Waching daily Jul 31 2018

Hello friends, welcome to the second video of our predictive control course

MPC based on non-linear model (NMPC) Today we will see how it is that

control is resolved by Combinations Linear My name is Sergio Castaño and

you know that all this information the you can find on the website of

https://controlautomaticoeducacion.com/

if you want you can increase the speed of the video so you can make the explanation much faster and more dynamic

Another type of solution strategies for our NMPC controller is

using linear combinations. Here, what we are going to do is solve the

control problem using or using several linear models,

near a break-even point or a work point of the process where

we are working. This type of solution is a little more familiar to

We have used it a lot on the page "automatic control education"

basically, if we represent in our system with a

static graph where we are representing the output

in relation to the input variable, which tells me the static behavior

of my system. The system will have a maximum output and a minimum output

where I also have a minimal control signal and

a maximum control signal. Inside this box would be all my

region of operation. If I do the static graph, I will see that this system

It has that behavior that is really non-linear. If it were linear then

we would see a straight line inside my work zone. But we see

that we have a non-linear system and with linear combinations

we can do another type of NMPC control that consists of taking

several points, for example this point here and linearize the point. We can

take this other point and linearize around that point

this other point and this other point. For example here take four points

In those four points linearized and four linear models are obtained

This linear model 1 serves for work points within this region

(inside the circle) and between further

this point, the model is no longer valid in that region.

The model of this point serves for

regions of the process that are within this area. The linear model 3 for

that are within this area and the linear model 4 for those who are

within this area. With these four linear models you can

Apply four linear predictive drivers

As we saw on the page. For example, we can

apply here a DMC1, DMC2, DMC3 and DMC4. We have 4 DMC to be

applied depending on the region where our process is located.

If the process is located in this static gain, we use the DMC1

if we are in some

point close to model 3, we use the DMC3. We are changing

the MPC that is going to be used. With this strategy they combine

the solutions found to generate the control to be applied. but which one are we going to use?

For that there are several strategies to select which of the

four drivers use. They can be for example strategies using

fuzzy logic or using weights by distance. For example, if I am

here, then I pondered the distance from the model to

this point. A weight is made including the next models

and so on

What happens if there is a point in the middle of two models?

Which of the two do you use?

the linear model 1 or 2? then we could by

think about making a linear combination of the two models that

I'm going to establish with some strategy that can be an example

with fuzzy logic or simply doing linear weights.

If we use linear weights then

the control DMC1 is calculated to obtain the control law 1 and also

the DMC2 control is calculated to obtain the control law 2. Then

a line weighting is made based on the distance with any parameter

(alpha) to determine the global control that is equal to

alpha * u1 + (1-alpha)

alpha is a parameter that is between 0 and 1 that ponders linearly

the 2 controls that were calculated. For example, if alpha = 1

will only apply u1 then it means that this point

It really is much closer to this solution, to this point. So

only DMC1 is used, if alpha = 0.5, weights half of the control action

u1 and u2 and so on. I hope you understand the idea of

the linear combination between the two control actions

calculated in this example. Another alternative way to calculate this driver

by linear combination is using a linear combination of the models

involved depending on the point where the process is located to obtain a single model and

with that model, the calculation of the linear control is done, for example the DMC

Basically what you would do is:

Calculate the predictions for

output 1 using this linear model 1 and

Calculate the predictions for the model linear 2.

Then a general prediction is made

using the weighting of the two outputs.

This weighted prediction

is formed by a linear combination of the two outputs and with that

output then it can already be applied in a linear MPC to

calculate the control law

With that friends

we come to the end of the second non-linear predictive control video NMPC

remembering then that in the next videos we will see other ways of

resolution of this algorithm and I remind you that in the last two or three

videos of this series, let's see how to implement the algorithm in matlab

I am going to explain some codes step by step, that I am preparing so that

You can reproduce them in your homes or universities. With this then

do not forget to comment in this video, do not forget to share it on your social networks

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next video.

For more infomation >> 20. NMPC 😎 Using Linear Combinations 💪 (Part 2 of 7) - Duration: 7:39.

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THIS SHORT DOCUMENTARY WILL CHANGE YOUR WAY OF THINKING - Duration: 1:31.

read the instructions for this medication and consult a pharmacist.

but what a pharmacist or what the fuck

I'm sure you've never consulted him son of bitch

you should know that this man has a family to feed

and consultations are his only job

every night this man returns home crestfallen

after a hard day's work at the Auswitch mine

because this is the only way

to be able to bring some food home

and thus be able to feed his 7 children

and his sick wife who suffers a strange illness

which doesn't allow her to leave home never

this man can only eat the few crumbs of bread (suffers from extreme thinness)

that their children leave, even though they barely manage to satisfy him

and much less manage to give him strength

for the hard day of work in the mine the next day

Mr. Pharmacist has been 54 years

without receiving a single consultation in his pharmacy

which was the dream of his whole life

the only thing that made this man want to form a big family

so that his children were pharmacists like him

gay subtitles

like if you want the second part