████ 难点词汇

████ 生僻词

████ 词组 & 惯用语

[学习本文需要基础词汇量：

hi everyone I'm Steve and this

is the first video lecture on a series

I'm calling a on control where

I'm going to rapidly go through the

highlights of and modern control

theory so this is going to include how

to write down a system description of a

control system with inputs and outputs

in terms of a system of linear

and now how to

design controllers to manipulate the

behavior of that system how to design

system this is not meant to be an

subject but really kept at a high level

and my goal is to first of all get you

familiar with the major types of

and modern control theory I want to

teach you how to use these in MATLAB to

actually work with a real system and

what I also want to give you a feeling

for is what in control theory is easy

and what's still quite challenging today

so that you can get up to speed on the

real pressing needs of control theory

today okay and again this is not

important to you and you want to you

know you like control theory and you

want to go more into depth there's

deeper treatments both on the math side

and only applied design side okay and so

I want to give you just a little bit of

perspective I think about the world in

terms of

of the state of your system and this has

been an extremely successful viewpoint

for

so we model the fluid flow over a wing

or the

the spread of a disease or the stock

market climate planets moving around the

solar system all of these are

very very successful framework to take

in data from the real world and build

models that you can use for prediction

but often we want to go beyond just

describing the system of interest and we

want to actually manipulate the system

actively to change its behavior

and so that could be just imposing some

control logic just setting inputs into

the that system in a certain pre-planned

way to manipulate it or you could

actually measure that system and make

decisions based on how the system is

responding to what you're doing okay and

so that's kind of the

and control theory is that you have some

a

make more stable you write down the

system of equations and then you design

some control policy that changes the

behavior of your system to be more

desirable okay so that's what we're

going to talk about and so I want to

begin by just talking about the various

types of control that there are so

there's lots of control that goes around

all around us every day that is not

active it's called

I'm going to draw just a diagram of the

different types of control so one type

that's very common you see all the time

is

if you see a large 18-wheeler transport

truck going down the highway and it has

those

form of

causing the air around the truck to

behave in a favorable way to reduce drag

and if you can get away with passive

control of your system that's actually

great because you just have to design an

up front and then there's no energy

expenditure and hopefully you get the

desired effective for example minimizing

drag on a truck but

typically not enough and so

we need to do something like active

control and so active control

essentially just means that this is

control when we're actually pumping

energy into the system to actively

manipulate its behavior okay and there's

lots and lots of different types of

active control so one that I'm going to

tell you about is open-loop this is

probably the most common form of active

control where essentially you have your

system of interest

and I'm just going to actually draw this

as a block here so you have some system

and the system has some input so I'm

going to call them variable U and it has

some outputs that are variable Y okay

and so what

essentially reverse designs your system

and

exactly what is the perfect input u to

get a desired output Y okay and so if I

take something like a

so we know that if I if I am very

careful I can stabilize this

that if you just pump this

and down at a high enough frequency it

will naturally stabilize the dynamics

okay so if my base just

high frequency

dynamics of this

you may be why is the angle of this

pendulum and my desired control is to

make this pendulum essentially stay at

vertical okay and so if I pump in energy

in a pre-planned way I just make my hand

go up and down in the

in a

Y that I want okay and essentially that

is open with control it's very commonly

used essentially you think about your

system you

just enact that control law okay but the

you're always putting in energy to this

to this u so in the

example I constantly have to be pumping

this thing up and down

the minute I stop the stability it

becomes

so the idea is that what we can do is

called closed-loop feed feedback control

so closed-loop feedback control

and essentially what this means is that

we take sensors bring my

out

we take sensors sensor measurements of

what the system is actually doing and

then somehow we build a controller I'm

just going to call this a controller and

we feed that back into our our input

signal that can manipulate the system so

for example in that

example as a human if I had a tall

enough pendulum so it's slow enough I

could actually measure with my eyes if

it's starting to

much more subtle control so if you have

ever played around with as a kid with a

you know that you can actually get

pretty good at it so that with very low

energy input or very small hand motions

you can stabilize this thing so that it

doesn't fall okay and so that's the

basic idea is that by measuring the

output you can often do much much better

than just feeding in kind of a

pre-planned control law okay so sensor

based feedback measuring the output and

then feeding that back as the input is

basically going to be the entire subject

of what we're going to talk about in

this control boot camp so closed-loop

feedback control is the name of the game

and that's that's most of what we're

going to talk about now that's not to

say that if you can design a good open

loop or a good

know there are some times you would do

that but in the systems we're going to

be interested in

based on sensors is going to give

dramatically better performance okay and

so I want to talk a little bit about why

you would have feedback so I just want

to make a quick list why feedback

because this is a very very important

important topic in control theory so I

want to motivate again just maybe in

more concrete terms

why would I actually measure the system

and feed it back instead of just

ignoring any measurements and using

open-loop so why feedback over open-loop

control okay so this is a question I

always ask my class and I let them think

for a little bit why would you actually

want to have

the sensors feeding back into your

system okay so one answer that I get

most often is maybe my system has some

system is uncertain

so uncertainty is one of the main and

enemies of open-loop control right so if

I have this pendulum and I perfectly

pre-planned what I want to do let's say

that

taller or it's a little bit heavier or

there's wind blowing or something like

that then any kind of uncertainty in

that system is going to make it so that

my pre-planned

but if I measure the outputs and I

realize that it's not doing what I want

it to do I can adjust my control law

even if I don't have a perfect model of

my system okay so uncertainty is a big

one

another really important one is

can never fundamentally change the

behavior of the system itself so in the

pendulum example I could pump in an

amount of energy with the

based motion that would force the system

to kind of correct itself up to vertical

but I'm not actually changing the

systems dynamics itself the system still

is

control I can directly manipulate the

actual dynamics of this closed-loop

system and I can change the the dynamic

properties I can change the

of this closed-loop system okay and I'm

going to show you that as the last

example in this

thing that I think is really really neat

is that with feedback control you can

also reject disturbances in your system

so let's say that I have some external

disturbance D that's coming into my

system and this happens all of the time

so so for example let's say in my

pendulum example there's

so that's a

disturbance that would be very hard for

me to predict or model or measure so

there's this

if I had an open lead strategy

essentially it might not be able to

correct for that

that

system dynamics will be

through some sensor and if my feedback

control is good enough I can actually

correct for that disturbance so I think

of uncertainty as internal system

uncertainty kind of disturbances to my

model and I think if disturbances as

external or

system that may be too difficult or too

costly or too complicated to to model or

predict or measure okay and feedback

essentially handles all of those basic

issues that can handle disturbances that

can handle uncertainty and it can

fundamentally change the stability of

your system to make it more or less

stable by actually changing the

and unfortunately open-loop can't do any

of those things which is a huge

and I guess the fourth one is energy or

efficiency

so I'll just say efficient control so

again in the case of

open-loop case I constantly had to pump

this thing up and down so I was always

putting energy in but in the case of

sensor-based or elegant feedback control

you can picture yourself trying to

stabilize this

doing a really good job if you have a

really good controller this thing is

barely moving at all and so you almost

have to put no energy in to correct it

so effective sensor based feedback

control is also much more efficient

which is really really important in lots

of applications so if you're going to

send a rocket somewhere you better have

an efficient controller because you

don't want to be wasting fuel okay so

the last thing I want to show you is

just this idea of why you can change the

fundamental system dynamic dynamics and

change the stability with feedback

control okay so the basic property that

we're going to or the basic mathematical

architecture we're going to be working

with in this class is going to be a stay

space system of

equations so we're going to have a state

variable X X as a vector that describes

all of the quantities of interest in my

system so for example in my pendulum it

could be the angle and

it could be two states if I have you

know an airplane going through the sky

it could be the three the position

vector XY and Z and also its its

okay so it could be like a six degree of

freedom or twelve state twelve component

vector X and so what we're going to look

at is the system X dot equals

we're going to start with

of equations that describe how those

states

so I'm going to assume that we're all

pretty comfortable with this linear

systems of OD e so for example we know

that the solution of this is X of T

equals e to

time x zero okay so we know how the

system behaves we know that if a has any

then the system will be

all of the

real part then these have stable

dynamics that they go to zero as time

goes

do in control theory is we're going to

add plus B U so we're going to add this

ability to

system okay so we're going to say that U

is our

its our

in the case of

the position of the base or it could be

the voltage onto a motor that controls

something but this is the

get to turn to try to stabilize our

system and B tells you how this control

change of my state okay and down the

road we're going to look at another

extension where we're actually going to

measure only certain aspects of the

state so we're going to measure so

this might actually be a limited set of

measurements we might not measure all of

this the state of its high-dimensional

and we might only have access to those

few sensor measurements in Y but for now

let's just talk about the top equation

so if I assume that I can measure

everything in the system and in this

case of

pretty good estimate of its vertical

position and how fast it's moving so

let's say I can measure all of X then we

can develop a control law let's say u

equals minus some matrix K times X okay

so I'm just going to say let's

basic control law that my control input

U is going to be some matrix times X

just some constant constant times the

components of X when I plug this in so

this is this is really sensor based

feedback where y equals x okay in this

case we're assuming that y equals x we

can measure all of our state and we're

going to feed that back into a control

law which is minus K u equals minus K

times X and we're going to try to modify

the dynamics so if you plug u equals

minus KX into our dynamics we basically

get and let's make another color here we

basically get X dot equals

minus B K X okay so B is maybe a tall

vector the same or set of vectors the

same height as X K it's kind of the

matrix of size n by n if X is an

n-dimensional state and so this equals a

minus BK times X so notice that by by

measuring the state in this case we're

measuring the full state X and feeding

that back to the control u through this

law u equals minus

a X we're able to actually change the

times X and so it's actually the

you if the system is stable so I can

have a really originally

like this

measuring the state and feeding it back

to my

stabilize the dynamics I can actually

make the system

okay and so figuring out when you can do

this so this doesn't work for all

systems and for all measurements and for

all

system is

this case so that it is well controlled

are going to be the subjects of the next

couple of lectures okay but really

really important feedback solve all of

these fundamental problems if I have an

uncertainty in my system I can

actually happening and feeding that back

if I have an

can actually change the dynamics with

this feedback and you can't really do

that with open-loop I can also account

for

wind that might have been really hard to

measure and could totally throw off your

pre-planned

measure what's happening you can account

for and correct for that

and finally feedback control is

efficient if you're doing effective

feedback control to stabilize a system

then the more effective you are the less

energy you have to put in okay

so this should be a really exciting set

of lectures I'm really hoping to get you

up to speed quickly and with MATLAB

examples so that you can control these

systems you can design controllers to

actually manipulate your system to do

what you want it to do okay thank you