A real control system - how to start designing

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I knew was somehow outdated and I had learned on the job exactly how people really do design and this kept me from just applying the techniques that I did know to learn from it even if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 what you think of this type of video below it's a bit different from my usual ones and a huge thank you to my patreon supporters for making this video possible if you would like to support me in my efforts on YouTube you can from the patreon link in the description below for any amount of support you can download a digital copy of my book in progress on control theory now I'm still actively writing the book so it's not complete but if you'd like a copy of what

I have so far but are unable to support through patreon for any reason just email me at control system lectures at gmail.com and I'll just send you a copy for free that way we can spread the knowledge and help everyone on their quest to becoming better control system engineers thanks everyone