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Model Predictive Control from Scratch: Derivation and Python Implementation-Optimal Control Tutorial

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#controltheory #mechatronics #systemidentification #machinelearning #datascience #recurrentneuralnetworks #timeseries #timeseriesanalysis #signalprocessing #dynamics #mechanics #statics #mechanicalengineering #controltheory #mechatronics #robotics
If you need help with your professional engineering problem, or you need to develop new skills in the fields of control, signal processing, embedded systems, programming, optimization, machine learning, robotics, etc., we are here to help. We provide engineering services, as well as tutoring and skill development services. We have significant industry, research, and university-level teaching experience. Describe your problem and we will send you a quote for our services.
Contact: ml.mecheng@gmail.com
It takes a significant amount of time and energy to create these free video tutorials. You can support my efforts in this way:
- Buy me a Coffee: www.buymeacoff...
- PayPal: www.paypal.me/...
- Patreon: www.patreon.co...
- You Can also press the Thanks RU-vid Dollar button
In this control engineering, system identification, and control theory tutorial, we explain:
1) How to derive a model predictive control algorithm from scratch.
2) How to implement the model predictive control algorithm in Python from scratch.
Starting from a state space model, we formulate an optimization problem and explain how to compute the closed form of the model predictive control solution.
The GitHub page with all the codes is given here:
github.com/Ale...
The website tutorial is given here:
aleksandarhabe...
The MPC algorithm implementation in C++:
• Model Predictive Contr...
The main challenge was how to make a tutorial that was easy for beginners without going immediately into nonlinear and complex optimization worlds, where students immediately get lost and immediately give up on studying MPC. This comment also applies to modern control theory. A number of control scientists publishing papers in Automatica/IEEE TAC simply do not put effort into explaining things such that everyone can understand the basic concepts. There is a trend to make the control theory as complex as possible and as a pure math discipline. I think that was not the vision of the founders of control theory, who were actually engineers solving real-life problems. In fact, control theory is super applicable and relatively easy. The only issue is that one has to conquer math to be able to apply it. Consequently, I start with the MPC formulation for linear systems and I try to stick as much as possible to basic linear algebra.
We explain how to formulate a least-squares cost function, and how to minimize it. The solution can be expressed in a closed form as a solution of a weighted least-squares problem. The input constraints can be implicitly handled by properly selecting weighting matrices. We then explain how to implement this algorithm in Python from scratch and in a disciplined and clean manner (by using Python classes). We test the algorithm on a classical system consisting of two objects connected by springs and dampers. In the second part of this tutorial series, we will consider constrained linear systems. In the third part, we will consider nonlinear smooth systems (the most general formulation). After we complete the Python model predictive control tutorials, we will start a new tutorial series on how to implement the algorithm in C++ by using the Eigen Library.

Опубликовано:

22 авг 2024

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Комментарии : 44

@aleksandarhaber 11 месяцев назад

If you need help with your professional engineering problem, or you need to develop new skills in the fields of control, signal processing, embedded systems, programming, machine learning, robotics, etc., we are here to help. We provide professional engineering services as well as tutoring and skill development services. We have more than 15 years of industry, research, and university-level teaching experience. Describe your problem and we will send you a quote for our services. The contact information is ml.mecheng@gmail.com It takes a significant amount of time and energy to create these free video tutorials. You can support my efforts in this way: - Buy me a Coffee: www.buymeacoffee.com/AleksandarHaber - PayPal: www.paypal.me/AleksandarHaber - Patreon: www.patreon.com/user?u=32080176&fan_landing=true - You Can also press the Thanks RU-vid Dollar button

@aleksandarhaber 19 дней назад

It takes a significant amount of time and energy to create these free video tutorials. You can support my efforts in this way: - Buy me a Coffee: www.buymeacoffee.com/AleksandarHaber - PayPal: www.paypal.me/AleksandarHaber - Patreon: www.patreon.com/user?u=32080176&fan_landing=true - You Can also press the Thanks RU-vid Dollar button

@krisnaanandakusuma9426 7 месяцев назад

the best tutorial about MPC! i've been looking such explanation out there until the very detail of MPC and I must say I have finally found it! Thank you very much

@aleksandarhaber 7 месяцев назад

This is because people who create RU-vid control tutorials do not properly understand control and they never implemented a simple PID control algorithm in real life.

@user-pq5me5dt3v 6 месяцев назад

Wow, it is amazing explanation and implementation about MPC which I’ve never seen before.

@aleksandarhaber 6 месяцев назад

I am glad you find it useful.

@Trextreks 7 месяцев назад

The best tutorial , thank you. Obrigado ! from Brazil ! Brasil 🇧🇷

@aleksandarhaber 7 месяцев назад

Thank you!

@aleksandarhaber 11 месяцев назад

The website tutorial is given here: aleksandarhaber.com/model-predictive-control-mpc-tutorial-1-unconstrained-formulation-derivation-and-implementation-in-python-from-scratch/ The GitHub page with all the codes is given here: github.com/AleksandarHaber/Model-Predictive-Control-Implementation-in-Python-1 The MPC algorithm implementation in C++: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-fgNz1RE2DG4.html

@markusbuchholz3518 11 месяцев назад

I want to express my appreciation for the effort and passion you put into creating your channel, website, and content. Your work is exceptional, and you are a brilliant person with exceptional teaching skills. I wish you the best of luck in all of your endeavors and objectives. Have a fantastic day!

@aleksandarhaber 11 месяцев назад

Thank you very much Markus for the kind words and encouraging comments! I spent a lot of time developing this channel. Sometimes I wonder does it is really worth my time to do all this since there is no proper financial compensation. However, the positive feedback I receive encourages me to keep on going. It is really go to know that people find these tutorials useful.

@markusbuchholz3518 11 месяцев назад

@@aleksandarhaberI completely understand your perspective as I also work in academia. Nevertheless, I hope you will receive great support for your endeavors. I always appreciate those who possess wisdom, an open mind, and a willingness to share. Wishing you the best of luck with all your pursuits!

@aleksandarhaber 11 месяцев назад

@@markusbuchholz3518 Thank you!

@AbhijitBhaktechd 4 месяца назад

Very precise and easy to understand explanation with implementation. Thanks @Aleksander 🙂

@aleksandarhaber 4 месяца назад

Glad it was helpful!

@behnammohseni496 5 месяцев назад

Such a fantastic video:)

@aleksandarhaber 5 месяцев назад

Glad you enjoyed it!

@user-nj5wl2sg3p 8 месяцев назад

Hey, there are some written errrors: in equation(13) the last line of matrix M, the power of A should be {f-1}, {f-2}, {f-3} the equation(15) has the same problem, and "C\bar{A}_{1,v}B" should be replaced by "C\bar{A}_{v+1,v}B". By the way, the tutorial is great that helps me a lot, thank you.

@aleksandarhaber 8 месяцев назад

Thank you! I will correct these typos in the updated tutorial and on the webpage.

@halihammer 6 месяцев назад

Very good content! Thank you very much for your effort! It helps alot :)

@aleksandarhaber 6 месяцев назад

You're very welcome!

@jafarmajali9255 7 месяцев назад

Brilliant !

@aleksandarhaber 7 месяцев назад

Thank you!

@user-lw9gv6bn5j 11 месяцев назад

Hi, Your tutorial videos are exactly what I am searching so far but didn't got any, The perfect combination of theory + code implementation from scratch. I am currently a final year engineering bachelor student and learning about Control systems , these video lecture series is noting less than a treasure for me. Thank you so much for helping me. I have a request, can you please make tutorials on the various state estimation techniques also and show how to integrate data from observation, multiple sensor inputs with the state model to get a more accurate state estimate, and a series on controlling non-linear control systems,

@aleksandarhaber 11 месяцев назад

Thank you. There are some videos on this channel covering these topics. However, more will follow. So stay tuned!

@MuhammadTahir-tm3lp 11 месяцев назад

Very interesting video .......

@aleksandarhaber 11 месяцев назад

Thank you. I see that you also have video tutorials. When I find some free time, I will look into them.

@emperor4102 3 месяца назад

Would love to see Mpc for boost converter in simulink

@aleksandarhaber 3 месяца назад

You will never learn control if you use Simulink.

@consuelovega1230 6 месяцев назад

Indeed, the best tutorial, thank you very much, can I ask if the model can be easily modified for a Multiple Input Single Output (MISO) system with 4 inputs and 1 output by changing r=1; m=4 and n= 1 ? or there are more considerations? Thanks for your time!

@aleksandarhaber 6 месяцев назад

Hello, these are free tutorials, and it took as a significant amount of time and energy to create them. Usually, you will have to pay thousands of dollars to enroll in a university course in the US to obtain this quality of lecture. Except providing these tutorials, we do not have time and energy to provide answers to particular questions. Spend some time to understand the algorithm and the code and your answer will follow immediately.

@amel3778 25 дней назад

Thank you for sharing. However, I have a question, please. I am currently implementing an MPC to control the temperature inside a room. To model the system, I used a neural network that takes as input a window of data (disturbance_w, control_w, output_w) to predict the output over a prediction horizon. Then, I use these predictions to calculate an objective function in order to obtain the first command to apply to my system to get the first output. For this, I use scipy, but the control proposed by this library remains constant regardless of the output values (the output does not follow the reference). Do you have any advice to improve this?

@aleksandarhaber 25 дней назад

Unfortunately, due to lack of time and energy, we do not provide free help and free consultation.

@amel3778 25 дней назад

@@aleksandarhaber No worries, thank you anyway for the effort you put in and for sharing this valuable information in your tutorials.

@MeinHerrDreyer 11 месяцев назад

Great video, thank you for this. Im commenting as Im working through your detailed explanation. I have 2 questions: 1. For 9:47, from equation (5), is there a B missing from the u_k | k term? Should it be C*(A^2)*B instead of C*(A^2)? I also realised the B term is missing until later on for equation (13) for the u_k|k term. 2. Why is it that we will need to obtain control inputs for time k+2 and later? Wouldn't having just control input at time k and k+1 be sufficient? Is this because we need the future control inputs to obtain the predicted trajectory for time instants k+2 and later?

@aleksandarhaber 11 месяцев назад

Yes, that is a typo. I will correct that. It is very obvious what is happening and that this is a typo.

@MeinHerrDreyer 11 месяцев назад

@@aleksandarhaber Thank you! I would also like to ask: Why is it that we will need to obtain control inputs for time k+2 and later? Wouldn't having just control input at time k and k+1 be sufficient since we wont be able to execute control inputs in the far future? Is this because we need the future control inputs to obtain the predicted trajectory for time instants k+2 and later?

@aleksandarhaber 11 месяцев назад

@@MeinHerrDreyer At the time instant k, the MPC computes the vectors u_{k|k},u_{k+1|k},...,u_{k+v-1|k}. At the time instant k, you only apply u_{k|k}. Then, you observe the state x_{k+1}, and then you repeat the complete procedure, and you compute u_{k+1|k+1},u_{k+2|k+1},...,u_{k+v|k+1}. Then, again, you only apply u_{k+1|k+1}, observe the state x_{k+2}, and you repeat the complete procedure.. That is, only the first control input is applied at avery time step and the prediction horizon window is shifted. This is the standard MPC. Of course you can deviate from this if you want. For example, if you do not have significant disturbance.

@MeinHerrDreyer 11 месяцев назад

@@aleksandarhaber Thanks for explaining. I realised that even though at time index k, we are only applying the control input calculated for the next time index, we still need to calculate for k+1 and beyond because without these future control inputs, we won't be able to obtain the predicted trajectory and hence adjust for future potential disturbances, am I right to say that?

@aleksandarhaber 11 месяцев назад

@@MeinHerrDreyer Not exactly. Disturbances are something that you cannot predict. That is why they are called disturbances. If you can predict them, you can include them as known inputs in the model, and then you can account for them when predicting the trajectory. We are only applying the first computed input since we want to get an update of what that input did to our system, and then by using the state feedback we can see what happened and repeat the computations again to have a better input for the next step. That is, if the disturbance acted on the system between the time steps k and k+1 through the state feedback we can see that disturbance and then adjust the future control inputs. However, if you apply u_{k} and u_{k+1} that are computed at the time instant k , and between the time step k and k+1 there was a disturbance, then u_{k} might be a valid signal, however, the input u_{k+1} is not since this signal is computed at the time instnat k without the knowledge of the future disturbance. You have to think logically about this and from the engineering perspective and everything will come together and become completely logical.