Otto Mayr on Feedback Systems, definitions & origins
Inc. Hellenistic innovation 3rd century BC: Ktesibios invented the first feedback device
Otto Mayr wrote:
Chapter 1
Introduction
… The concept of feedback is abstract; it is not tied to any particular physical medium. In technology it can be used in mechanical, pneumatic, hydraulic, or electrical systems alike. But its main significance today is that it can also be applied profitably in economics, sociology, or biology: The mathematical methods of control dynamics are equally valid in all of these fields. The importance of the concept of feedback is illustrated by the fact that it gave cybernetics its name. When in 1947 Norbert Wiener christened the newly founded discipline (he had not known that in 1834 A.M. Ampere had proposed cybernétiqne as a term for the science of government), he made use of the Greek word for steersman [omitted]. He had come upon this through the etymology of the word governor (English to govern — Latin gubernare — Greek [omitted]), the familiar term for the first popular feedback device.
The Definition of Feedback
The purpose of this section is, first, to explain the concept of feedback in terms of an example, verbally and in the language of block diagrams; second, to introduce a few technical terms used in control engineering; and finally, to derive an exact definition of feedback. It addresses itself mainly to readers unfamiliar with control engineering.
An Example: James Watt's Centrifugal Governor
Figures 1 and 2 show the steam-engine governor in its earliest form … Its purpose is to maintain the speed of rotation of the engine (the controlled variable) at a constant predetermined value (command signal) in spite of any changes in load and steam pressure (disturbances). It accomplishes this by sensing the actual speed and adjusting the steam inlet valve of the engine accordingly. The speed of rotation is measured by a pair of centrifugal pendulums. Connected with the flywheel by ropes and pulleys, and rotating at engine speed, they swing outward with increasing speed under the influence of centrifugal force. A linkage in the form of lazy tongs transmits this motion to a sleeve which slides up or down along the axis of rotation of the governor. An arrange¬ ment of levers connects the sleeve with the steam valve in such a manner that the flow of steam is throttled with increasing speed.
If the load upon the running engine is suddenly increased, its speed will decrease. The flyweights will swing back, and the sleeve will slide upward, causing the steam valve to open. The increase in the flow rate of steam, and hence in torque, will accelerate the engine. The centrifugal weights will fly outward again, reducing the aperture of the valve. Ultimately, the engine will reach an equilibrium at a new speed that lies somewhat below the equilibrium speed prior to the load increase. This offset due to lasting disturbances or changes in the command signal is a characteristic of all proportional control systems. The increased load requires an increased flow of steam which can be provided only by a changed position of the flyweights. The desired running speed can be preset by the operator. The command signal is represented by the length of the vertical link on the right of Fig. 2, which connects the large horizontal lever with the small lever on the valve. It could easily be made adjustable by some appropriate device, as for example a turnbuckle. …
Criteria for the Identification of Feedback Control Systems
In 1951 the American Institute of Electrical Engineers published a set of “Proposed Symbols and Terms for Feedback Control Systems” which has since been widely accepted by American engineers. It offers this definition: “A Feedback Control System is a control system which tends to maintain a prescribed relationship of one system variable to another by comparing functions of these variables and using the difference as a means of control.”
The corresponding definition published by the British Standard Institution in 1967 is similar. It defines the term closed-loop control system as: “a control system possessing monitoring feedback, the deviation signal formed as a result of this feedback being used to control the action of a final control element in such a way as to tend to reduce the deviation to zero.” It further specifies feedback as “the transmission of a signal from a later to an earlier stage”, and monitoring feedback as “the feedback of a signal representing the controlled condition along a separate path provided for that purpose, for comparison with a signal representing the command signal to form a signal representing the deviation”.
For purposes of the present study, it is essential to define the concept feedback, the history of which we are investigating, as rigorously as possible. In order to obtain an instrument with which we can irrefutably identify feedback control systems, we shall summarize their various characteristics in the following criteria. (We will here consider only automatic feedback systems, in contrast to manual closed-loop control where the functions of comparison and control action are fulfilled by a human operator. Manual feedback control can be recognized in many timeless human activities, but these are not within the scope of the present study.)
1. The purpose of a feedback system is to maintain a prescribed relationship of one system variable to another. The system has the task of automatically maintaining some given variable equal to a desired value in spite of external disturbances. In short, its purpose is to carry out a command automatically.
2. This is done by comparing functions of these variables (i.e., command and controlled variable) and using the difference as a means of control In the words of Norbert Wiener, “feedback is a method of controlling a system by reinserting into it the results of its past performance”. For the purpose of comparison, a function of the controlled variable — the feedback signal — is transmitted from the output side of the system back to the input side. The cause-and-effect chain which constitutes the system is thus closed, forming the characteristic “closed loop”. To say that the control is based on the difference between command and controlled variable implies that a subtraction takes place. Once a signal travels around the loop, its sign must be reversed (the system has negative feedback). This requirement is essential. A closed loop without the reversal of sign would be unstable; it would be a “vicious circle”.
3. The criteria obtained so far are necessary to identify feedback systems but they do not suffice. Numerous systems exist where input and output are maintained in a “prescribed relationship”, and where, either by physical reasoning or by mathematical formalism, a closed loop with negative feedback can be identified. Examples are analog computer programs for differential equations, or simple physical systems with self-regulation, such as the water level upstream of a weir, the R-C circuit, or the weather vane. Indeed, all systems in which the denominator of the transfer function consists of a polynomial containing an absolute member can be represented formally, by means of block diagram algebra, as closed loops with negative feedback. To eliminate systems of this sort we shall consider therefore as genuine feedback control systems only arrangements where the comparator, the feedback path, and the sensing element, or at least one of these, can be recognized as physically distinct elements.
The three criteria we have now obtained contain a sufficiently complete definition of the concept. Briefly repeated, they are:
The purpose of a feedback control system is to carry out commands; the system maintains the controlled variable equal to the command signal in spite of external disturbances.
The system operates as a closed loop with negative feedback.
The system includes a sensing element and a comparator, at least one of which can be distinguished as a physically separate element.
Chapter 2
Feedback Control in Hellenistic Technology
… We usually associate the culmination of ancient technology during the Hellenistic period with the names of the three mechanicians Ktesibios, Philon, and Heron. Among their works, we find the earliest feedback devices known, and it can be shown that the tradition of these inventions survived until the Arabic Middle Ages.
1. Ktesibios
Ktesibios lived in Alexandria, had originally been — according to Vitruvius — a barber, and served as a mechanician under the Ptolemies, more specifically probably under King Ptolemy II Philadelphus (285 to 247 B.C.). He is thus presumed to have lived in the first half of the third century B.C. … Ktesibios’ own writings … have not survived. We know of him only through seven ancient secondary sources, the most informative of which is Vitruvius’ De architectura. In ancient times Ktesibios had been famous. Vitruvius ranked him as an equal to Archimedes. He is credited with having invented the force pump, the water organ, several catapults, and the water clock. Vitruvius’ account of the Ktesibian water clocks contains a passage (9:8:4-7), unfortunately vague, which is a description of the earliest feedback device on record (Fig. 5), at least according to Diels’ interpretation. As this interpretation has been contested by some notable scholars, it will have to be examined in some detail, along with the alternatives proposed. The text of the passage reads as follows:
[Latin version omitted]
First he made an opening of pure gold or of a pierced gem; for these materials are not worn down by the flow of water, nor do they collect dirt whereby they might be obstructed. The water, then, flowing in evenly through the opening, raises up an inverted bowl [a float] known to the artisans by the term “cork,” or “drum.” Mounted on it is a rule and also a disk that can rotate. Both are equipped with equal teeth which, engaged into each other, carry out corresponding rotations and motions. Similarly, other rods and drums, toothed in the same manner and kept in rotation by one moving force, produce effects and varieties of motions, moving pup¬ pets, rotating signposts, letting pebbles or eggs drop, sounding trumpets, and other by-works. Among these also, the hours are marked on a column or pillar, indicated during the whole day by a figurine with a wand, which rises up from the lowest point. Adding or removing wedges for individual days or months takes care of the increases or decreases in the hours’ length. Valves to regulate the flow of water are constructed thus: Two cones are made, one solid, one hollow, finished on a lathe in such a way that one can enter and fit into the other and that by the same principle, their loosening or tightening will produce either a strong or a weak current of water flowing into the vessel. Based on such reasoning and mechanisms, arrangements of water clocks are devised for the use in winter. If it should happen, however, that by adding or removing wedges the increases or decreases in the days’ length are not accurately indicated by introducing or removing wedges, because these wedges often cause trouble, then one must proceed as follows: . . .
Insofar as this [preceding] text is clear, it presents the following picture of a water clock: Water trickles through a carefully made orifice into a measuring vessel, where the water level rises slowly. With it rises a float, which — via linkages and gears-sets into motion a variety of time-indicating mechanisms. Two points, however, remain obscure. The length of the hours (the “temporary hour” used in antiquity was one twelfth of the interval between sunrise and sundown) is claimed to be adjustable for the time of year by “adding or removing of wedges.” Nothing is said, however, about the nature and the location of these wedges. Presumably they were inserted into the orifice itself, restricting the flow of water. As this method admittedly caused difficulties (“quod cunei saepissime vitia faciunt”), an adjustable scale was adopted instead and was calibrated for the different seasons of the year (9:8:7).
The second question concerns the arrangement for supplying the clock with water. If it had consisted of nothing but a simple supply vessel installed upstream of the metering orifice, filled at the start, and then issuing into the clock, then the decrease in the rate of flow caused by the sinking water level would have caused intolerable errors. It was crucial, therefore, that the water should trickle into the measuring vessel at a constant rate. The words aequaliter. . . influens aqua — “the water... flowing in evenly” (9:8:5) prove that Vitruvius and Ktesibios were aware of this necessity. How was the supply vessel constructed that fed the clock with water at a constant rate of flow? The answer obviously lies in the sentences beginning with Praeclusiones aquamm ad temperandum.. .— “valves to regulate the flow of water..” (9:8:6), but they are obscure and have been interpreted in different ways. The wording of the text alone is simply not sufficient for an indisputable reconstruction. We are dealing with a complicated apparatus described inadequately by Vitruvius for lack of either thoroughness or comprehension. Rehm had “.. the impression that [Vitruvius] compiled from literary sources with but little understanding”. In Vitruvius’ defense it must be added, however, that clocks are quite far removed from his main topic, architecture.
Rehm suggested the following interpretation for this passage: the word regula is taken to mean a valve rod equipped with a thread. By means of this threaded rod the solid cone can be screwed into the hollow cone, thus forming a finely adjustable metering valve. This valve is installed at the outlet of the feed vessel, issuing into a third vessel with overflow, placed between the feed vessel and the measuring vessel. The flow through the metering valve is adjusted by attendants in such a manner that the overflow vessel will always be full. The current into the measuring vessel of the clock is thus assured of a constant head.
The following objections against this interpretation come to mind: Apart from the fact that it is rather farfetched to translate regula with “threaded valve rod” (Rehm had used this term not explicitly but only in paraphrase), there is no evidence that such valves were used in antiquity. Nothing in the text refers to an additional overflow vessel, even though Vitruvius would have had no difficulty understanding and describing it. Finally, a clock whose accuracy depended on human attendants would be an invention of questionable value for which Ktesibios would hardly have cared to take credit. Man is singularly unsuited to monotonous tasks requiring long-sustained concentration. Such a clock could never have been more reliable than its attendants.
The hypothesis of the overflow vessel is also supported by Drachmann, who is of the opinion that the wedges were used to adjust the distance between cone and valve seat in order to change the length of the hour; the details of construction or the technical merits of such an arrangement are not discussed.
Water clocks based on overflow vessels have undoubtedly been used in antiquity. They were advantageous when an abundant water supply was available at all times. But to supply a water clock based on overflow from a stationary reservoir would have required a reservoir of disproportionately large size compared with the clock itself. The result would have been an unwieldy arrangement requiring not only much room but also a great deal of attendance. The text gives no support to the hypothetical overflow vessel. Furthermore, this interpretation assigns to the wedges and cones a role which is improbable both from the point of view of the actual text and from that of practical mechanics.
The most convincing reconstruction is advanced by Hermann Diels. He recognizes in the solid cone (meta solida) a float, swimming in a regulating vessel upstream of the metering orifice, projecting into the conical valve opening which is connected to the water supply, and throttling the inflow of water with rising level (see Fig. 5: G float, E metering orifice, BCDE regulating vessel, A water supply). The solid cone is at once float and valve plug, while the hollow cone (meta cava) is the valve seat. With sinking level the valve is opened, water flows in, letting the level rise again. The arrangement achieves a constant level in the regulating vessel and hence a constant flow through the metering orifice.
This interpretation is based on the reading of some Arabic texts on water clocks that have made use of the float valve and that profess to be based on ancient sources. Diels’ reconstruction in no wise [sic?] contradicts the text, and it alone makes otherwise obscure words technologically meaningful. The only philological objection against it is that Vitruvius did not refer to the valve cone expressly as a float. The first sentence of 9:8:5 shows, however, that Vitruvius knew of no specific term for “float”; he used various paraphrases instead. The remaining objections by Rehm and Drachmann, both classic philologists, are nonphilological in character.
Rehm points out that on the Arabic clocks the float valve regulator is employed to control the outflow, and not, as on the clock of Ktesibios, the inflow. This he considers a difference of principle and therefore an argument against a historical connection, although in fact the two arrangements have not only the same purpose but also great physical resemblance …
… Drachmann’s objection that the purpose of the valve is to regulate not the level but the rate of flow overlooks the fact that the flow is regulated indirectly by the water level. He believes therefore that valve and wedges belong together in some unspecified way. As further evidence against Diels’ reconstruction, Drachmann points out that Heron of Alexandria, Ktesibios’ heir, was not aware of float valves of this type. Actually, Heron’s float valve of Pneumatica 1:20 is equivalent in principle to that of Ktesibios; they have identical block diagrams. Dissimilarities in outward appearance are due to differences in application and to accidents in the transmission of the manuscript figures.
The remaining question is whether the float valve of Ktesibios is a feedback device according to our criteria. The controlled variable of the system, the water level in the small regulating vessel BCDE, is sensed by float G whose tip is a valve that opens when the level falls and closes as it rises. The command, i.e., the desired water level, is represented by the height of the float, i.e., by the distance between water level and tip. A block diagram [omitted] of the system shows a closed loop.
The only outside disturbance is the pressure in the water supply. The float valve fulfills a dual function: As a float it serves to sense the output, while its upper part in the role of a valve cone performs the control action. The functions of sensing and corrective action are separated, although only indistinctly. Satisfying the criteria established earlier, the float valve of Ktesibios may therefore be regarded as the oldest known feedback device.
In the eyes of his immediate posterity Ktesibios was the outstanding inventor of his era. His intellectual environment was unique. His native city, Alexandria, was the scene of unprecedented scientific achievements that made it the center of the scholarly world. Among his fellow citizens — and perhaps his friends — were men like Aristarchos, Euclid, Archimedes, and Eratosthenes. With such few facts known about Ktesibios, he may well be considered the inventor of the first feedback device.
The Source:
Otto Mayr, The Origins of Feedback Control, The M.I.T. Press 1970
[Originally published by R. Oldenbourg Verlag, Munich and Vienna, under the title “Zur Friihgeschichte der Technischen Regelungen” 1969 by R. Oldenbourg, Munchen, English translation 1970 for MIT by the author Otto Mayr.]
Evolutions of social order from the earliest humans to the present day and future machine age.