A24: PID CONTROL  . . .



COROLLARY THEOREMS: "reality is never what it appears to be."


Up to this point we wrote Amazing Articles after Amazing Articles, though we are certain that most readers take them as just "extensions" of our SF books. That is not true, dear friends; our intention is to discuss in these articles about science, only. Sure, there are a few similarities to the SF literature, but that is only because very advanced science, or knowledge, will always appear to be Science Fiction (like).


GREEN LEAF LImagine that you go back in time 10 000 years ago, and you try to explain electricity to a group of fine Neanderthal gentlemen. Naturally, they will not believe you.

Regardless of your efforts, they will consider that a sharp, smart rock, or a sturdy, "scientifically"-spiked club are way more efficient in delivering fresh meat for their next meal.



In A20 we started presenting a few alternative options to the fossil oil produced energy, and we mentioned 2 particular situations in which routine takes over science. The first one was, cooling hot iron (Fe) in water may lead to horrible accidents, because Fe will separate/reduce the oxygen atom from the water molecule, and it will release hydrogen. This type of accidents happened before, and we noticed that people couldn't explain them: they have labeled those particular accidents as "unexplained".

The second one is a common, continuing firefighters' practice: using water to put out very strong fires will feed, in fact, the fire with hydrogen, because red-hot carbon is again capable of separating/reducing the oxygen atoms, therefore it will release hydrogen from the water vapors. Both instances are well known chemical reactions to (a few) chemists, but it seems that little or no corrective actions are taken. The best substances to put out difficult fires are dirt-dust, and sand.

We could present many particular instances of malpractice in the industry, and in our day to day life but . . . Fact is, the trend today is to hire people in management positions based on experience, therefore the result is only one: we continue repeating the mistakes of the past.

During the peak of intelligence (around 1974) in USA, it was a well known fact that it takes people with a large range of qualifications to work on a particular new design/technology/project. In other words, when designing an electrical product, or a software program for example, a complex team of professionals is needed, and their qualifications must be as diverse technically as possible. That practice was abandoned in time, though things do not work very well today.

Anyway, we intend to present one practical example of routine practice which complicates unnecessarily our engineering activity, and our social-life. Now, everybody is aware that most countries spend enormous amounts of money on military research technology. One of the toughest issue is the "interceptor missiles" which are supposed to destroy incoming enemy missiles. Many billion dollars were (and are) spent on perfecting the PID control routines needed for that technology to work properly. [Please discover on the Internet the history of the PATRIOT missiles project, and many similar ones.]

Now, what is this PID? PID stands for Proportional, Integral, Derivative closed-loop control systems, and all engineers know it very well because they work a lot with it. The PID control method is applied in almost all automatic control processes, and the theory behind it is no joke. In fact, a good PID control system is almost a military secret due to its complex implementation. However, the entire PID control technology is a mistake which people persist on repeating, because the psychological drive behind this control method is too strong to overcome.


Closed-Loop Control System

The above figure represents the main hardware modules of a closed-loop control system, and we are certain that all engineers are well familiar with it. The only place where some interesting action happens is in the PID/FUZZY Controller. To start, we shall discuss first the PID controller.

What people use to do is, they work with a formula in continuous-time domain inside the processor (or within the hardware electronic circuits) of the PID Controller—here it is: 

Continuous-time domain PID closed-loop control formula

CV = Kp*Er + Ki∫Erdt + Kd*(Er/dt)

In the above formula, in the right member, there are three terms, and each deals with one type of a control: proportional, integral, and derivative. Now, the formula is in a continuous-time domain, therefore we cannot work with it directly because the PID System has a cyclic, discrete-time mode of operation. For example, the PID system reads the Process Variable (PV), then it calculates a new Control Variable (CV) at discrete time intervals.

That is the first major complication, therefore people use to transform the continuous-time PID control formula into a discrete-time one, like this:

Discrete-time PID closed-loop control formula

CVn = CVn-1 + Kp*(Ern +Ern-1) + Kp*Ki*ΔT*Ern - (Kp*Kd/ΔT)*(PVn -2PVn-1 + PVn-2)

We should explain the terms in the above formula, though we are not going to do it. As always, the most important thing is the Global Picture, not the details. After transforming the continuous-time formula into a discrete-time one, people are able to obtain a practical value for the Control Variable (CVn).

Now, the discrete-time formula presented above is a particular case, despite the fact it has the most general format; note that there are many other implementations possible. In order to obtain the right discrete-time formula, people work with a few "transfer functions" named Laplace Transforms. The mathematical theory behind this process is well documented in many books having thousands of pages, and it is very difficult to master.

PID ControlAnyway, once we do come up with a decent discrete-time formula, similar to the one presented above, comes the second, practical, difficult problem: finding the right values for Kp, Ki, and Kd constants. It is such a difficult issue to discover the right constants for each specific implementation, that new books having other thousands of pages have been written specifically for that.

The most known method of "tuning" the PID constants is named Ziegler-Nicholas. However, working manually with that method is a true nightmare. Sure, we do have the option to spend a few more thousand (or million) dollars on purchasing a software program specially designed to discover the right constants for any specific application.

Now, suppose we have found the right constants, and we are able to start our automatic PID Control System. Despite all efforts, the PID System may not work correctly in all possible situations! Even worse, the accuracy of the control itself is fairly poor, therefore people have to spend more money and way more time to further "fine-tune" the PID system—it is a real pain!

As you can see, designing automatic systems to behave intelligently is not easy. The point to note is, all those troubles come when there is little intelligence behind the initial decision to implement a PID Control System. As mentioned, people are selected for managerial/design jobs based on experience. Their experience says: we have worked successfully with PID since the electronic control circuits were analog, therefore we cannot implement anything better.

Today all controls circuits are digital, therefore working with the continuous-time PID closed-loop control formula is just a worthless dinosaur from the forgotten past.


The plain and incredibly simple alternative is the Fuzzy Logic method of closed-loop automatic control. Its implementation is thousand to million times cheaper in value; hundred times less time-consuming to implement; and it is way more efficient than any PID control system because it is a digital method designed to work with digital systems.

Unfortunately, people do not understand the theory behind both methods, and we suspect it is the name of the last method that bothers that much: "FUZZY LOGIC"! Due to that improper naming used, people think the logic behind this particular control method is also fuzzy. No, Sir. In fact, the proper name for this method should be: Discrete-Time, Logic, Closed-Loop Control.

The second psychological aspect is, Fuzzy Logic is way too simple compared to thousands of pages describing the PID theory. People consider that the more complex the theory behind a practical application is, then it is bound to be better! Well, not so, dear friends.

FUZZY Logic ControlWe have designed and tested many control systems using Fuzzy Logic discrete-time closed-loop control systems, therefore we are able to confess: it takes 1 (one) programmer only a few work-days to implement and fine-tune Fuzzy Logic without any major efforts. Fact is, it is even fun to work with any Fuzzy-Logic application. Practical results depend, naturally, on the intelligence of the programmer, but we can assure everybody that Fuzzy-Logic is far more efficient from all points of view than PID is, and it allows for further fine-tuning beyond your wildest dreams. Think only of a Statistical Trend Routine (this is a learning algorithm): it takes only one day to implement it in firmware!

The theory behind Fuzzy Logic spans on maximum 1 (one) page, compared to tons of PID formulas, graphs, and tables. The way it works is this: in one processor loop PV is read, then CV is updated, based on the error (calculated as "Set Value/Point" minus PV), and a on simple table of data. That is all!

Now, the true beauty is: Fuzzy Logic works in all situations, it is way more efficient than PID, and it is incredibly cheap. The possibilities of fine-tuning Fuzzy Logic method of closed-loop control systems are simply limitless, and we have total control over it! The control table we have mentioned could be very simple, or quite complex, depending on the accuracy needed—note that this is a relative complexity, because Fuzzy Logic will forever be thousand times less complex to implement than any PID. Now, because we do have total control over Fuzzy Logic, we can even change the control table at run-time, the way it pleases us most!

Methods like Fuzzy Logic require a certain amount of customization for each application, plus a good logic method of implementation. Although it contains no control algorithms, we do encourage the readers to study LEARN HARDWARE FIRMWARE AND SOFTWARE DESIGN because it is an excellent example of a logic design. In addition, you can discover in our book many simple alternatives, similar to the Fuzzy Logic method presented here.


We shall continue referring to this topic in future Amazing Articles because the social-psychology implications described here are very important. Even more, we feel tempted to present you a second practical example in one of the following Amazing Article . . . Who knows, it may help.


First published on August 02, 2005
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