Single Loop Control Methods - Control Tuning // Chapter 5

this episode or this video series is going to be on single loop control methods tuning we're finally up to tuning we're going to talk about how do you tune a self-regulating process several episodes ago we talked about the process how to identify it then we talked about the controller proportional integral derivative now we're going to talk about how can we link these together this is a we're finally at the point where you can actually tune something when we're finished what's awesome about control tuning is that you get to define how the loop responds you can either make it respond in a nice smooth transition if you want to do a little bit of an overshoot you can do that or if you want to oscillate you can do that simply by changing the parameters of proportional integral you can take a signal that responds this way and convert it to this that's what's tuning you have to kind of know the where you want to go with it and then once you know what kind of response you want then with the process you make what you want by adjusting the tuning parameters that's what we're going to talk about in this particular discussion you have to decide what you want and there's a lot of different discussions if you get into phase leads and gain margins we're not going to talk about that we're basically going to say do you want to have an overshoot yes or no and so we'll talk about that the first one here is called a first order process or a no overshoot in other words I changed the setpoint and the process comes right up to it and we're trying to figure out how to come up with tuning parameters to make that happen this is the one that I like to use it's a very stable tuning techniques they will refer to this as direct synthesis sometimes you'll have heard it referred to as lambda tuning or pole placement those are different names for virtually the same tuning technique we're going to call it direct synthesis but it results in no overshoot I will also quickly talk about the Ziegler Nichols tuning technique in a couple different ways that's been around since the 40s and it provides what's called a quarter wave decay and it's where the each positive hump is 1/4 you know this pump is 1/4 of the first time it's called quarter wave decay and so you can come up with tuning parameters to make that happen and we'll talk about that regardless of which method you use you have to start with the process you have to look at the process and identify the dynamics of that process and we spent a whole lesson talking about that whether you do a bump test or you look at the first principles or you do a visual inspection you have to have an idea of the dynamics of the process now we'll review that in a little bit when we go through this but once you've identified the process dynamics then you come up with tuning parameter so that you can either have a fast response moderate response or a slow response the nice thing is that you get to identify that that speed we're going to introduce a new term called tau ratio the Tau ratio is what is like a knob that allows you to decide whether you want to be fast medium or slow and we'll talk about that when we get into it the math and don't gloss over we're not going to spend time on this but I just wanted to show you that there is a theoretical background behind the math that is used to calculate these tuning rules so the way I like to think of tuning is it's a calibration process if you can imagine you're your transducer with a zero in the span if a guy's just adjusting the zero and span until it reads right is he really calibrated the transmitter most people say no well if you're just throwing tuning numbers in until it stops oscillating are you really tuning my answer is no you need to understand the dynamics figure out what kind of result result you want and then use the tuning to match those two that's called tuning and that's called tuning setup and that's what I find fascinating and it's based upon very rigid theory and there's another course that maybe we'll do someday on control theory Laplace transforms and s domains and frequency domains that's neat stuff but that's not what we're going to cover today what's interesting is as complexes that math is the tuning rows rules are really pretty simple is remember we said in the last clip that the proportional gain and the process gain were inverted they are they're inversely proportional and then there's this term I called tau ratio I'll talk about that that's like your knob if it's a big number you have a slow response if it's a small number you have a fast response so you it's your knob for tuning and notice we said that the integral time and the process time constant were related they're not just related they're set equal this is why I like the standard form of the PID algorithm once you set your once you identify the process time constant that is your integral time remember what I said about units the units that you use for your process identification has to match the units used for your controller I've had people really mess up you know the you know 1 minute and 60 seconds you could be off by factor of 60 and not even know it well you would know it once you turn the control on and if you're trying if you're dealing with a first order model which is the most simple model remember it's the process gain and the time constant you don't even need derivative remember I said derivatives not used very often the tuning role which is the math when you plug all this stuff together I have a first order model with a standard PA algorithm and I have an adjustment of tau ratio where a small number is fast and a big number is slow boom it comes up to this simple tuning I also just want to identify here that most controllers are in percent so if you calculate your process gain in process units then you'll have to convert it to percent some manufacturers that percent conversion is built into the game some is built into a conversion some it's up to you just make sure you know how the manufacturer is normalizing the game that's all I'll mention here if you calculate your game than percent it's it's probably going to be right if you calculate in the process units you'll have to convert it to percent based upon the range of the transmitter so that's in the book and I want you to spend a little more time on that but in the simplest form you calculate your process gain and your time constant and then you pick the Tau ratio well the question that comes up is well what's the Tau ratio tau ratio is a ratio of remember tau is the Greek symbol tau represents time constant we're talking about the ratio of the closed-loop time constant which is when I change the setpoint how long to take to get there let's say it takes four minutes to reach the set point in automatic but an open loop if I change the valve it takes a minute to settle so the ratio is four so that would be at our ratio for literally the tower ratio is defined is how much slower than the dynamics of the process do I want this controller to run well I always originally taught this this method they said just pick a number any number will be fine and I was like well it needs to be biased to the dynamics of the process don't use the term fast and slow that's irrelevant fast and slow has to be biased to the dynamics of the process if I'm talking about a tank that has a an hour time constant and I tuned it to have a half-hour time constant that's really fast for that control loop in time it's slow but for that control loop it would be considered fast that's why I like the term tau ratio is it biases your choice to the dynamics that you're working with it really simplifies and that's what we're going to talk about if you if I ever sit down and do tuning with you you'll see me make a table like this usually I pick four times four tower ratios one two three and four they don't have to be one two three or four they could be one point five two point two it doesn't it's just a number but I will make a series notice here the integral time stays the same if you're using the standard form I've kind of been engrained to think in terms of the standard form that's true that locks in the time constant and you don't have to mess with it and then your speed of response is strictly a function of the proportional gain notice you've already calibrated it to be invert the inversely related to the process gain and then we got this one too so literally the bigger the tower ratio the slower your response but slow is now normalized to be in relationship to the dynamics of the process let me show you what I'm talking about if I pick a tower ratio of one when I change the set point I should expect that the ratio of open-loop time constant to closed-loop time constant to be one that's what this is saying my open-loop time constant should equal my clothes that's what a one does so now if I look at the air subtract the set point in the measured value you'll get this kind of a that's just that's the air so remember what we said proportional if you just looked at the proportional component it would look like this it's proportional to the air that's what proportional does remember what integral does integral is the area under the curve in the last series we always showed a step change in the air okay that's why the integral was a slope but here the area actually goes to zero so look at the integral it comes up and stops you never get to see the proportional acting by itself and the integral acting by itself you always see the proportional integral acting together so you see the output of your controller so it looks like it was a step change and a lot of people will incorrectly say well it's just a proportional correction no it was a it's the it's a perfectly calibrated loop a lot of times I'll do that is if I think I've got it nailed I'll pick at our ratio one change the setpoint and make sure my output looks like a step then I know that the proportional will back off at exactly the same time the integral goes up we're looking like it was just a proportional kick that's what's going on behind the scenes now let's look at what happens at at our ratio of two at at our ratio to your closed-loop time constant should be two times the open-loop time constant and what that means is it takes twice as long to step to subtle as it did if you just went and changed the actuator so I changed the setpoint and it's going to take twice as long now if I take the difference here set point minus beta value notice my error is taking longer places long to get to the set point notice the proportional here I've got a superimposed but the proportional kick the proportional looks just like the air and then the integral remember you're integrating that area it looks like this so when I add these two together I get this shape you get this initial kick and then it comes on up notice that the size of the initial kick is half of the total output that's another trick if I use at our ratio of two and I change the setpoint I will look at the initial step compared to the final step and if they're not half I know something's wrong I messed up my process gaynor I have a non-linearity going on or I miscalculated something there's always a validation step most people ignore that they do their bump test they come up with their tuning and they plug it in and they walk away don't do that change the set point and watch your control work it should do what you told it to do and if it doesn't you missed something you got the time constant wrong the gain wrong there's a non-linearity the valves in a different position it needs to match this the theory always works that's the hard part is the theory is always right if the application doesn't act like the theory then you did something wrong maybe you got the range wrong I've seen that happen I there's a lot of cases so it should do you're the one in control you're the one telling the controller how to respond so if you say at our ratio to the first step should be half of the final and it should take twice as long to get there than if you just did an open loop bump now people say well I got to have that pea kick I've got to have it I've got to lead the process remember the example I talked about getting in a cold car and you turn everything up hot and then you back off on it well how can you do that with a PI algorithm well you know at our ratio of less than 1 at our ratio here's an example of 0.5 it says that my closed-loop time constant will be 1/2 of the open-loop time constant so if I wouldn't change the actuator and it took you know 4 minutes to get there it would have a one minute time constant well if I Tower ratio 0.5 it'll have a 30-second time constant and it'll take whatever that is 2 minutes to get there half as long well how does that happen well same thing this time I don't show the difference because I think you can see it by now notice that the proportional looks just like that air that I had before and the integral it doesn't have to integrate as much because the air is so small and when you add these look what you get you're proportional kick is exactly twice where you're going to end up because we had a tower ratio of 0.5 your initial kick is gonna be double and then it'll race right down and it should take half as long to get there this is also what I caution people about this step is very on actuators it's just hard or that big kick so I don't like going with towel ratios that low because of this reason also what I would do is do what they call set point and ramp rate so that instead of doing an abrupt change in the set point you actually do a working set point ramp rate and then that reduces that that kick whenever you have a large error because when you have a set point ramp rate you limit that so you get a nice lead action those are some of the caveats when you go with a towel ratio of less than one now what towel ratio should I use that's the question is like well this is great you know I have a knob now that I can spin but how do I know should I go fast should I go slow show you you know what what do we do this goes back to when we talked about model mismatch you need to calibrate your towel ratio to your model mismatch and that's what we're going to talk about here you know it would seem that a towel ratio of one would be a good idea because then if you change the set point or change the actuator they both would get there at the same time but what about model confidence what if the process has dead time in it or is it's you know something you know you don't really want to be that aggressive so it's a little bit like an archer shooting you know at a target if he's able to hit the bull's eye every time you don't really need much of a bull's-eye but if he's bad like me he could be all over it you need a big bullseye well think of the towel ratio as a sizing element and the more uncertainty you have the bigger the target has to become so that's what I'm talking about here with towel ratio and confidence I've got four different bump tests that I've done on four different processes so in the first one I bumped it and I recommend bumping it like we've talked about in the bump test section knew more than once you know to make sure that you can predict the gain and the time constant so you're assuming as a first order if your first order model and your process match so that the difference is small you could you can get away with the towel ratio one that's not a problem in this case I've got delay you know it may be a first order plus delay but it's not a first order model so I have a big bigger err so I should probably go with a bigger towel ratio it's currently like if your towel ratio is too small compared to the process the controller literally starts hunting for it and a hunting controller is one that oscillates oscillations are not good they cause product instability product quality run ability issues all that stuff so when you err err on the side of your towel ratio being a little bigger so this isn't a case typically if you see this you should stop and fix the problem your actuator is broken or your valve positioner is broken this case this is a very common one this this under damped response is that under damped response I'm sorry it's a it's actually called over damped it's a second-order / damp because there's no oscillation but the first-order you have an additional lag here so I wouldn't go with the towel ratio one because what happens is this error becomes the valve moving more than it needs to and I've got a couple of examples of that so this idea the arrow so I both I do four arrows boom boom boom and if I group meaning they all hit the same spot and and they hit my model and my model is a first-order so I'm saying I bump this thing a hundred times it looks the same it's very predictable it's very stable I could go with at our ratio one and it'll it'll be fine but you have to worry about what happens what do you think happens when valves wear or instruments where they tend to slow down so as they slow down you need to adjust your model so if you have your controller tuned very aggressive and over time it moves out of the window oscillations occur so it's better to set your target just a little bigger so that you allow your process to wiggle and you won't get called in in the middle of the night now this is a case this is what I like to talk about this one is repeatability and aggressive Tao ratios are not the same thing in this case I but you can see they clustered really really well but they are off the tower a co one tower Asia one is when there's no model mismatch so in this case we assumed a model to be a first order but the process is repeatable but it's not a first order that doesn't mean you can't tune it with a PI algorithm you just need a bigger target that's that the rest of the story there is is when you get into advanced levels of control is not everything has to be modeled as a first order or as a PI algorithm but that's a that's the topic for a different class this case is actually the most frustrating case is where most the time where I've messed up is I've done one bump test boom I said wow it's a first order process and I stopped I tuned it for tau ratio one and this thing looks great and then I leave and in the middle of the night almost always the process changes it's now outside the area that my controller set up for and I start oscillating so when I go back into the site the next day instead of the nice carpet warm welcome they're all lined up with clubs and what did you do and that's usually I didn't do my due diligence I didn't pay attention to the process and it moved outside the window that I had tuned it for I that's why I recommend bump tests that's why I recommend the electronic log or a log of some sort to cover yourself say when I bumped it this was the model another example I was in a place I bumped this thing a bunch of times and I got the same model every time and I tuned it and solved the problem that had been around for a long time the next day I came in and it was all over the place and they said I told you it wasn't going to work and I said well this control theory it just doesn't break so I said let me go back and do another bump test so we did a bump test on the same process but the the parameters were completely different so I brought the prize I said look at this I said yesterday this was the process today it's this they're completely different what happened well it turned out they had different lines were running and when one line would run the dynamics would change when two lights would run you'd get a different dynamic this has been going on for the history of this particular plan we simply put in gain scheduling say well when both lines are running use these gains when one lines running use these gains and it solved a persistent problem that had been going for years because of this if you can calculate or predict what causes the model to change you can adapt for it but it's knowing what control can do knowing how to calculate the process and you can get it so bigger targets it is a little slower but it's more stable so when I would I usually will make this chart and if you look in the back of the book or some of the reference you'll see these or you can make a spreadsheet you always pick a couple tout ratios and my head fast as compared to the dynamics of the process a for slow as compared to the dynamics of the process if you're using a standard PID algorithm the TI and the time constant are the same make sure that the units that you're using for the dynamic and the units for the integral are the same and then the control gain is inversely related to the process gain and then the Tau ratio changes the speed of the response keep in mind scaling there's several different controllers out there that integrate the range of the transmitter into this or not but that's something that you can identify when you look at the documentation so here's an example we walk up to a unit and we do a bump test and so you can see here's my set point here's my output change the controls in manual and I've got a process response so now I've got a bump test and there's my response so now what type of process is this you know go back and remember there were six areas there was pure gain first-order second-order / damp second-order under damped first-order plus dead time integrating process which one is this this happens to be a second-order over damped process that's the classes classification we're still going to assume it's a first order process and this is going to take you a little while I recommend you do it by hand but there's a lot of tools we have software that will model this for you but I recommend that you start getting calibrate your eye to what a first order process looks like so the process gain is the change in the process over the change in the output that produced it so in this case we made a 15% change which is huge and a 25% change in the output so I got a game of 1.67 boom I like to do a couple different bump tests to make sure that 1.67 is consistent over the operating range of my process this is very it correlates well to valve position I've been in other places where you know if your valve that's 60 10 90 that's 60 30 60 90 10 rule is that between 30 and 60 percent of your valve you get 10 to 90 percent of your range it's pretty accurate between there your process gain is well constant on the ends your process gain can be really really different and that's why I like to look at my valve position while I'm getting ready to do this change this this bump test or over history the other thing you want to do now is calculate the time constant basically I like to take when did this thing settle call that the dynamic transition time and divide that by four that are the dynamic settling time so in this case it took roughly 50 seconds divided by 4 that's 12 and a half so 12 and a half seconds remember the other techniques we talked about is divide this in thirds and where the one-third part is that's roughly 63 or 66% that's two-thirds that's the time constant so total time divided before or breaking into 38 thirds and find out where it crosses at your time constant error on the side of being big and that's it induces stability into the system so now we have the time constant of 12 and a half and the process gain of one point six seven then I fill in this chart well before I fill in the chart I kind of estimate what's the model of mismatch I said well it's not a pure gain or it's not a first order process but it's closed so right off the bat you shouldn't be thinking Tower ratio one but it's not too far off so start with the tower ratio three and see how that looks so in this case I fill in the chart tower h2 one through four notice my gains point six point three point two point in but my interval times the same we applied the tuning rule that we calculate I showed you earlier which comes from a mathematical proof or derivation then we do a bump test the validation step forget the validation step so we start with a towel ratio of three and a towel ratio of three what you can see is we change the setpoint and you know remember what our ratio three how big should this kick be as compared to the total 1/3 so you can see that that's 1/3 it's very stable but maybe it's a little on the slow side so let's try our ratio to towel ratio of two you can see the initial kicks 1/2 then the total that's not bad actually tyresö - so then we start at our ratio of 100 now people may say well that looks really good I said yeah but it's not doing what I asked it to do and so why is there an overshoot look at the valve it it had my proportional kick was boom so if you noticed the original step and the final step is the same but it did all this gyration where that gyration come from remember model mismatch it came from I hate to do this but this area right here this if you look at this shape this model mismatch take a picture that in your head and then go over here it's the same thing the model mismatch shows up in valve searching for the process that's bad that's the that's unstable and so eventually it's going to break so for me what I would do is say well let's take a look at this at at our ratio of 3 it was very stable at our ratio to still look good tie ratio 1 I just crossed over where I I would feel comfortable with this loop so basically it's at our ratio of 1 the process is very repeatable but at our ratio one is just a little bit oscillatory not bad but at our ratio 2 there is no overshoot and it's how a ratio 3 is even even better so then that way you can make a decisions like well maybe take a 2 and a half and then you're done and you don't have to worry about it and then if someday in the future someone says hey that loops breaking then do another bump test make sure that the gain and the time costs are the same they probably aren't because that's what changes over time is the dynamics are what change based on a lot of different conditions and so you may have to update your tuning but then you would have a method to follow now what I like about direct synthesis tuning it's it's very stable it's based on the process and you get to pick the speed of the response that's what's exciting about direct synthesis is you pick the you say I'm going to assume all processes that are self-regulating are first order which means there's a process gain and a time constant I'm going to use the PI algorithm and I'm going to pick a towel ratio that will adjust the speed of the response you pick the speed of the response as a function of model mismatch and you can tune your loops now very quickly now I want to show you the Ziegler Nichols because that's one that's still presented in college it came out in the 40s and it was designed to have you know warships follow airplanes in the sky so at that time these big gun turrets were having a hard time shooting airplanes out of the sky and they came up with a way to a method to tune those so that they could track an airplane and when they see rode in on it if it's if it sent a spray of bullets it was more effective that was designed in the 40s then it was called the Ziegler Nichols that's the name of two guys that actually worked for Taylor instruments but which is now part of ABB so a long way we've had a long heritage of ABB work ABS had a long Harwich in automation and tuning solutions but it was developed in the 40s and it's designed to give a quarter wave decay but it still starts with the process now remember to that time period there was an electronic controllers there really wasn't even that much the pneumatic controllers were just getting started I've seen some of those controllers there was knobs there weren't numbers like we have today so the idea of tuning by field you really could feel when you got it right that was the idea and it's still taught in schools today there's a couple different steps and that they've modified and it's called the ultimate gain method where you set the integral to zero you cause a disturbance well here's the picture and you start adjusting the gain until you get a sustainable oscillation once you've got so when I've tried to do this I pick again a set point if it's if it's starting to attenuate I know that it's I don't have the right gain or I don't have the ultimate game then what I do is I increase the gain in scoops I went this is going unstable so then I know I've got the gain somewhere between there and I can then figure out how to make a sustained oscillation once you have the gain that produces a sustained oscillation then you plug in your ultimate gain if you're using a peony controller you do this if you're using a PI controller you do this if you're using a PID and what this will do is it'll give you that quarter wave decay where the it'll it'll oscillate again the questions that come up from your operators will be well how much of an oscillation will I get well I don't know it depends well how long will the oscillation take well I don't know how much will the output move you're like well I don't know and unfortunately that may be the last bump test you get to do so we don't that's a hard one to do in industry today but there's been techniques where they do clipping circuits until you get a square wave and then there's this one called the point of inflection where you actually do a bump test and then you try to figure out where is the point that the slope goes from going up to a slope going down that's the point of inflection you draw a line through there and you calculate the slope and you calculate the delay and then that goes into here this equation but they're all designed to give you a quarter wave decay some industries that are slow-moving or I will say that when you're doing a tracking tracking error where you're trying to track a set point is moving this does produce the smallest what they call velocity air you can keep up with it it's just when you stop it's going to ring that's the drawback direct synthesis it's more designed the way industrial plants operate you know set points your you know so it's more stable you do one bump test you you look at the physics and you can calculate the tuning parameters so my bias is towards the direct synthesis technique but my point here when we're wrapping up is tuning isn't just throw in some numbers and see what happens I hope you're seeing that what we're doing is we started with the process and we're trying to match that process to the controller you do a bump test you calculate the model you use the tuning rules to come up with tuning and boom you have a very stable process to come up with loop tuning or tuning of your plant and what that will do is result in money for you you'll have less downtime you have less defects you'll have higher production higher quality and a more stable plant you know more stable plant means they can run faster run longer and have a better product at higher quality that's the trick loop performance and automation services for today make this a reality if you know what you're doing start with the process understand your controller link the two together and you hit a home run every time

Channel: ABB Process Automation

Views: 17,085

Keywords: Control Theory (Field Of Study), Control, Mind, single loop, control methods, kevin starr, ABB Ltd (Business Operation), abb service, process automation, loop performance, Remote, big data, cloud computing, machine learning, data scientist, white box, grey box, black box, non deterministic modeling, prescriptive maintenance, proactive

Id: m_LhFFfuKfo

Length: 32min 30sec (1950 seconds)

Published: Thu Dec 18 2014