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Electronics => Beginners => Topic started by: RoGeorge on November 07, 2021, 07:37:28 am

Title: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: RoGeorge on November 07, 2021, 07:37:28 am
Looking for good/classic learning material, interested more in understanding how/why/when it is used, and about building an intuition in using Laplace as an engineering tool than in Laplace as pure math.

What should I study for that?
Title: Re: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: armandine2 on November 07, 2021, 01:13:00 pm
Laplace crops up in plenty of ee textbooks - the one I have chosen here has the simple recommendation that the first author was one of my past tutors. It's also a hands on text accompanied with software.
https://www.amazon.co.uk/Control-System-Design-Simulation-Golten/dp/0077074122 (https://www.amazon.co.uk/Control-System-Design-Simulation-Golten/dp/0077074122)
Title: Re: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: Just_another_Dave on November 07, 2021, 01:46:22 pm
When I was studying I used Modern Control Engineering by Ogata or Feedback Systems: An Introduction for Scientists and Engineers by Aström and Murray. Both are easy to find
Title: Re: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: mawyatt on November 07, 2021, 02:12:39 pm
Believe Heavyside first used the algebraic technique to solve differential equations that arose with the early long communication transmission lines. Later his technique became known as Laplace, but IMO Heavyside should be given more credit.

The technique is extremely powerful and useful in all sorts of electronics and we've been using it as a daily development tool for over 50 years.


Best,
Title: Re: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: rstofer on November 07, 2021, 02:26:44 pm
There's a ton of information on the Internet including this playlist.  About 3/4 the way down she starts with Intro To Control:
https://www.youtube.com/c/katkimshow/videos (https://www.youtube.com/c/katkimshow/videos)

KhanAcademy does a decent job
https://www.khanacademy.org/math/differential-equations/laplace-transform (https://www.khanacademy.org/math/differential-equations/laplace-transform)

It seems to me that you will need some background in differential equations and perhaps even partial differential equations.  Preceding DEs and PDEs is differential calculus and integral calculus and preceding those subjects are the usual suspects:  Algebra and trig.  It is not lightweight math.  Actually, the algebraic part is pretty easy, it's the rest of the subject that is challenging.  Pay attention when you get to 'partial fraction expansion' in Algebra since it ties right in to Laplace Transforms:

https://lpsa.swarthmore.edu/BackGround/PartialFraction/PartialFraction.html (https://lpsa.swarthmore.edu/BackGround/PartialFraction/PartialFraction.html)


Title: Re: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: rstofer on November 07, 2021, 02:43:33 pm
Google for 'Laplace intuition' - there are a bunch of videos
Title: Re: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: mawyatt on November 07, 2021, 02:50:31 pm
Somewhat related on control theory concepts, way back we relied on Root-Locus techniques to "visualize" the feedback system behavior wrt to changes in loop gain, feedback, compensation, and other effects.

Sampled feedback systems were not as easy to "view" until a paper by someone that proposed a technique where the Root-Locus was still used, and the real axis radius was the sample rate. This brilliant concept allowed one to visualize the effects of sampling rate on the system. The poles and zeros don't move and are dictated by the system characteristics just like in conventional feedback, however the imaginary axis "bends" due to the real axis radius which is the sample rate and you can easily see the effects of sample rate on system stability as the axis bends!! Absolutely brilliant technique IMO  :-+

What this really represented is that conventional feedback systems are just special cases of a sampled feedback system with an infinite sample rate, not the reverse!!

If you are truly interested, please spend some quality time thinking about this, maybe see if you can find the paper (sorry but I can't remember the exact details). Create a simple 2nd order feedback system, plot the root locus, then introduce the sampled feedback and begin to reduce the sample rate and see how this effects the system damping until the sample rate causes the imaginary axis to intersect the complex poles and damping is zero and you have an oscillator.

Best,
Title: Re: What textbook and classes to understand Laplace for EE and Control Theory?
Post by: rstofer on November 07, 2021, 03:43:10 pm
These videos show how to get the transfer function for simple high and low pass filters and create the Bode' plot with MATLAB.
MATLAB does all the grunt work of creating the transfer function and MATLAB is my favorite tool.  I suspect, but haven't proven, that the commands she uses at the end of the second video will also work on Octave.

https://www.youtube.com/watch?v=KDN8W_HaeAY&ab_channel=katkimshow (https://www.youtube.com/watch?v=KDN8W_HaeAY&ab_channel=katkimshow)
https://www.youtube.com/watch?v=bojKlLeuNGE&ab_channel=katkimshow (https://www.youtube.com/watch?v=bojKlLeuNGE&ab_channel=katkimshow)

I tested the commands in Octave and they work after you load the control package

> pkg load control  -- this could be added to the script,  The control package needs to be installed.

Code: [Select]
R = 1e3
L = 100e-3
C = 500e-6

figure('Name','Low Pass Filter');
GpRC = tf([1],[R*C 1])
bode(GpRC)

figure('Name','High Pass Filter');
GpRL = tf([L 0],[L R])
bode(GpRL)