matlab now a days

[@Amine-gz7gq]

At university, I was taught how to use it (system control and image processing). Matlab should provide a free unlimited version for individuals, I have to use an old pirate version to use the Matlab code I wrote when I was a student. There's GNU Octave but I don't know If we can use it for system control.

[@mariotabali2603]

I love matlab but i feel i must learn more python ...

[@Amine-gz7gq]

or GNU Octave. Matlab should provide a free unlimited version for individuals, I have to use an old pirate version to use the Matlab code I wrote when I was a student.