Model Predictive Control of Boost Converter

Summary

本视频详细讲解了如何为Boost转换器设计模型预测控制（MPC）系统，重点是输入电流或输出电压控制。通过介绍系统参数、导出转换器的微分方程，视频逐步引导观众理解有限控制集模型预测控制和Boost转换器的基础知识。控制变量为电感电流，使用Euler前向方法进行预测。视频还深入分析了Boost转换器的电路模型，并根据开关状态推导出电感电流的导数方程。接着，通过Matlab Simulink演示了模型预测控制的编码过程，包括预测函数的编写、成本函数的确定以及最小化误差的策略。此外，还探讨了如何通过调整成本函数减少开关频率，以及如何利用PI控制器间接控制输出电压，最后通过动态调节PI控制器参数以优化系统性能。

Takeaways

• 🔌 设计了一个用于Boost转换器的模型预测控制（MPC），专注于输入电流或输出电压的控制。
• 📈 引入了系统参数和转换器的导数方程，这是理解和设计MPC的基础。
• 🛠️ 讨论了有限控制集模型预测控制的概念，并将其应用于Boost转换器，以电感电流作为控制变量。
• 🔢 使用Euler前向方法对控制变量进行预测，提供了预测功能的数学表达式。
• ⚙️ 分析了Boost转换器的电路模型，强调了开关状态对电路分析的重要性，并导出了两个可能的开关状态下的电感电压函数。
• 📊 提出了成本函数（误差函数），用于评估电感电流的预测值与参考值之间的偏差。
• 🔍 通过最小化成本函数来寻找最优开关状态，这是MPC策略的核心。
• 💻 展示了如何在Matlab Simulink中实现MPC，包括预测函数和最小化误差的过程。
• 🎛️ 引入了一个新的成本函数来控制开关频率，通过调整权重因子来平衡系统性能与开关频率。
• 🔋 展示了如何设计输出电压控制，包括PI控制器的应用以产生电感电流参考，从而间接控制输出电压。
• 📝 讨论了PI控制器参数的手动调整过程，以及如何通过实验确定这些参数以优化系统的动态响应。

Q & A

什么是模型预测控制？

模型预测控制（MPC）是一种先进的控制策略，用于实时调节复杂系统的性能。通过对系统未来行为的预测，以及通过优化控制输入来最小化某个成本函数，MPC能够有效地控制系统输出。

为什么在设计升压转换器时选择使用模型预测控制？

模型预测控制能够提供对升压转换器的精确控制，尤其是在处理输入电流或输出电压控制时。通过预测和优化控制变量（如电感电流），MPC能够提高转换器的性能和效率。

在模型预测控制中，成本函数的作用是什么？

在模型预测控制中，成本函数用于衡量系统当前状态与期望状态之间的偏差。通过最小化成本函数，控制策略能够确定最优的控制动作，以达到期望的系统性能。

使用欧拉前向法有什么优势？

使用欧拉前向法可以简化对控制变量（如电感电流）未来值的预测，该方法通过当前状态的导数估计未来状态，适用于实时控制系统中的近似计算，提高了计算效率。

升压转换器有哪些可能的开关状态？

升压转换器有两种可能的开关状态：开（S=1）和关（S=0）。这两种状态改变了电路图，从而影响电感电压和电流的计算。

什么是电感电流的预测函数，并且它是如何派生的？

电感电流的预测函数基于电感电流的导数以及系统参数（如采样时间和电感电流的当前测量值）计算电感电流的未来值。该函数通过将电感电流的导数方程整合进预测模型来派生。

在MPC中如何实现开关状态的优化选择？

在MPC中，通过计算每个可能的开关状态下的成本函数值，并选择使成本函数最小化的开关状态，实现对开关状态的优化选择。这涉及到评估所有可能状态下的预测误差，并选择误差最小的状态。

为什么要在成本函数中添加对开关频率的考虑？

在成本函数中添加对开关频率的考虑，可以控制升压转换器的开关频率，从而减少开关损耗和电磁干扰。通过调节开关频率，可以优化转换器的性能和效率。

PI控制器在输出电压控制中的作用是什么？

PI控制器在输出电压控制中用于生成基于输出电压误差的电感电流参考值。通过调整PI控制器的参数，可以优化系统的动态响应，实现对输出电压的精确控制。

为什么要手动调节PI控制器参数，而不使用自动化方法？

作者选择手动调节PI控制器参数，可能是因为手动调节可以根据具体应用和系统动态特性进行更精细的控制。虽然自动化方法可以简化调节过程，但在某些情况下，手动调节能够提供更高的灵活性和性能优化。

Outlines

00:00

🔌 提升变换器的模型预测控制设计概述

本段介绍了设计提升变换器的模型预测控制（MPC）的基本步骤。首先，强调了设计MPC的必要性，即为了对输入电流或输出电压进行控制。接着，提到了设计过程需要系统参数、变换器的导数方程，以及如何通过有限控制集模型预测控制来实现。详细解释了如何使用欧拉前向法对控制变量（电感电流）进行预测，包括如何根据开关状态分析变换器的行为，并导出了电感电流的预测方程。

05:02

🔄 模型预测控制的实现和系统变量定义

在这一部分中，详细介绍了模型预测控制（MPC）的实现步骤，包括预测函数的编写、系统变量的定义（如采样时间、电感和电感内阻），以及如何根据可能的开关状态来评估这个函数。通过使用循环遍历所有可能的开关状态，介绍了如何计算每种状态下的预测电感电流，并进一步说明了如何通过比较这些预测值与参考值之间的误差来选择最优的开关状态，从而实现对电感电流的控制。

10:02

🔍 最小化误差和优化开关状态的选择

本段深入探讨了如何通过最小化误差函数来优化开关状态的选择。首先定义了一个初始的高误差值，然后通过比较不同开关状态下的预测误差来逐步找到最小误差，从而确定最优的开关状态。这个过程包括了如何根据误差函数的结果来动态调整开关状态，以实现对电感电流的精确控制，并通过模拟实验验证了控制算法的有效性。

15:15

🛠️ 控制策略的改进与开关频率的调节

这一段讨论了通过引入一个额外的成本函数来改进控制策略，以降低开关频率并优化系统性能。详细说明了如何通过比较当前和之前的开关状态来调整开关频率，以及如何通过调整权重因子来平衡误差最小化和开关频率降低之间的关系。此外，展示了通过调整权重因子来观察开关频率变化的效果，并指出了调节开关频率以满足不同应用需求的重要性。

20:21

📉 输出电压控制设计与PI控制器的应用

介绍了输出电压控制设计的过程，特别是如何使用PI控制器根据输出电压误差生成电感电流的参考值。详细讨论了PI控制器参数的选择和调整，以及如何通过对输出电压和电感电流的参考值进行实时调整来达到所需的控制目标。同时，也提到了如何通过调整PI控制器的参数来优化系统的动态响应，以及如何通过实验验证控制策略的有效性。

25:23

🔄 动态响应优化与PI控制器参数调整

本段重点介绍了通过调整PI控制器参数来优化系统的动态响应，特别是如何通过实验来找到最佳的参数设置，以减少超调和提高系统的稳定性。详细描述了调整过程中观察到的系统行为变化，包括输出电压和电感电流的变化，以及如何通过细致的参数调整来达到更好的控制效果。

30:26

🎓 结论与感谢

在最后一段中，作者总结了视频的主要内容，包括模型预测控制（MPC）的设计和实现过程，以及通过调整控制参数来优化系统性能的重要性。同时，向观众表示了感谢，鼓励他们应用这些知识来解决实际问题，并提供了进一步学习和研究的建议。

Keywords

💡模型预测控制

模型预测控制（MPC）是一种先进的过程控制方法，通过对系统未来行为的预测和优化来实现对系统的控制。在视频中，MPC用于控制Boost转换器的输入电流或输出电压。通过建立控制对象（如电感电流）的数学模型，MPC可以预测未来的系统行为，并计算出使系统性能达到最优的控制策略。

💡Boost转换器

Boost转换器是一种将输入电压提升到更高输出电压的DC-DC转换器。视频中提到的设计MPC是为了控制这种转换器的输入电流或输出电压。Boost转换器在电源管理和可再生能源系统中广泛应用，因其能有效地提高电压水平。

💡电感电流

电感电流是通过电感器的电流。在视频中，电感电流作为Boost转换器的控制变量，需要被精确控制以达到预定的输出电压或电流要求。电感电流的预测和控制是实现高效能量转换的关键。

💡误差函数

误差函数（或成本函数）在MPC中用于衡量实际输出与期望输出之间的差异。视频中通过计算电感电流的实际值与参考值之间的误差，来调整控制策略，以最小化这一误差，达到期望的控制效果。

💡欧拉前向法

欧拉前向法是一种数值微分方程的求解方法，用于近似预测控制变量的变化。视频中利用这种方法来预测电感电流的变化，为实现对Boost转换器的有效控制提供了一种计算手段。

💡开关状态

开关状态指的是Boost转换器中开关的导通与截止状态。视频中分析了转换器在不同开关状态下的电路模型，进而推导出电感电流的变化规律。开关状态的不同组合直接影响了转换器的工作性能。

💡采样时间

采样时间是控制系统中采集数据的时间间隔。视频中提到的采样时间对MPC的设计至关重要，它影响到控制策略的更新频率和系统的响应速度。合适的采样时间可以确保系统既稳定又具有良好的动态性能。

💡最小化误差

最小化误差是MPC设计中的一个核心目标，旨在通过调整控制策略，使得系统输出与目标值之间的误差最小。视频中通过计算不同控制策略下的成本函数值，选择使误差最小的策略作为最优控制动作。

💡PI控制器

PI控制器是一种常见的反馈控制器，包含比例（P）和积分（I）两个部分。视频中通过使用PI控制器来生成基于输出电压误差的电感电流参考值，从而间接控制Boost转换器的输出电压。这种方法能有效调节系统至期望状态。

💡切换频率

切换频率指的是Boost转换器中开关元件导通与截止转换的频率。视频中讨论了如何通过调整成本函数来控制切换频率，以降低能耗和提高转换效率。切换频率的优化是提高电力电子设备性能的重要方面。

Highlights

Introduction to model predictive control for boost converters.

Discussion on system parameters and derivation of the converter's equation.

Explanation of finite control set model predictive control.

Detailing the control variable as inductor current in boost converters.

Use of Euler's method for predicting control variable.

Analysis of boost converter circuit depending on switching state.

Derivation of inductor current's derivative equation from circuit functions.

Integration of predictive function into Matlab Simulink for modeling.

Design of the predictive function for inductor current.

Setting up system variables for the predictive control model.

Minimization process in model predictive control to find optimum switching state.

Introduction to cost function in model predictive control.

Dynamic response analysis of the controller to changes in reference current.

Adjustment of switching frequency to improve controller performance.

Design of output voltage control using PI controller in model predictive control.

Tuning of PI controller parameters to achieve desired output voltage response.

Transcripts

foreign

in this video I will show the design of

model predictive control for Boost

converter

here the conventional boost converter

we have to design a model predictive

control for

input current or output voltage control

of push converter

so first we need system parameters we

need a derivative equation of the

converter

I'll try to talk about about finite

control set model predictive control and

boost converter

our control variable is inductor current

so input currents of the

[Music]

post converter and we need the error

function or cost function in the model

predictive control here this is the

inductor current reference it is a

constant value

so it is DC quantity and this is the

predicted value of the inductor current

uh we need the prediction of the control

variable here we can use Euler's forward

method for approximation

Define it here

we need this part of the equation so the

final equation is this

here IL is the measured value of the

inductor currents we will measure it and

TS is the sampling time of the control

algorithm and this is the derivative of

the control variable so the derivative

of inductor current

so now we need the red part of the

equation we have to analyze the Boost

converter

the circuit model of the post converter

here

we can analyze the Boost converter

depending on the switching State because

the the series Vision State change the

circuit diagram

so we have two possible switching States

as can be one or zero so as can be on

positioned or off position

here the circuit diagram for uh s

1

in this case the inductor voltage is

equal to difference between input

voltage and voltage drop on RL RL is the

internal resistance of the inductor

so we can get such a function for

inductor voltage so ldi ldi DT is equal

to the difference between these two

volume and also when s is off positioned

we can get such a circuit diagram and uh

the

inductor voltage is equal to this

equation

okay now we have

these two functions we can put as

for S is equal to 1 when s is on

position it

the equation will be effective when is s

is of position of the equation will be

effective on the total system so we can

get the uh derivative of inductor

current by combining these two equations

and we have such a function uh for the

derivative of the control variable

then we can put this derivative equation

into the prediction function and finally

we can get such a function for the

for prediction of the in inductor

current

okay now we can design

it in the uh

Matlab simulink

this is our

prediction function

and we need

laptop function

below

I will write code for the model

predictive control

name is NPC boost

this is the output variable we need the

switching

[Music]

State for the output and

we will write

the input of this below

so first we can write the predictive

function

like

here

IL K1

and

[Music]

be in

1 minus s

and plus

I

okay now we have to Define system

variables this is the sampling time 10

microseconds

and one

Milli Henry inductor and the resistance

of the inductor is 0.2 ohm

and we have to measure inductor currents

input voltage

output voltage

okay

so

the equation is dependent on the

savaging state

but to evaluate this function

we have to use these two options here

if s can be 1 and S can be zero I am

defining the series impossible switching

States

Vector here

B1 and 0.

and instead of using uh the actual

switching State we have to try it we

have the related depending on the

possible switching state

I'm defining and

here and I will put this function into a

for Loop and

starts one and end

to

okay

now this is our predictive function and

we have to put one more

okay

this is our prediction function

here

we can obtain the predicted value of the

inductor current with this equation

then I'm returning back to the cost

function

the cost function is G is equal to

inductor current reference difference

between inductor current reference and

the predicted value

G absolute error

IL ref minus

ilk1

yeah

okay now we have to know the reference

of the inductor current

now we obtain the

cost function

this is our cost function

and the control methods Works depending

on

finding the minimum error

in the steady state the error

should be zero

in a real application it will not be

zero but it the errors will turn around

to zero

so it means that we have to find which

option options are here

which options gives less error so

I will write the minimization part

here we are calculating

the error in in the cost function

and if the calculated error is less than

Optimum

G

uh

we can determine depending on the list

less error by using such a minimization

here

and

of is equal to

n and g o will be equal to

G

okay

we have to Define initial value of jio I

am defining a big value for G of 1 A6

so why I am defining such a big value

for example when the surging State

when the for Loop evaluates the one and

is

here

will be 1 and we will get a cost value

it will be less than one E6

okay the control algorithm will

determine the first Optimum value

depending on switch one then in the

second option the second option is uh

zero it will be zero then it will get it

will give a different value here

as a result of cost function the control

method the minimization part will check

this

which option so when servicing State

when switching state is one the error

for example one amps

after the switching state

we are calculating the second option

then if we get less error than 1 amps

one amp

the result will be two so the optimum

sevision state will be 2 as a result of

such evaluation and we can generate the

uh

signal depending on this

Evolution

and here

the optimum switching state is

determined here I am putting it into the

result function but we have to Define

the initial value of the

and we can write one it is not important

because

the equations will evaluate the function

and it will get we will get some result

depending on this

okay now I'm returning back to uh

simonink

we have to put

required measured and reference

variables

and we

this is the reference

and

at the output of the

model predictive control we will get the

switching State directly

we will not use any modulation strategy

it will generate directly saving

position and we can put

some logic to here

to convert this Boolean type

okay it seems ready we can run the

software

okay

yes it is regulated to reference

five amps

here

the red one is the reference of the

inductor current defined here and W1 is

the measured value of the inductor

current and

this is the output voltage and this is

the blue one is the input voltage

okay now we can change the

in Dr current reference

but before I want to change

time scale

okay we can check the dynamic response

of the controller

okay here the reference current is

changed from 5 amps to 10 amps

it is directly increasing to 10 amps

but here we can analyze

yeah

the results show that

on the solution frequency is very high

the solution frequency is equal to half

of the sampling time

the sample frequency half of the

sampling preferencing so it is not

acceptable for many applications and the

accuracy of the controller

[Music]

may not good in such implementation so

we need to

we need to reduce the switching

frequency to get proper operation

to do this we need a

one more

[Music]

cost function

to reduce the sewaging frequency we can

change it

Gil

and we can Define one of

cost function for the Civil engine state

now I will Define then I will explain

this is our new

the previous value

the switch in the cost function

calculates the difference between the

evolution

State and the

actual civilian state so

as a result of such a cost function we

will get one or zero

n minus 1.

because of ABS the result of GSW will be

equal to 0 or

1. defining such a

cost function will change the uh with a

low amount so it means that for example

up the current errors reached for

example 5.6 amp it allows to keep the

solution position

at the previous value

if the error will reach out of the bond

Define Bond I will show defined Bond

it will allow to change the surging

position

in that case in that case the solution

frequency will reduce because for

example if the serving states start here

up to here the civilian State cannot be

changed after here it can change so it

will

it will change depending on the defined

value now we need the total cost

function to minimize the error we can

write the total cost function here

[Music]

Gil Plus

saving and we need to awaiting Factor

here the waiting Factor

adjust the weight of the jsw on the

total cost function

we can select any value there and it

will be effective on the

on the Savior frequency

but now we need one more variable here

as old is equal to

as the previous volume it will be

previous value and

as old will store the

[Music]

as while you're here so we need

persistent

variable

assault and if

foreign

we can return back to uh

simulink we have to Define weight and

Factor

okay first I'm defining zero it means

that the

second post variable will not effective

on the system then I will change and we

will observe the value

thank you

okay now waiting factor is zero and the

switching frequency

is the same as

previous

so it is equal to half of sampling time

we can Define any value here to here but

it will change the inductor current

Ripple here for example first I will try

0.5

at this point it is changed to 0.5

yes

now we can see that the solution

frequency is changed

because the period is larger than

this part

so we can control the

switching frequency here

now we can try some different value

for example zero point three

okay

the inductor current triple is reduced

it means that sewaging frequency is

higher than this part

and a solution frequency is less than

this part okay

we can adjust it and I have a solution

about this

it is published in one of our papers I

don't want to talk about more this if

you want to control switching frequency

you can check the the analysis in the

in our paper

now I would like to show the output

voltage control design of output voltage

control

and

I will indirectly control the output

voltage so I will put a pi controller to

generate inductor current reference

depending on the output voltage error

okay

this is PID controller

it discrete time and pi and you can

enter the

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KP and Ki value

and

also I'd like to talk about the

Pi controller the selection of Pi

controller parameters I am tuning

manually I'm not using any methods you

can find any method in the literature

you can check but I am not using

with the methods

and we need the error between output

voltage and its reference

and

we have to compare it

this is way out and

can define v ref

and we can select 48

volt

okay now such a control method the pi

controller will generate a reference

current and the model predictive control

will provide the inductor current

voltage interactor current

in the output side

so I would like to put

one more variable to here

if

okay

we will tune the pi controllers first I

want to check the result

okay

the red one is the reference of input

output voltage

so it is regulated its reference

the inductor current reference is around

4 amps

it's about 4 amps and we can change for

example 60 volt

we can check the transition time

foreign

results

but when I'm tuning the controller

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I will put a pulse

generator

I will create a step a change

into

24

Plus 36.

so it means that the output voltage

reference will change between 36 and 60

volts

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and now we can run it again we will turn

this value and we have to change the

time range

okay

this is not uh

it seems not good we have to increase

the dynamic response of the

pi controller

you can increase it

for example

to any

yes it is better than before we can

increase it

we have to increase it up to show up to

see uh opposite overshot

for example

100 we can try yes

bullshits in both inductor current and

also in the output voltage so we can

select the radius and the volume

we can try 90

we have our should

okay

we have small

I think this is

good but we can reduce it

okay and we can slightly increase it

yes

and I would write 80 again

thank you

in the inductor current we have still

overshoot and undershoot

but

here there is no too much overshoot and

undershoot

if the result is enough

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for you you can use these value as

defined here

okay thank you so much for watching my

videos