Linearizing a Simulink Model Using the Linear Analysis Tool and ‘linmod’
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- čas přidán 24. 07. 2024
- In this video we show how to linearize a non-linear Simulink model using numerical techniques. This approach is extremely powerful as it allows automatic generation of linear models of a complicated model about different trim/operating points. We investigate how to linearize using the Linear Analysis Tool as well as using the ‘linmod’ function. Finally, we compare the response from both the linear and non-linear models to verify accuracy/fidelity.
Topics and timestamps:
0:00 - Introduction.
0:46 - Review of trim points.
5:18 - Preparing the Simulink model for linearization via the Linear Analysis Tool.
24:46 - Preparing the Simulink model for linearization via the ‘linmod’ command.
30:39 - Linearizing about a different trim point.
36:32 - Linearization of a MIMO system.
49:02 - Simulating both linear and nonlinear models to verify accuracy of linearization.
Lecture notes and code can be downloaded from github.com/clum/CZcams/tree/...
Other videos in this series:
-Trimming a Model of a Dynamic System Using Numerical Optimization ( • Trimming a Model of a ... )
-Equations of Motion for a Planar Vehicle (TBD)
-Trimming a Simulink Model Using the Linear Analysis Tool ( • Trimming a Simulink Mo... )
- Linearizing a Simulink Model Using the Linear Analysis Tool and ‘linmod’ ( • Linearizing a Simulink... )
-MathWorks page describing differences in linearization process (www.mathworks.com/help/slcont...)
-Brian Douglas’ video on Simulink linearization - ( • Linearizing Simulink M... )
All Matlab/Simulink videos in a single playlist ( • Working with Matlab )
#Matlab #Simulink
You can support this channel via Patreon at / christopherwlum or by clicking on the ‘Thanks’ button underneath the video. Thank you for your help!
In case it is helpful, here are all my Matlab videos in a single playlist czcams.com/play/PLxdnSsBqCrrEU0dLSrTcl0-w9cVYKMTaF.html. Please let me know what you think in the comments. Thanks for watching!
AE 512: Discussion of the end game of linearizing these systems in the last minute of the video was really helpful for me, thanks!
This was actually SO FANTASTIC. THANKS!
A lot of info packed into this video. Great video, thanks!
I want to thank you for your enlightening videos, appreciate!
Glad you like them!
Thanks for the showing the tools to linearize a system!
That's a very good video. Clear and organized. Keep the work going! You just earned a new subscriber
I'm glad it was helpful, thanks for watching!
thank you for the lecture, definitely need to play around with the linearization more.
I worked alongside the tutorial. Easy to follow.
AA516: Thanks for sharing about the linmod tool and how I can linearize blocks of my SImulink models to reach a linear state-space model.
AE 512: Good tutorial.
AE511: nice video, great way to see how different inputs will affect specific outputs
AE511: Developing and then using the planar vehicle model throughout the class and building the controllers on top of it was really cool. Thanks for a fun quarter!
Thank you so much for your excellent explanation
Glad it was helpful!
Hi Professor the videos are very helpful thank you for sharing .
AA516: Good video! I am excited to apply it to the RCAM model
Great video.
Linmod is extremely powerful and this video is a great demonstration of it!
AA516 - I'm enjoying the lectures; looking forward to applying the techniques introduced this week to RCAM
AE511: awesome! Thanks Chris, now I can try to use this linearization technique on my final project!
Great, I'm excited to see what you do with it!
Thanks professor. I liked the video, but I think it would be better with a little more up front discussion on why we want to linearize the model. It would help drive the discussion. Maybe this is because I may have missed an earlier video.
AE511: great video on using Matlab to linearize a nonlinear system model.
You are amazing. Thank you
Rahul, thanks again for watching!
AA516: It's interesting to see how there's two fairly convenient ways to linearize non-linear Simulink models!
thank you for your presentation. would you please show us the steps how to model planner vehicle in Simulink?
AE511: Interesting to see the differences between the non linear and linear models, especially for velocity as the step input increased
AA516: I think everything is coming together. So first we model a nonlinear system, linearize it at a trim point, then create a feedback control system like a simple PID controller and actuator(s) to make the system stay in the trim point. NICE
AE511: Wow, Matlab really is a powerful tool!
AE512: Would love to see how these two optimization/trimming techniques could be applied within Simscape
Thanks for this excellent work. Using the linear analysis tool is great but it appears one needs a separate subscription for that. When I use the linmode, the step response does not behave similar to the output i obtained from then linmode. What am I not doing correctly? Thanks.
I am able to answer question directly through my Patreon page at www.patreon.com/christopherwlum. Please free to submit your question there and we can discuss. Thanks for watching and for supporting the channel!
Hi Christopher,
i have a question regarding designing a linear controller for the linearized model, when we linearize the model in the desired trim point. For example the watertank model givin by simulink.
Why does the linear controller (e.g. PID) works fine with the non-linear system afterward? The reference of the height can be set arbitrarly, altohugh i linearized the model for a certain height and not for all height. But afterwards it works with all reference heights.
Hi,
Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on CZcams due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!
-Chris
AA516 - Thanks for another great lecture. Assuming that you are using Matlab and Simulink in industry, I am curious whether you tend to define system models within the Simulink GUI or as a function referenced by the Simulink "Matlab Function" call or something comparable.
Good question, it really is a combination of both methods. Generally it is easier to use a Matlab Function if the algorithm is complex.
Hello,
"The values of the "Numerator" and "Denominator" properties must be row vectors or cell arrays of row vectors, where
each vector is nonempty and containing numeric data. Type "help tf.num" or "help tf.den" for more information". I have that kind of error I didnt find the proper solution for this. Do you have any idea?
Hello,
Did you figure out? I faced this problem, too. Can you help me if you figure out?
AA516: Thank you!
AA516: Sick!
I did for 2input-3output MIMO system. I got the result that the system has decoupled. Available transfer function only Input 1 respecting to output 1 & 2, and also input 2 respecting to output 3. For me, it is not logic in the first place, because every state variable dependent to each other in every differential equation. Is it reliable that they can have decoupled system like this? I plotted the response, it seems that linearized model still follow the nonlinear one
Hi,
Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on CZcams due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!
-Chris
AA516 How can you tell if an operating point is stable or unstable based on the linearization of a system?
Kenneth, great question. The second you have your linearization, you can check the eigenvalues of the A matrix to understand the stability of this trim point.
Jason-AE512: I really like the code explanation part, but if I can have the source code to practice, that will be much helpful.
AE512: while it is cool that you can linearize about the trim point, I don't quite understand why this is necessary if you have access to a nonlinear plant that should produce more accurate results... Perhaps it is just for control design?
Thanks for catching up on the comments, I've got you down for participation now
great
show us building amatlab/simulink model of planner vehicle
AE 511. Impressively power tools in MATLAB.
A A 516: Ojasvi Kamboj
Matlab tools for linearizing a Simulink model
Hi sir, do you have fiver account ?
AA516
AA516:Po