hey everyone welcome back to you control

system lectures let's design a control

system the way you might approach it in

a real situation rather than an academic

one now before we begin in earnest let

me take a few minutes to set a little

context for this video you know like I

tend to do I found out quickly when I

graduated college and entered the

working world that it was hard for me to

apply the theory I learned to a

practical application sure if I was

given a mathematical model of a system

and was asked to design a specific

controller I could do that but I lacked

the ability to start a problem from

scratch especially when that problem

seemed nebulous and that there was more

than one right answer where do I begin

how should I model the system and which

type of controller should I choose my

problem came from lack of experience for

sure but the other part came from my

belief that every problem had one best

solution and then they needed to know

before I even started what the proper

approach was going to be I had assumed

that the theory I knew was somehow

outdated and I had learned on the job

exactly how people really do design and

this kept me from just applying the

techniques that I did know to learn from

it even if it's not the optimal solution

but here's the thing there is never a

single right way to solve a control

system problem there are many different

types of controllers that will produce

satisfactory results and there are

numerous ways to model test and

implement that controller if you ask for

engineers you'll probably get five

opinions on how to go about designing

something part of this is because in

addition to meeting your performance and

stability requirements there are a lot

of other aspects of engineering design

that are just as important cost schedule

mass power and manufacturability just to

name a few and a good solution must

consider them as well often you won't

know what a good answer will look like

until you jump into the problem and

start exploring it take a few wrong

turns and evolve your solution over time

until you're left with something that is

ok and those four engineers with five

opinions might all wind up with

different but perfectly okay solutions

as well so keep that in mind as we walk

through just a single approach in this

video now this is going to be packed

with a lot of information and it's going

to be presented quickly

without a whole lot of explanation you

may not be able to follow along with

everything that I go through but that's

alright it's the process and the

excitement of exploring a new problem

that I want you to take away from this

hopefully this will motivate you to go

off and tinker with some real hardware

and practice the theory that you're

learning so that you develop your own

method for tackling new designs that way

you're a little bit more knowledgeable

and at ease when you're given one of

those open-ended problems at work okay

so with all of that out of the way

let's get to our own open-ended problem

we're part of a team that is developing

an earth orbiting satellite and at the

moment we're mostly concerned with the

vehicles thermal control system that's

the system that keeps everything within

the right temperature range space is

cold and parts of the satellite that are

exposed to deep space can get very cold

like minus 150 degrees C or colder but

the parts that directly face the Sun can

get very hot up to 120 degrees C or more

and as the spacecraft orbits the earth

and goes into and out of eclipse and

rotates around the thermal gradient from

one side of the vehicle to the other can

be very extreme and changing all the

time the interior of the spacecraft is

protected from these extreme temperature

swings a bit because they sit within a

mass that has some thermal inertia if

you look at a typical temperature plot

over time the external temperatures tend

to swing wildly since they're not

protected while the internal

temperatures have that low pass filter

of thermal inertia smoothing out the

swings and creating a less dynamic

environment even still some internal

components can see temperatures that are

outside of their desired operating

ranges and we need to figure out a way

to maintain their proper temperature

let's say for this example that we

predicted the average internal

temperature for our spacecraft to be

around -5 degrees C so what does that

mean for us

well our spacecraft has batteries and

they like to operate between ranges like

0 to 20 degrees Celsius or so it depends

on the battery chemistry so if it gets

outside that range the spacecraft and

the entire mission could be in trouble

and our job is to develop a way to keep

the batteries in this temperature range

and since we predict the average

temperature to be rather cold most

likely we will need to warm them up

rather than cool them down a reasonable

approach could be to use passive thermal

control

like rap being multi-layer insulation or

an M Li blanket around it so that it

traps the heat in just like a regular

blanket or we could use thermal straps

that connect it to another hotter

component to move heat towards it but on

this particular project it was already

decided for us that we would control the

battery temperature with a dedicated

strip heater if you have the power to

spare then a heater is a robust way to

ensure that the lower bound temperature

will not be exceeded you have a lot more

control over it with a heater and a

temperature sensor bonded to the battery

now the heater batteries temperature

sensors and the computer that will run

the heater controller were all chosen by

a different team long before we were

asked to solve this problem so we get to

work with what we're given and now that

we know the nebulous problem that we've

gotten ourselves into I think for the

next step it's important to understand

the physics of your system at least

qualitatively if not mathematically

before you just jump right in on

crafting a control solution I like to

think about how the system can move and

what it does when it's subjected to

forces where does the energy come from

how is it dissipated what are the

sources of errors and disturbances in

the system I'd like to have this general

understanding before I start because it

helps guide me later on when I feel

stuck on a particular problem a thermal

control system is all about heat

transfer if we think of the battery

system as a closed boundary then heat

goes into that boundary and heat can

leave that boundary when it's in steady

state operation the idea is to supply

the exact same amount of heat into the

system that is lost out of it so that

the temperature stays the same or at

least within acceptable bounds from a

simplistic standpoint if more heat

enters the boundary then leaves the net

heat transfer is into the battery system

and the batteries will get hotter and

the opposite is true if more heat leaves

then enters then the battery will get

colder

so what are the heat transfer mechanisms

well we have conduction radiation and

convection are the possible ways for

heat to enter and leave this system

conduction is the flow of heat through

individual particles bumping into each

other and transferring energy between

them when a high energy or high

temperature particle

bumps into a lower energy particle some

of that energy is transferred this type

of heat transfer occurs when there is a

physical interaction like we have

between the strip heater and the battery

and the battery with the spacecraft

structure so we need to pay attention to

these physical connections thermal

radiation is the transfer of heat

through photons or another way of

putting it through electromagnetic

energy in the infrared spectrum it's

like how the predator sees things with

his heat map vision actually on a side

note I think it's amazing actually that

every object warmer than absolute zero

gives off photons

it's a crazy concept to think that

humans are just lightbulbs in the

infrared

all right well our battery system emits

photons also which are absorbed by the

surrounding structure which then emits

it off into deep space or if we're in

the Sun the photons from the Sun radiate

into our spacecraft heating it up

lastly convection is when you physically

move hotter particles out of your system

as opposed to conduction where the

particles stay and just the energy is

transferred we experience convection on

earth when the wind blows and physically

moves the hot air particles that were

surrounding our body away from us taking

their thermal energy along with it

there's not a whole lot of convection in

space at least not for our battery

system and hopefully that's obvious so

we don't have to worry about air or

other bulk masses moving heat around

however as you'll see later we do have

to deal with convection as a source of

error when we're testing our system on

earth now the heat sources for our

system come from the Sun as I've already

mentioned but there's also internal

heating due to the battery's internal

resistance and from other hot components

in the spacecraft radiating and

conducting in and of course from our

heater and our heaters the thing that we

have the control over as for error

sources there are a few but I want to

highlight just one the temp sensors

themselves will have error in the

reading and probably more importantly

they only represent a single temperature

point on the batteries if the

temperature isn't homogeneous we may

have problems with part of the battery

getting too hot or too cold and our sins

are not being in the right spot to

measure it

so where should we go from here well if

we knew the battery system perfectly

that is how much heat enters and leaves

the system while on orbit and we knew

how the Delta heat changed the

temperature of the battery system then

we could just set the heater to the

proper supply value to make up the

difference and be done this is an

open-loop control design because the

heater setpoint doesn't rely on feeding

back the battery temperature with this

design if we're wrong about the outgoing

or incoming thermal energy then the

battery temperature will be off from

what we desire and the controller will

have no way to compensate for that error

it's a predetermined set point now this

might be a good approach if the system

was going to operate in a well

controlled environment however that is

not space because the external

environment is always changing we have

different spacecraft components that are

being turned on and off there's eclipse

as it orbits and different spacecraft

rotations to take into account even the

sun's output changes over time know the

open-loop approach feels risky for a

critical spacecraft component because I

don't have confidence that we can

predict the environment that well so we

should implement feedback control at

least of some type we need something

that determines the heater setpoint

based on the actual temperature of the

battery system something that feeds back

the temperature in order to do that we

need a temperature sensor now the temp

sensor the heater and the battery system

are all hardware components to get to

where we can develop a software based

controller we need some kind of sensor

manager that can read and interpret the

voltage from the sensor and produce a

meaningful measure now with this

measured temperature we can subtract it

from our desired temperature to get an

error term or how far off our actual

temperature is from the desired

temperature for example if we wanted the

battery to be at 10 degrees C but it was

measured to be -5 degrees C then there

would be a plus 15 degree difference and

we would need our heater to supply more

heat this is fed into a controller that

takes that error and tries to calculate

the right heater setpoint when we're

developing a controller we're trying to

determine how that conversion is done

and the output of that controller would

go into a heat manager which would

generate the voltage

needed to drive the heater alright now

that we've connected the battery

temperature back to the heater setpoint

we have the framework for our feedback

control system but now what well

unfortunately we weren't given any

transfer functions for the heater the

battery system or the temperature sensor

and I don't want to create a control log

without knowing a bit more about the

system for example it's important to

know how the system will behave when

subjected to actuator commands or in

this case what does it do when we turn

on the heat if we don't have that it

seems a bit like shooting in the dark

and to proceed we need to know more

about the physical hardware and luckily

we do have access to a physical test bed

with RealFlight components so let's play

around with those and see what we can

learn in this video the hardware I'll be

using is this temperature control lab

which runs on an Arduino microcontroller

clearly this is not real spacecraft

flight components but for this video it

will still do just fine because it has

heaters sensors thermal mass and a

computer just like our problem we'll be

able to learn a lot from operating this

hardware but to tie it back to our

spacecraft you'll just need to use a

little imagination let's walk through it

in more detail there are two sets of

heaters and temp sensors but we're just

going to use a single one for our test

the temp sensor is highlighted in green

and it's bonded to the heater in red

with white thermal epoxy in between the

two the thermal epoxy creates a good

conductive path between the heater in

the sensor surrounding the heater is a

radiator that helps distribute the heat

and gives the system a bit of thermal

mass there are no physical batteries in

this test hardware however these

radiators will serve the same purpose

they are a thermal mass that we can heat

up and when hot they lose heat to their

environment the heaters are controlled

by and the sensors are read by the

microcontroller underneath now this

setup provides several ways for the heat

to get to the sensor there's a

conductive path through the epoxy and

another weaker conductive path down

through the copper in the board and back

up through the sensors pins and we have

some thermal radiation coming in from

the aptly-named radiator and we also

have some convection heat transfer due

to the moving

err we shouldn't need to worry too much

about the impact of convection because

the conductive path through the epoxy

should dominate when you're running a

test you should take note of how that

test differs from the real operating

environment it would be a shame to

design a control system that could

perfectly control your testbed only to

find out later that the real hardware in

the real operating environment doesn't

behave the same way now there's a lot of

differences in my test setup however I

want to highlight a few important ones I

already mentioned that there's no air

convection in space but in other is that

we don't have the rest of the satellite

which can radiate heat to or from our

system and finally the ambient

temperature is not -5 degrees I don't

think my AC can go that cold so with

these differences the dynamics of our

test will definitely be off but we can

still learn a lot from a physical test

like this if we set up our control

system well we can then tune and

configure it with simple software

commands later on this difficulty in

having a representative test environment

is why even after everything has been

designed and built a spacecraft will

still go into a giant thermal vacuum

chamber and test all of its components

in a more space like environment if we

go back to the block diagram everything

I'm circling in orange would normally

run on the battery control processor or

the Arduino in our test however rather

than attempting to design and tweak a

controller on the target processor it'll

be easier for us to do all of that

design work using a program like MATLAB

or Python the Arduino will still be

responsible for managing the heater and

sensor devices but we'll send the

temperature back to my main computer run

the control law there and then send the

heater commands back to the test

hardware and then once we're satisfied

with our controller design then we can

load our controller code onto the

spacecraft and have it run for real this

type of testing is called Hardware in

the loop because rather than simulating

the entire system with mathematical

models some parts of the system like the

sensors actuators and thermal mass are

real physical Hardware getting the

software for this test to run is easy

because the temperature control lab

comes with all of those files if we go

to AP monitor comm heat htm' we can

download the device

managers and the code that will allow

your computer to talk to the hardware

using either MATLAB or Python it's your

choice

the device manager is the TC lab Ino

file that will load directly onto the

Arduino and this file defines which pins

the heaters and sensors are connected to

reads and writes to those pins and

interprets commands from my computer now

I'm using MATLAB for the interface

because I think Simulink provides a

better visual for what we're doing here

and I think it's easier for you guys to

follow along I'll open the Simulink file

and show a very basic system the orange

block is the software that communicates

with the test hardware you can think of

this block as the physical Hardware

sitting on my desk if I send a heater

command to it it will physically turn on

the heater now I can set the heater

between zero and 100 percent and get the

resulting temperature back from the

hardware this gray box ensures that when

I run this test it will run at real-time

speed and at this point I just need to

hook up the hardware to my computer so

it can talk over a serial bus and also

to a power supply to run the heater and

now we're in business for this first

test I'll set the heater open-loop to

35% this will be a step input from 0 to

35 and we should see a step response

from our hardware that starts at room

temperature and rises to some steady

state temperature now temperature

doesn't change that quickly so I ended

up running this for about 10 minutes

I'll speed it up and spare you the time

notice the shape of this response it

increases quickly at first and then

tapers off to about 55 degrees by the

end if we were trying to hold the

temperature at 40 degrees this would be

too high

we'd have to lower the heat point by

some amount but remember open-loop isn't

the solution we're going for so let's

change our system to be closed-loop for

my first attempt I'm going to create a

bang-bang controller this is a very

simple nonlinear controller that will

turn the heat on at 100% if the

temperature is below 40 degrees and turn

the heater completely off if it gets

above 40 let's run this controller and

see how it does again I'll speed it up

okay let me pause it here look what

happened with this controller the

temperature rose faster this time since

the heater was on full blast but it

overshot 40 degrees before settling back

down and hovering around our setpoint

why would this controller overshoot it

doesn't make sense that the temperature

would continue to get hotter after we

stop supplying Heat right well the

heater will stop getting hotter the

problem is that there's a delay between

the heater getting hot and the temp

sensor sensing it the heat has to flow

through the thermal epoxy and so the

heater was actually much hotter than 40

degrees when we turned it off and that

extra temperature caused heat to still

conduct to the sensor after we turned it

off and I don't like that overshoot so

let's see how to get around it let's

just change the heater setpoint to 25

percent when it's on rather than a

hundred percent this should reduce how

hot the heater gets and lower the

overshoot after we turn it off and look

at that no overshoot but now we've

introduced a new problem because the

temperature doesn't rise as fast with

this lower setpoint and we needed to be

able to respond quickly to the changing

thermal environment so this won't do

either

we need a controller that can set the

heater high at first to heat up quickly

but back off earlier to slow the rising

temperature before we overshoot and we

can do that with a PID controller I'm

using the built-in PID controller with

Simulink and I set the P I and D

parameters to a first guess and if I run

this you'll notice a few differences

from the bang-bang controller first the

heater setpoint on the left is no longer

jumping between a max and min value but

is being set to a continuous set of

values high at first when we want the

temperature to rise quickly and then

lower as it reaches its desired

temperature now there's still an

overshoot which means I don't have it

tuned very well I could probably

increase the D term to remove the

overshoot however there's something else

that I want you to notice when the

temperature is steady at 40 degrees we

can see the heater setpoint is steady

around 17% this means that the heat that

is supplied at 17% is exactly the amount

of heat that has lost to the surrounding

environment this is the portion that our

heater makes up so you might be tempted

to just go back to

open-loop system and set the heater to

17% and be done however this will only

work if the environment stays the same

watch what happens when I remove more

heat with a hair dryer set to cool the

temperature immediately drops and the

PID controller Rises the setpoint to

counteract it eventually the temperature

gets back to 40 degrees but now you can

see with this changed environment the

heater setpoint settles at around 75%

and not 17% this is reinforcing that we

really do need this feedback controller

okay at this point I could go back and

tweak the PID gains and see if we can

get a better controller but it takes 10

minutes every time I run this and this

is taking a long time not only that but

most of the controller designs that I

want to try require me to have a

mathematical model of the system which I

don't have we've done everything so far

without really knowing anything about

our hardware so at this point I want to

do some system identification for system

identification we could take the white

box approach taking note of the material

properties and the dimensions and write

out the differential equations directly

however we have the hardware so let's

fit a transfer function to our real

system the way I'm going to do that is

by applying a step function to our

system and recording the step response

this is exactly what we did at the

beginning of all of this except this

time I'm going to save the data in an

array to use later and that's nearly the

same step response that we saw earlier

except this time with a heater setpoint

of 40% I'm going to try to approximate

this system with a first order transfer

function we'll need to include a delay

term or dead time as well since we

already know that there's delay in the

system a first-order plus dead time

transfer function requires three things

the gain the time constant and the delay

the gain can be found by dividing the

rise in temperature by the rise in the

setpoint the temperature went from about

20 to 60 degrees and the setpoint went

from zero to 40% so the gain works out

to be about 40 over 40 or 1 the delay

term is how long it takes for the

temperature to start rising after the

step is applied it's hard to tell

exactly but it looks to be about 10

seconds and the time constant

is a measure of how fast the system

rises it takes about five time constant

periods to go from zero to 98% of the

steady state value for us it gets to

steady-state around 500 seconds so minus

10 seconds for the delay and divide by

five gives us a time constant of 98

seconds I can use the TF command in

MATLAB to generate the first order plus

dead time transfer function and I get e

to the minus 10 s which is the 10-second

delay times 1 over 98 s plus 1 or since

I'm working in Simulink I can just build

it there as well

now this is just the dynamic portion of

the system and if we input it as 0 for

the heater the output of the system

would also be 0 for this transfer

function but we know zero input means

room temperature output so we have to

add a constant room temperature value to

the output to create our mathematical

model

and there we have it now I'll comment

out the top system and run our model

against the real hardware so we can see

how well it does all right I can see

that it's rising faster than the real

hardware so it's already a little bit

off but while it runs in the background

I'm going to generate a better first

order plus dead time model using a

Python program from the AP monitor site

that will find the optimal combination

of gain time constant and delay based on

the step response values that I saved

earlier I'll set the initial guess to

what I calculated by hand and then kick

it off running the script takes a three

column data file time input and output

starts at the initial guess and then

tweaks those values to minimize the sum

of the squares of the error between the

real data and the current model alright

now it's done you can see the blue line

which was our original guess

rising much faster than our data just

like we see with what's going on with

the tests were running right now but the

optimized set of parameters fall right

on top of the test data and we can see

the optimized parameters in the script

output the gain is one point zero four

seven and the time constant is 150 two

point four and the delay is eighteen

point six seconds and now we can go back

to Simulink and change these parameters

to the optimized ones we'll have a much

better first order model of our system

with these parameters now at least for a

while we don't need our hardware to

design a controller we can use this new

model to perfect our PID controller try

some feed forward control or build an

optimal model predictive controller and

we may find later that the first order

model doesn't accurately represent

higher-order dynamics and we need to

improve it and then we will just do that

designing a control system is usually an

iterative process and that's what we did

here we went from open-loop to bang bang

- PID without a model - developing a

model which will allow us to quickly

tweak our PID game

or develop a more optimal controller

okay I know this video was really fast

but hopefully it still gave you a better

understanding of how to just jump into a

problem and make your way through some

of the confusion that you might have

also how control system theory is tied

back to the larger engineering problem

now the temperature control lab that I

was using was developed by associate

professor John heading grin at BYU at

his ap Monitor website you can explore

all of the different ways to learn

control theory using simple hardware

like this if you don't have hardware to

play around with it would be a good

engineering exercise to try to build one

yourself it doesn't have to be

temperature related or if you want you

can buy a temperature control lab

directly from this webpage now this

video isn't sponsored by BYU or

professor heading written in any way I

just like the hardware and I think that

it's a great way to practice more

realistic control theory if you made it

this far thanks for watching this

marathon video I always liked reading

everyone's comments so please tell me

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below it's a bit different from my usual

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everyone