COROLLARY THEOREMS - AMAZING ARTICLES A24: The Perplexing PID Control Inertia

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A24: The Perplexing PID Control Inertia

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COROLLARY THEOREMS: Mathematics is built on two basic operations only

A24: The Perplexing PID Control Inertia

Up to this point we wrote articles after articles, and we am certain most readers take them as just some extensions of our SF books. That is not true. Our intention is to discuss in these articles about pure science, only. Sure, there are few similarities to the SF literature, but that is only because very advanced science or knowledge will always appear to be pure Science Fiction.

Imagine you go back in time 10000 years ago, and you try to explain to a group of Neanderthal gentlemen electricity. Of course, they will not believe you, and they will consider that a sharp, smart rock, or a sturdy, well-spiked club are way more efficient in delivering fresh meat for their next meal.

In A20 we started presenting few alternative options for energy, and we mentioned 2 particular situations in which the "routine" takes over science. The first one was, cooling hot iron (Fe) in water may lead to terrible accidents, because Fe will take the oxygen atom from the water molecule, and it will release hydrogen. That 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, in fact, feed the fire with hydrogen, because red-hot carbon is again capable of isolating the oxygen atoms and to release hydrogen from water vapors. Both cases are well known chemical reactions to (few) chemists, but it looks that no, or little, corrective actions are taken. The best substances to put up 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: the result is, we continue repeating mistakes of the past. During the peak of intelligence (around 1974) in USA, it was well known there are needed people with a large range of qualifications to work on a particular new design. In other words, when designing an electrical product, or a regulatory procedure 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, and things do not work very well today.

Anyway, we intend to present few practical examples of routine practice, which complicate unnecessarily very simple "things" in our engineering activity, and in our life. Now, everybody is aware that most countries spend enormous amounts of money on military research. 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 data on the Internet about the PATRIOT missiles, and many others.)

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 importance. However, the entire PID control is a mistake which people persist on repeating it, because psychological fundament behind this control method it is too strong to overcome.

The PID Control System:
PID Control System

The above figure represents the PID control system, and we are certain that all engineers are well familiar with it. The only place where some interesting action happens is the PID Controller. What people use to do is, they work with a formula in continuous-time domain, inside the processor, or the electronic circuits of the PID Controller--here it is:

Continuous-time PID control formula:

CV = K_p*Er + K_i∫Erdt + K_d*(Er/dt)

In the above formula, in the right member, there are three terms, and each deals with one type of control: proportional, integral, and derivative. Now, the formula is in continuous-time domain, and we cannot work with it directly, because the PID System has a cyclic, or a discrete 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 complication, and people use to transform continuous-time PID control formula, into a discrete-time one, like this:

Discrete-time PID control formula:

CV_n = CV_n-1 + K_p*(Er_n +Er_n-1) + K_p*K_i*ΔT*Er_n - (K_p*K_d/ΔT)*(PV_n -2PV_n-1 + PV_n-2)

We should explain the terms in the above formula, but we are not going to do it. As always, the important thing is Global Picture, not details. After transforming continuous-time formula into discrete-time, people are able to obtain a practical value for the Control Variable (CV_n). The discrete-time formula presented above is a particular case, despite the fact it has the most general format; however, there are many other implementations possible. In order to obtain the right discrete-time formula, people work with 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.

Anyway, once we do come up with a decent discrete-time formula, similar to the one presented above, comes the true, practical, difficult problem: finding the right values for K_p, K_i, and K_d constants. It is such a tough 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 it is a true nightmare. Sure, we do have the option to spend few more thousand (or million) dollars, and buy a software program specially designed to discover the right constants for any specific application.

Suppose we have found the right constants, and we are able to start our automatic PID Control System. Despite all efforts, the PID System will not work in all possible situations! Even worse, the accuracy of the control itself is fairly poor, and 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 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 electronic control circuits were analog, and we cannot implement anything better. Today all controls are digital, therefore working with continuous-time PID control formula is just a dinosaur of the forgotten past.

The plain and incredibly simple alternative is the Fuzzy Logic method of automatic control. The 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 of that control method is also fuzzy. No! In fact, the proper name for that method should be: Discrete-Time Logic Control. The second psychological aspect is, Fuzzy Logic is way too simple when compared to thousands of pages describing PID theory: people consider that the more theory is supporting a method, it is "bound" to be better! Not so, dear friends.

We have designed and tested many control systems using Fuzzy Logic Discrete-Time Control, therefore we are able to confess: it takes 1 (one) programmer only few days to implement and fine-tune Fuzzy Logic without major efforts. The result depends, of course, on the intelligence of the programmer, but we can assure everybody it is more efficient from all points of view than PID, 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 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 and CV is updated, based on "error" and a on simple table of data. That is all! The true beauty is, it works in all situations; it is way more efficient than PID; and it is incredibly cheap. The possibilities of fine-tuning the Fuzzy Logic method of automated control systems are simply limitless, and we have total control over it. The control table we mentioned could be very simple, or quite complex, depending on the accuracy needed--this is relative complexity, because Fuzzy Logic will forever be thousand times less complex to implement than 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, and 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 logic design. In addition, you will discover there many simple alternatives, similar to the Fuzzy Logic method presented here.

We will continue referring to this topic in future articles, because psychological implications described here are great. Even more, we feel tempted to present a second practical example in next article ... Who knows; it could help.

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LINKS TO OTHER PAGES

1. LEARN HARDWARE FIRMWARE AND SOFTWARE DESIGN - the easy way!
2. LOGICALLY STRUCTURED ENGLISH GRAMMAR - a must have.

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