PID Controller Explained

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⌚Timestamps:
00:00 - Intro
00:49 - Examples
02:21 - PID Controller
03:28 - PLC vs. stand-alone PID controller
03:59 - PID controller parameters
05:29 - Controller tuning
06:20 - Controller tuning methods
=============================
In this video, we’re going to talk about the PID Controller and its transformation from a single station device to what it has evolved into today. We’re going to explain why PID Controllers are used in industrial processes.
We’ll illustrate how Controller settings affect different processes under control. We’ll also provide an overview of Controller Tuning.
Let’s start with a discussion about home temperature control.
If the room temperature is below the setpoint, the furnace is turned ON. When the room temperature increases above the setpoint, the furnace turns OFF.
This type of control is referred to as ON/OFF or Bang-Bang Control. The temperature is not exactly held at the setpoint of 70°F, but cycles above and below the setpoint.
ON/OFF control may be ok for your house, but it is not ok for industrial processes or motion control. Let’s look at an example of tank level control to explain why.
The Valve fills the tank as the pump drains it. If the valve is operated with ON/OFF control, the water will fluctuate around the 50% setpoint. For our purpose, let’s say the fluctuation is ±10%. In most industrial applications, this fluctuation around the setpoint is not acceptable.
What if it’s possible to throttle the valve and place it in any position between ON and OFF?
Let’s look at how a PID Controller fits into a feedback control loop. The Controller is responsible for ensuring that the Process remains as close to the desired value as possible regardless of various disruptions.
The controller compares the Transmitter Process Variable (PV) signal, and the Setpoint.
Let’s refer to the difference between the Process Variable and the Setpoint as the Error signal.
Based on that comparison, the controller produces an output signal to operate the Final Control Element. This PID Controller output is capable of operating the Final Control Element over its entire 100% range.
The PID controller determines how much and how quickly correction is applied by using varying amounts of Proportional, Integral, and Derivative action. Each block contributes a unique signal that is added together to create the controller output signal.
- The proportional block creates an output signal proportional to the magnitude of the Error Signal.
Unfortunately, the closer you get to the setpoint, the less it pushes. Eventually, the process just runs continuously close to the setpoint, but not quite there.
- The integral block creates an output proportional to the duration and magnitude of the Error Signal. The longer the error and the greater the amount, the larger the integral output.
As long as an Error exists, Integral action will continue.
- The derivative block creates an output signal proportional to the rate of change of the error signal. The faster the error changes, the larger the derivative output.
Derivative control looks ahead to see what the error will be in the future and contributes to the controller output accordingly. That brings us to a term called Controller Tuning.
There are many different manual methods for tuning a controller that involves observing the process response after inflicting controller setpoint changes.
One method involves increasing the amount of setpoint change and repeating the procedure until the process enters a state of steady-state oscillation.
Most process controllers, PLC, and DCS loop controllers sold today have Autotuning capability.
The PID controller learns how the process responds to a change in setpoint, and suggested PID settings.
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- What are PID Tuning Parameters? realpars.com/pid-tuning-param...
- PID Tuning | How to Tune a PID Controller realpars.com/pid-tuning
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#RealPars #PID #IndustrialAutomation

[@cordaxg6261]

Today i continued my education to become a Enviromental Operating technician (Water & Sewage) Today we started our course in Automation. Im a Swede with a pretty good grasp of the english language. I can tell you, these videos from a total beginners perspective, and not having english as a main/native language these videos were both easy to understand and grasp/follow. Great videos !

[@realpars]

That's amazing to hear! Thank you very much for sharing.

[@cordaxg6261]

@@realpars likewise ! Thank you

[@nyahhbinghi]

I love it when my furnace kicks in at 65º and then heats the house to 75º, that 10º fluctuation is so glorious.

[@johng5295]

Thanks in a million. Great content. Awesome. Very well explained. I couldn't find this explanation--simply put anywhere else. Great teachers are hard to find. Grade: A++💥

[@realpars]

Glad it was helpful! Thanks a lot for your positive feedback, John!

[@ricardogarcia3900]

What an educative and iteresting channel. Congrats again.

[@realpars]

Glad you enjoyed it, Ricardo! We appreciate your kind feedback.

[@arletacostagonzalez7364]

Very good explination. Concise and easy to understand. Thank you very much.

[@realpars]

Glad you liked it! Happy learning

[@MeltingRubberZ28]

Good video. I'm an ME so I don't have to work directly on PID loops, but work in automation so I'm around them often. Back in college when we programmed them in our circuits class they had us manually use a fan to cool a resistor to a specific temperature, and then a PID loop. The precision was night and day.

[@realpars]

Hi @MeltingRubberZ28. Sounds like your fan/resistor activity was interesting. Was the temperature controlled by modulating the fan speed?

[@MeltingRubberZ28]

@@realpars yes

[@keenheat3335]

my college did a similar thing, but it was controlling an inverted pendulum and trying to keep it straight up while inverted. If tuned properly and the error is not large enough saturate the control gain, it can keep an object at naturally unstable equilibrium really well. Although if you have a naturally stable system, then it's even better in case there was a failure in the pid system, at least there is some backup.

[@JB-ri6zp]

I'm an ME too. Do you enjoy automation? I really enjoy learning about electronics, programming, logic, and efficiency. I can spend hours reading and thinking about it. Maybe I should of done software or electrical haha

[@MeltingRubberZ28]

@@JB-ri6zp yeah. Job is rewarding and the pay is good.

[@eugenepohjola258]

Howdy. I like how RealPars focus on the essential in these tutorials. Digital controllers are usually described as summing of the P, I and D blocks. As in the clip. There are still lots of analog controllers in use. They are usually bulit using operational amplifiers. The description usually is the P, I and D in cascode or series. The math is different for summing and cascode. However. The derivative parameter Td usually is at most 1/10 of the integral parameter Ti. Usually Td is even way smaller than 1/10 of Ti. The math for both summing and cascode will be the same closely enough. Regards.

[@yungerallenelectricalcontr6415]

By Far the Best Explanation for PID's I have ever had the pleasure to Learn. This is a game changer for my foundation.

[@realpars]

You're very welcome! Glad to hear that our video courses have been so helpful to you!

[@atarperach9319]

Thank you very much! By far its the best explanation I have heard for PID controllers...

[@realpars]

Glad you liked it!

[@fifaham]

Very good refreshing - I took 6 courses in Control Systems in the University long years ago and I loved this subject a lot, I was A student in this subject doing it with Analog circuits but today I do it with microcontollers along with Analog + DigiPots and Digital Variable Capacitor along with keyboard and switches. This is amazing.

[@realpars]

Glad it was helpful! Thanks for your kind support, Firas!

[@WeconTechnology]

Very detailed video. Our Wecon PLC support PID tuning.

[@realpars]

Glad it helped!

[@tbengineering7066]

Thanks for the video. It really helps a lot. PID Controllers are such an important concept that can be very difficult to grasp at first. I'm going to recommend this video to some students at my alma mater. I think it will really help them understand what the Control Systems professors are talking about.

[@realpars]

Glad to hear that! Thank you very much for your kind support.

[@johnatansilveira53]

Thank you for your videos! I'm learning a lot from you. 🇧🇷

[@realpars]

Glad you like them!

[@ilhuihdez]

Great amazing content. It really facilitates understanding of the topic. Thank you thank you thank you.

[@realpars]

Glad to hear that! Happy learning

[@mortenlund1418]

Cool of you to go here. Thanks for the effort. Great video,

[@realpars]

Thank you, Morten!

[@eugeneleroux1842]

Thank you for a very informative presentation.

[@realpars]

Glad it was helpful!

[@akibsabri6104]

Fantastic video! Thank you

[@realpars]

Thank you very much!

[@MuhammadRaza-qc5nn]

Awesome content. Highly recommended

[@realpars]

Much appreciated!

[@IngDzib]

Amazing! Many thanks

[@realpars]

Our pleasure!

[@mahmoodahmedmughal]

very informative and conceptual video.

[@realpars]

Glad you liked it! Thank you for sharing.

[@adapterscapter285]

Well done

[@victorblanco234]

Great job!... Congratulations!

[@realpars]

Thank you so much!

[@radhamohandash5865]

Nice explanation. Thanks a lot 🙏

[@realpars]

Glad you liked it!

[@fahimahmadosmani3618]

Suppppper... Thanks a lot. Very clear and understandable

[@realpars]

You're very welcome! Happy learning

[@SEALTRONICS]

ReaLPara you are just too much, Love u guys, Keep the work

[@realpars]

Thank you!

[@1atera3]

Thank you really very useful video and you make thing very simple

[@realpars]

Glad it helped, you're very welcome!

[@KevinNguyen-tw5ml]

Thank you very much!

[@realpars]

Our pleasure! Happy learning

[@Surajkumar-pk5ux]

Very well explained.

[@realpars]

Glad you think so!

[@juanpanguinao6657]

@@realpars hola que tal, saludos desde Argentina, los cursos que hay en la página, ¿Son todos en idioma ingles? Hago la pregunta porque yo no se el idioma ingles hablo solamente el idioma español.

[@ramtelange1007]

Thanks sir you making my day Today actually I daily face PID setting...

[@realpars]

Glad to hear that! You're very welcome!

[@motazadil4395]

Thank you realpars engineer to help me to understand this thinks

[@realpars]

You're very welcome!

[@alantownsend5468]

Automotive guy here; when viewing ECU "live data" with a scan tool the term PID is used... I think I understand why now. Cool video!

[@realpars]

Thank you, Alan!

[@realpars]

Hi @Alan Townsend. Just out of curiosity, what piece of equipment is the ECU out of?

[@alantownsend5468]

Networked control units in light duty automotive; engine / powertrain, body, stability control, etc.

[@jamesacosta6090]

Nice little introduction! thumbs up!

[@realpars]

Thanks a lot, James! Happy learning

[@8ZER08]

Nice vídeo, will be great to show some others control techniques

[@realpars]

Thanks for the suggestion! Will happily pass this on to our course developers. Thanks for sharing and happy learning :)

[@aminokamad1681]

Awesome video sir 🔥🔥🔥

[@realpars]

Thank you, Amino!

[@samalfellah2066]

This Video answers alot of my questions, thanks but about your PLC material, I'm an Allen Bradley guy and would like to check your AB PLC course .

[@bhanukadayawansa5576]

Great Video

[@realpars]

Glad you enjoyed it!

[@Phemakorn]

Thank you so much.

[@realpars]

Our pleasure!

[@avactronic1853]

دس خوش ....... Excellent This is one of the most useful video that I've ever seen

[@realpars]

Glad you liked it!

[@chethankumar1541]

Supper sir tq❤

[@anacamilacuevasgonzalez2553]

Excellent video, I almost understood haha. This topic is very difficult aaaaaah maybe i'm just a poor high school student with no enough context of what's going on, but I liked the explanation very much.

[@realpars]

Glad to hear that our video helped out! Always feel free to leave us any questions if anything remains unclear. Happy learning!

[@melbourneopera]

Building service engineer may not need to know as deep as such.....but this video is good for beginner.

[@sakthiff1710]

Very helpful

[@realpars]

Glad to hear that!

[@turkiyem9465]

Thank you very much

[@realpars]

Our pleasure!

[@L2.Lagrange]

Really good video

[@realpars]

Glad you think so! Thank you for sharing

[@Neander104]

It's a good survey.

[@l.zwieble6819]

You made my brain click the whole thing like after 5 minutes..

[@SEALTRONICS]

Love u guys

[@novneetdhar7186]

Very useful

[@realpars]

Glad to hear that!

[@isakoqv]

Nice video, but I think it's a mistake to introduce the PID parameters without mentioning that there are different types of PID controllers. The model presented here is parallell PID, where each parameter is applied to the error separately. In the industry, another very common type instead defines a parameter called gain which is then applied to the proportional, integral and derivative parameters. The I and D parts of the PID are then usually called Integral Time and Derivative Time. If one applies the same values to these different models of PID or tries to tune it the same way as is presented here it could lead to a lot of problems.

[@realpars]

Hi @isakoqv. Thanks for your feedback and comments. It’s difficult to encapsulate PID details in a short KZbin video. Your comments about Gain, Integral Time, and Derivative Time are true and those terms are important. We hope to discuss those terms and more such as Reset Windup, MPR and RPM in later videos. Discussing and observing P, I, and D response to error is an interesting challenge because obviously in a dynamic environment, the error is always changing because of the controller response. As for tuning, there are lots of so-called tuning methods and as you say, not all are appropriate or advised as blanket methods for every application.

[@lexsoft3969]

@@realpars It was years ago when I learned Ziegler-Nichols method and Cohen-Coon for tuning a PID controller. Now, I forget all of them. I turned to become a programmer not related to Control System/Engineering. Only occasionally I want to relearn this interesting field.

[@sankaranbaskar6165]

@@realpars sir, is it possible to make pid controller with equation of heating and cooling.

[@jarnix2]

You're just a hater

[@isakoqv]

@@jarnix2 Huh?

[@lovrorb]

I'm using an PI controller in most cases, sometimes even P is good enough. I also use FFWD in combination

[@realpars]

Hello @Lovro Sipovac. Thanks for your input. In fact, when maintaining the process at an exact setpoint value is not critical, P-only controllers will do just fine. And, as you say PI controllers are is sufficient in most cases. Adding D to some loops can cause no end of troubles.

[@lovrorb]

@@realpars I benefited from adding a D in a very few cases when I wanted to "choke" the abrupt change, but yes, it's mostly a headache :) But adding a feed forward value is a fantastic measure if an approximate value is known. A good example would be tension control when spooling out VFD controlled winch (motors actually) when you have a good estimate of required holding torque and uncertanties are represented by inertia/friction in the complete driveline. For instance, you want to hold 10T on the winch while it spools out .... you calculate that in order to do so you need to hold 20% torque on motor(s) in ideal system (no friction etc.) ... then you just feed forward that value, or whatever you calculate for particular tension, tweak it so it works well on variable setpoint and voila! :)

[@montesdeocaf.2797]

Nice!

[@realpars]

Thank you!

[@neotheek]

Can you do a video on " how Exactly does data transfer happen in physical level in wires or fiber optic cable."So that even non tech savvy person can understand. How exactly is 1 bit transferred between two points like New York and London ,like by switching the Voltage for s bit the whole distance? Switching it for each bits? Smart ways? How? For 1 packet ? Update: sure get highly technical but start from simpler level and get into the depth slowly. And the reason I'm asking it here because I believe no other can explain it better than you.❤️

[@isakoqv]

Sort of an impossible question to answer without getting technical. There are lots of different protocols using different ways to encode signals on the "physical level". Electrical signals have properties like amplitude, frequency and phase. You can use any combination of these to encode signals. The protocol determines the meaning of a given change to a given property.

[@realpars]

Thanks for your feedback and suggestion! I will certainly share this with our course developers, hopefully we can focus on that in a future video courses. Thanks again for sharing and happy learning!

[@Build_the_Future]

I hope you guys into explaining the math or at the very lest the transfer function of the system in future videos.

[@YewrMan]

A good shout Eric. I managed to scrape through Control Systems online but found the formulae tough going. A good explain with practical examples would have helped a lot.

[@mortenlund1418]

@@YewrMan We had a teacher who really did not get it, to simplify this subject. Quite the opposite. Later we had a teacher who knew the formulas and told us. They are plain math. No fancy stuff, not even the integral part which is just the sum of something.

[@YewrMan]

@@mortenlund1418 Morten, is there any KZbin channels or elsewhere you can recommend that shows good practical explains of the mathematics of Control Systems. I think online study can be hit or miss depending on the lecturer. Some are brilliant and patient in explaining stuff and check that you understand and you learn the topic not just how to answer questions. But others just want to get through their online lecture quickly and at the end of the semester give you loads of hints to get you to pass the exam even though you barely understand the topics on it.

[@lexsoft3969]

It will need an introduction to Laplace transform for describing a PID controller to find the transfer function of the system.

[@realpars]

Thank you for sharing your feedback, Eric! I will certainly go ahead and pass this on to our course developers for future video courses. Thanks again, and happy learning!

[@panzznine713]

hi, ty for wonderful explaination about PID, can i ask for some pointers or suggestion on what type of water valves can i use for PID controll?

[@realpars]

Hi there, Thanks for reaching out. That's a tough question to answer. Can you provide more details please? Do you have power near the valve? Can it be electric? Will it be pneumatic? Is the water clean? What flow rate are you considering? Thanks!

[@panzznine713]

@@realpars gud day sir, ty for the time for giving a reply, i'm a student working on a thesis, im planning to apply PID control on adjusting water flow for aquaponics, inorder to do that i've done some checking on which component i'm going use and a "Motorized Valve" has a good potential in it, the project prototype is a small scale so im going to use a modified version of it "A Servo Motor + Ball Valve (for water)"

[@Pertamax7-HD]

Good remider for C

[@di9838]

If the output is a relay and the final element is a pump than the pump will be on and off multiple times and the inrush current will damage the electric motor in time.

[@realpars]

@D I. You are bang on. Lare motors are not made to be cycled on and off repeatedly.

[@tanphan91]

nice

[@vuuctien1663]

This is a good explanation video. May i know how to make video like this? I love the animations. i really want to learn how to make video like yours.

[@realpars]

Thanks for your kind compliment! I am actually not sure about that, as this is all done by our graphic and animation department.

[@uts786]

I need to control dc motor speed using PID, any guidance?

[@RAJIBLOCHANDAS]

Good

[@jazzjohn2]

If the step response of a system is known, can correct values of PID be calculated to achieve a desired response, or is tuning always required?

[@realpars]

Hi @john. Several manual tuning methods begin by observing the process variable dynamic response to a setpoint step response. This response is then used to determine PI and D settings if required. As mentioned in the video, manual or auto-tuning will result in preliminary PID values but more often than not, further tweaking is required.

[@jazzjohn2]

@@realpars yes, thank you. My question wasn't clear. Is there an analytical way to determine the exact feedback parameters if the transfer function of the "plant" is known?

[@realpars]

@@jazzjohn2 Hi @john. I've not done such an exercise personally but I have read that software such as Simulink and Mathlab is capable of assisting. Sorry I can't be of more help.

[@Quotenbrtchen]

@@jazzjohn2 Student of Electrical Energy Systems Engineering here. Yes, there are methods for analytically calculating controller gains based on the desired response and transfer function of the plant, for example full state feedback etc. You can learn more about this in classes about control systems and even here on KZbin. Unfortunately, I am a bit rusty with the exact methods but at least I can tell you that such methods exist.

[@jayrajsinh78]

Please make videos on MPC model predictive control.

[@realpars]

Thanks for your topic suggestion, I will happily share it with our content developers. Thanks again for sharing, and happy learning!

[@soumyajitdas1647]

I'm trying to control the temperature as a process variable, and the control element is heater. I'm using relay to control heater. Will I able to implement PID system in the current settings ? This project is being developed using Arduino. My current system is running using On/ Off control which is not accurate. Please help !

[@realpars]

Hi there. Thanks for reaching out. ON/OFF control of any heating loop will not produce anything acceptable. (Accept in our homes apparently). As for Arduino PID, there are oodles of very helpful online sources. If you do a search for "Arduino POD", I think you'll be pleased with the available help.

[@NU-tt8ox]

I think, that violet curve in graph at time 0:39 is wrong. It have bring near SP line, not go over line. Or not?

[@realpars]

Hi @101NU70. Thanks for your comment. We included those curves just to illustrate how different PID settings might affect the process variable. As we try to illustrate later in the video, desired PID response differs greatly from one process to another. A PID controller response for one process may be disastrous for another process.

[@khushinmakim8013]

Can anybody explain fuzzy PId which used in commercial temperature controller to avoid overshoot and reduce rise tine

[@nyahhbinghi]

probably incorporate other data points...tmk PID often is only self-referential, but smarter controllers can take in more data, and basically use non-linear control algorithms

[@khushinmakim8013]

If you see like, Shinko or Omega temperature controller there implementations are perfect. I also have developed PID controller but not like Shinko performance they use first auto tune which oscillate 2 cycles to find P,I,D,ARW(anti reset windup),and then control. They used Fuzzy PID I check many times, with graph and different setup. In this you get Error and rate of error as input with that Kp,Ki,Kd calculate with fuzzy interference and find control output to operate the heater. But in shinko device graph of the control always same minimum rise time and almost no overshoot . But in my case graph is not always the same. My question how to correct this algorithm? for this we donot need powerful MCU, 8-bit MCU is enough it is all about algorithm.

[@abulfazibrahimov1990]

👍

[@TrollMeister_]

5:00 As long as an error exists the integral action will continue”. That is not correctly stated. What he said is applicable to proportional control as well. So what is it that differentiates proportional control from integral control ? The correct statement is “As long as an error exists the integral output will continue TO INCREASE (over time).” With proportional control if the error hold steady, so does the controller output . But with integral control even if the error holds steady, the controller output will continue to increase.

[@realpars]

Hello @MyMusic. Thanks for reaching out. The problem with Proportional-Only control is that once the error become stable, there is no proportional action therefore no corrective action. This results in something called Offset. Adding Integral action will attempt to remove the offset. You are correct when you stated “As long as an error exists the integral output will continue TO INCREASE (over time). As this video was at an introductory level, we did not go into a great amount of detail. If you are interested, you can check out our free series on PID Control at: learn.realpars.com/courses/PID-Controller One of the videos in this free series is available on KZbin at: kzbin.info/www/bejne/e2ibYXWGhM9-ra8 Thanks again for your comments and feedback! It’s always great to hear from our viewers!

[@onel276]

Which software is use for animation ??

[@realpars]

Thanks for your comment! I am actually not sure about this, as this is done by our animation and graphic department.

[@richmond4884]

👍👍👍👍👍

[@amarskills1299]

How to make this video. What software has been used?

[@realpars]

Thank you, Amar! I am actually not sure, as the animations are created by our graphic and animation department.

[@amarskills1299]

@@realpars Thanks. I like your tutorial. Follow everything. And i enroll your paid Course. 🥰

[@singleaspringle6941]

I don't understand one part of the process. How does the PID output control the working element. The output from PID is basically a sum of three different error perspectives. The larger the error, the longer it exists and the more it fluctuates, the bigger the output from PID is. But how does it affect the working element. Let's say we have a valve that controls water flow. How do we convert the PID output (a value) to the signal that controls the valve?

[@realpars]

Hi @singleaspringle. Thanks for your question. Please excuse me if I have misunderstood your question ...... but here goes my answer. The controller output is a variable 4 to 20 mA signal which corresponds to 0 to 100% of the controller output range. The control valve is a pneumatic device operated over its entire 0 to 100% stroke by an air signal of 3 to 15 psi. The instrument that converts current to pneumatics is called an I/P converter. In a nutshell, when the controller output is at 4ma, the valve gets 3 psi and the valve is either fully closed or fully open. (Depending upon the system design). So, we can stroke the valve from 0% to 100% by changing the current output of the controller. I hope that helps?

[@singleaspringle6941]

@@realpars so the way to control the device with PID output is dependant on the specific system we are implementing PID to? For different devices the converting needs to be done differently?

[@realpars]

@@singleaspringle6941 We're not actually "controlling" a device. We "operate" a device that acts on the process. We are controlling a process. We manipulate the process with some type of final actuator that is operated by the controller.

[@derrajinordean8134]

@@realpars excellente response

[@owlboom6458]

@@realpars This is called Executive Unit

[@juanm8582]

Lots of know-it-all frogmen in this comment section...Thank you realPars, for this very informative and introductory video to PIDs.

[@realpars]

Glad you enjoyed it! You're very welcome

[@lexsoft3969]

I only know from the classic book by Katsuhiko Ogata without seeing real physical instrument used in industry.

[@medikondasreebalaji6051]

Can you please tell the book name

[@lexsoft3969]

@@medikondasreebalaji6051 Modern Control Engineering

[@medikondasreebalaji6051]

Thank you

[@lexsoft3969]

@@medikondasreebalaji6051 It's a pleasure. Hope you enjoy reading that classic book.

[@masbawang7361]

PID vs fuzzy logic controller

[@gustavoaquino7273]

The proportional control is wrong, You can't have an output bigger than the set point only with a proportional. When the Kp tends to infinity the stationary error tends to zero, but It is only theory, in practice when the Kp is very big, the output oscilate.

[@realpars]

Hello @Gustavo Aquino. Thanks for reaching out........ About your fist point, check out our reply to Mihai Dinca 2 months ago where we explained that on rare occasions, graphics that are in an original storyboard don't get translated as they should. As per your second point, we agree totally. Increasing the Gain will certainly get you closer to the septpoint, but if you set it too high, the output will oscillate.

[@fanman421]

@@realpars Well said. And if you want to get into a real world oscillation issue, try setting a PID when there is a lag of a couple of hours between process input and process variable response. 😳 The Temperature of the glass in the out-feed of a glass furnace against the fuel supply to the furnace itself. 😉

[@stinkymccheese8010]

Why not use an analog system instead of a digital system?

[@realpars]

Hi @Stinky McCheese. sorry, but I'm not sure what digital system you are referring to?

[@mihaidinca9670]

The graph PV vs. time at 4:36 is completely wrong. With proportional term only, the PV steady value can not be larger than PV. Read again the classical textbooks or run more carefully the simulators!

[@realpars]

Hello Mihai Dinca. You have a fine eye for detail. We're assuming you are referring to SP and PV. We thank you for pointing out this graphical faux pas. On rare occasions, graphics that are in an original storyboard don't get translated as they should. We look forward to hearing from you again in the future.

[@intheshell35ify]

AI content. The machines lie.

[@samimecaniqetelectrique5712]

Thank you very much

[@realpars]

You are very welcome!