How does Maxwell, the unified electromagnetics, affect the development of systems science?

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How does Maxwell, the unified electromagnetics, affect the development of systems science?

The title is James Clark Maxway (James Clerk Maxwell,1831~1879, British physicist and mathematician. The founder of classical electrodynamics and one of the founders of statistical physics.

The main reason Maxwell is familiar is his contribution to electromagnetics. In fact, as a physicist, Maxwell's research on system control has lasted for many years, and his early exploration of controllers has deeply influenced Weiner et al.

In charge of the helm: Maxway

This year (2019) November 5th is the 140th anniversary of the death of Maxwell.

James Clark Maxway (James Clerk Maxwell), was born in Edinburgh, Scotland, on June 13, 1831. He is a great mathematical physicist, the founder of classical electrodynamics and one of the founders of statistical physics. His most representative contribution is to establish "field theory", to unify electricity, magnetism and light into electromagnetic field theory, and to establish a mathematical model called Maxwell differential equations today, and predict the existence of electromagnetic waves.

Figure 1 Maxwell, a great mathematical physicist, is the founder of classical electrodynamics and one of the founders of statistical physics.

Einstein's study is said to contain portraits of three people: Newton, Faraday and Maxway. In fact, Einstein wrote in his 1931 collection commemorating the 100th anniversary of Maxwell's birth: "since Newton laid the foundation of theoretical physics, The greatest change in the axiomatic foundation of physics was caused by Faraday and Maxway's work on electromagnetic phenomena. " "this great change is always associated with the names of Faraday, Maxway and Hertz," he commented. And a large part of this change comes from Maxway. " This is enough to illustrate the brilliance of Maxway. Among the many scientific contributions of Maxway, we are particularly interested in his creative thinking and novel methods in control theory, feedback design and system stability.

In 1948, when Norbert Wiener (1894-1964) considered a new field, he remembered Maxwell: "We have decided to give a name to the entire field of control and communication, whether it involves machines or animals. Called Cybernetics, it comes from the Greek kubernetes, the helm. When choosing this term, we should go back to the first paper published by Clark Maxwell in 1868 to discuss the feedback mechanism, which is about Governor. And the term is derived from the Latin of kubernetes."

Weiner mentioned that Maxway's paper, entitled "on Governor" (On Governors), was published in Proceedings of the Royal Society,Vol.. 16, pp. 270 / 283, 1868. It is pointed out that: "A machine with governor can still move in a uniform way under the condition of disturbance, in which disturbance is the synthesis of the motion of many components."

These components can be roughly divided into four categories:

(1) the disturbance increases continuously;

(2) The disturbance is continuously attenuated;

(3) The disturbance oscillates in such a way that the amplitude continuously increases;

(4) The disturbance oscillates in such a manner that the amplitude is continuously reduced.

The first and third conditions above are incompatible with the stability of the motion; the second and fourth cases are compatible with good governors. This condition is mathematically equivalent to the negative of all real and complex roots of an equation. In this article, Maxwell adopted the linearization of nonlinear systems, introduced the concept of motion stability, and gave the criteria for the stability of low-order systems.

In 1876, the Russian scholar Ivan Alekseyevich Vyshnegradsky (1832 / 1895) gave a similar stability condition independently. Maxway explained in the above paper: "I have not yet been able to fully determine the conditions higher than the third-order equation, but I hope this research topic will attract the attention of mathematicians." By 1877, this higher order polynomial stability problem had a discriminant condition: Rawls (Edward John Routh, 1831 ≤ 1907) took part in a scientific competition called "dynamic Stability". The paper entitled "A Treatise on the Stability of a Given State of Motion" won the Adams Award (Adams Prize), which was established by Cambridge University in 1848 and presented by the School of Mathematics. He gave us the Rouse criterion we know today. Since then, the study of system stability has been developed rapidly.

a physicist who is passionate about system control

Why is Maxwell, a physicist, keen on studying system control? Although system control is also a physical category, this matter has to be discussed from the steam engine that the governor is servoing.

The world's first steam engine prototype can be traced back to the Aeolipile invented by the ancient Greek math physicist Hero of Alexandria in the first century AD. Of course, perhaps earlier, Vitruvius has mentioned a brass container with a small opening in De Architectura, which is steamed and then burned with fire. He calls it For "æolipylæ".

In any case, Hiro's (Pneumatics) describes in detail the structure and working principle of the steam ball, which is connected by a hollow sphere and a sealed pot containing water in two hollow tubes, when heated at the bottom of the pot to make the water boil. The steam in the pot enters the ball through the pipe, and finally the steam is ejected from both sides of the sphere to push the sphere to rotate. (see figure 2)

Figure 2 Hiro's steaming ball

The steam engine in the modern sense will not be born until the 17th century. In 1679, the French physicist Dennis Pappan (Denis Papin, 1647 / 1712) created the working model of the first steam engine, (Steam Digester). Later, three British engineers, Thomas Seville (Thomas Savery, 1650 / 1715) in 1698, Thomas Newcomen (Thomas Newcomen,1663-1729) in 1712 and James Watt (James von Breda Watt, 1736 / 1819) the early industrial steam engine was designed and improved in 1769.

Among them, Watt's great contribution was to improve the design of Christiaan Huygens (1629-1695) to create a more practical centrifugal governor (1788, see Figure 3), which greatly improved the efficiency of the steam engine. So it is quickly promoted. In 1807, American engineer Robert Fulton (1765-1815) successfully installed a steam engine for a long-distance steamer, but that was a story. Watt's centrifugal governors have been working very well, when about 75,000 centrifugal governors in the UK were used in industry. Later, the speed of the steam engine increased, and the governor frequently became unstable, so that it could not work and even caused the machine to be damaged, so that all the engineers racked their brains and could not do anything about it.

Mechanical application research often resorts to mathematicians and physicists in such difficult times. Maxwell’s participation is at the right time. Perhaps after years of research (we don't know), he published the famous paper "On Governors", which provides a rigorous and solid mathematical foundation for the improvement and use of Watt centrifugal governors.

Mathematical physicists who express the basic idea of proportional and integral controlle

At the time, Maxwell also expressed the basic idea of ​​the proportional and integral controllers we know today.

Fig. 3 Flyball centrifugal governor designed by watt

He describes in this article: "Most governors rely on the centrifugal force of a piece of machine attached to the shaft. As the speed increases, the centrifugal force increases, either increasing the pressure on the surface of the part, or the part Move away, thus acting as a brake or a valve.” He pointed out: “But if centrifugal force acts on the part rather than directly on the machine, then there is a design as long as the speed of movement is above a certain normal value. , it will continue to increase the resistance, and when the speed is lower than this value, it will reverse its effect, so that regardless of any change in drive or resistance (within the working range of the machine), this governor will guide the speed to The same standard value.” In this paper, he refers to the governor with proportional control as Moderator, and the governor with proportional and integral control is called Genuine governor.

Maxway's article analyzes three kinds of governors.

First, the distance between the centrifugal force component and the shaft remains unchanged, but its pressure on the friction surface varies with the speed.

Second, the centrifugal force member is free to move off-axis, but it is limited by a force such that the strength of the force varies with the position of the centrifugal member, so if the rotational speed has a normal value, the centrifugal force member is at each position. Are in balance.

Third, the liquid is pumped out and thrown off the sides of the rotating cup. The cup is connected by its axis by screws and springs. If the rotation of the shaft is before the cup, the cup is lowered while pumping more liquid. If this adjustment can be done perfectly, the cup will maintain its normal rotational speed within the appropriate driving range. Maxwell went on to say, "Under certain conditions, sudden disturbances in the machine will not pass through the differential system to affect the governor, or vice versa. When these conditions are met, the corresponding equation of motion is not only simple, but also The motion itself does not cause disturbances caused by the interaction of the machine with the governor."

For the first time, Maxwell's 1868 paper gave clear mathematical conditions for stability and pointed out how to design a governor to meet these conditions. In addition, although Maxwell's article does not use the word "Feedback", it is easy to see that his article runs through the feedback ideas and methods. In fact, the subject governor he studied was a typical feedback controller.

Math physicist working on celestial bodies

As a physicist, Maxway also works on the stability of celestial bodies, especially terrestrial rings (see figure 4).

Figure 4 Saturn Ring

Galileo was the first astronomer to see the rings of Saturn through a telescope, and Laplace was the first mathematician to study the stability of Saturn's rings. Laplace's conclusion is that if the rings are solid, they must consist of a large number of very small rings, and each ring rotates around Saturn at a specific rate.

Maxwell assumed that the Saturn ring was not solid, and studied the effect of dynamic disturbance on the cross-section of non-rigid small blocks on the ring. He found that in order to ensure the stability of the torus, the ring must have sufficient irregularities. "We can more confidently conclude that if these rings are solid and uniform, their movements will be unstable and they will be destroyed; but they are not destroyed, and their movement is very Stable, so they are either uneven or non-solid. I have not found any research by Laplace or modern mathematicians." He pointed out: "I have proved this phenomenon in this article. It does exist, but it is a dynamic condition that translates into stability through the evolution of the ring."

Next, he describes the transformation of this state of motion, and then considers how the earth star ring will break into countless small particles and become "meteor shower, earth dust, or ash" if the stability conditions are not satisfied. The average density of the rings is given to maintain the global stability of the rings.

“The final result of the theoretical analysis of mechanics is,” he concludes. “The only ring that can exist is composed of countless small particles that are not connected to each other. They run and evolve around Saturn at different speeds at different distances.”

Maxwell won his 1856 Adams Award for his thesis "On the Stability of the Motion of Saturn's Rings: An Essay" (later published in the book, MacMillan and Co., 1859), which established him as the greatest mathematical physics. The lofty academic status of the family.

Mathematical physicist who values ​​empirical research

Maxwell, a theoretical physicist and mathematician, also attaches great importance to empirical research and often does various experiments. In 1874, he was responsible for the establishment of the Cavendish laboratory, which was later hailed as the "cradle of the Nobel Prize in Physics" at Cambridge University, and served as the laboratory director until his death in 1879. Gastric cancer. Scorpio talent, only let him live at the age of 48. Figure 5 shows the Maxwell statue in Edinburgh, England.

Figure 5 Maxwell Statue at George Street, Edinburgh

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