Wikipedia:Reference desk/Archives/Mathematics/2010 November 21

= November 21 =

Control systems: A conceptual question
Researching the bio of Harold L. Hazen, an associate of Vannevar Bush and later the MIT EE department head, I ran into the history of what now seems to be a fairly pedestrian math subject - history of control systems science. What could be simpler than a Bode plot or the Nyquist stability criterion? dislaimer: I'm a former electronic engineer, indoctrinated in things like phase margin - these were perceived as rock-solid, centuries-old foundation when I studied them ...

As I understand it, the need for a clear, unified theory of control arose in the early 1920s, when former small regional power grids were being consolidated into larger systems (which turned out unstable and unmanageable, which called for research in control systems ...). Then, in the 1930s, re-militarization of the navies and bomber threat demanded new fire control systems (ship-to-ship and flak). Then there was the war; a unified systems did not emerge until after WW2. Military jobs were classified, but civilian applications were public. Throughout the 1930s Bode, Nyqyist, Bush, Hazen, Gordon Brown et al. developed and shared competing theories but no one grasped the whole subject yet (and it's only a snapshot of American situation - the Germans and Soviets followed their own, parallel and different routes to the same objectives). Some operated in time domain, others in frequency domain; some, like Hazen, developed control systems without ever using the concept of feedback, etc. Today, it seems almost like blind men and an elephant.

So, beat me if it's a stupid question: how come that such a straightforward, mathematically simple subject took so long to develop? Mathematicians of the 18th and the 19th century put forward mind-bogging, highly abstract concepts that were far ahead of engineering needs (like the contribution of Riemann). The Fourier analysis was known well before it became widely appied in engineering. But when it came to applying already existing math apparatus to a real-world problem (with all the GE and AT&T money behind it) - it took a quarter of a century to formulate properly. Why?

And how did it happen that a subject (correct me if I'm wrong) was left to engineers alone (and most of them corporate engineers, not academics)? Where were the mathematicians? East of Borschov 21:00, 21 November 2010 (UTC)


 * I'm not a mathmatician but ..... didnt Norbert Weiner "discover" feedback when studying gun control systems during wartime, and when no longer secret published in a popular account in his book Cybernetics? A lot of ego-led organisations have still not discovered the idea of feedback. 92.15.6.86 (talk) 13:01, 23 November 2010 (UTC)
 * Wiener followed the path already beaten by the Bell Labs group (Nyquist, Bode et al.). It is true that wartime secrecy prevented publication of what was deemed sensitive, but then (a) a lot of knowledge was published before the war, and my question was really about the 1930s (b) during the war, American experts worked in a coordinated fashion and shared knowledge among themselves. For example, censorship banned publication of a 1940 paper by Gordon S. Brown but then the classified paper was distributed to all experts in the field. East of Borschov 09:21, 24 November 2010 (UTC)


 * Probably because there were not many or any of the kinds of automatic machines where control system theory was needed. 92.15.13.42 (talk) 20:32, 23 November 2010 (UTC)
 * Correct, but the kinds where it was needed (military, power utilities, telecoms) were among the wealthiest clients of the time, even in the worst of the Depression. There was real money and real willingness to invest it into working knowledge. East of Borschov 09:15, 24 November 2010 (UTC)
 * Three reasons I can think of: 1) electronics (such as radio) was not widespread before at least the 1930s, so feedback did not have that embodyment; 2) the management theory of that time and before was about a dominant authoritarian strength of will forcing others to submit without any backchat (and still is for a lot of unenlightened bosses and organisations). The influential French management theorist Henri Fayol had part of his text mistranslated by the translator in to English, so that the 'controlling' part omitted the idea of feedback. I thought there was mention of this in one of the articles, but that seems to have gone now. I seem to remember that "checking" was translated as "controlling". This is mentioned here: http://webcache.googleusercontent.com/search?q=cache:IHyyumPWg4IJ:www.thefreelibrary.com/Henri%2BFayol%253A%2Bplanning,%2Borganisation,%2Bcommand,%2Bcoordination,%2Bcontrol.-a099932523+checking+fayol&cd=1&hl=en&ct=clnk&gl=uk http://www.thefullwiki.org/Henri_Fayol_and_the_Administrative_theory I've asked about this on the Language Desk. 3) In circa WW1 military situations, no feedback seemed to be involved. For example a General would I imagine look at a map of the enemies positions, and then order that location to be shelled. No obvious feedback involved. In business or manufacturing situations, the overseer would literally be able to see what was happening with their own eyes, so again no obvious feedback. Deming's PDCA only came about later. 92.15.15.224 (talk) 12:04, 24 November 2010 (UTC)

Fourier Transform
Hi. I'm trying to find the Fourier Transform of $$ f(w)=\frac{1-iw}{1+w^2} $$, given by $$ f(t) = \int_{-\infty}^{\infty}\frac{1-iw}{1+w^2} e^{-iwt} dw $$ but am having trouble with the integration. I am not meant to do this using any techniques from Complex Analysis, which I haven't studied yet, and so the only tool I have available to me is real integration. There is clearly some trick I'm missing on how to do it but I just can't spot it. Can someone give me a hint? Thanks asyndeton   talk  23:35, 21 November 2010 (UTC)
 * 1 + w2 = (1 &minus; iw)(1 + iw) by the difference of two squares. This will allow you to cancel the numerator and save yourself a lot of work. — Anonymous Dissident  Talk 09:37, 22 November 2010 (UTC)
 * ....and next, think about integrating by parts..... Michael Hardy (talk) 23:51, 22 November 2010 (UTC)