Modern Control Engineering

Edward Routh was born in 1831 in Quebec. He came to England at the age of 11, was educated at University College School and entered University College as a student in 1847. In 1851 he entered Peterhouse, where he was contemporary with Maxwell, and in fact beat Maxwell in the final examinations.

Routh was Senior Wrangler while Maxwell only came second. It is said that Maxwell was so confident that he did not bother to attend the announcement of the examination results, merely sending his servant along. When the servant returned Maxwell greeted him with "Well, who was second?" and was somewhat shaken by the response "You were, sir."

Routh remained in Cambridge where his real love was in teaching undergraduates. Over 30 years no less than 500 of his students became wranglers, and for 22 successive years (1861-1882) the senior wrangler was one of his students. In his spare time he wrote papers on mathematical topics. In one of these he described a simple test to determine whether a polynomial was a Hurwitz polynomial. This test is now known as the Routh-Hurwitz criterion.

The combined work of Routh and Hurwitz provided the first practical test for the stability of feedback control systems but a full understanding of the significance of this test was not initially apparent. Several further steps were needed.

This understanding came over the next forty years from work on long distance telecommunication systems. The development of the thermionic valve at the start of the 20th century made it possible to amplify telephone signals. The losses in the transmission lines could be overcome and by inserting amplifiers every 10 or 20 miles, high quality telephone transmission over thousands of miles was a real possibility.

One difficulty remained, the amplifiers were not perfect and when transmitting through several hundred successive amplifiers in succession the build up of distortions could become quite intolerable. The solution to this problem was recognized round about 1920. It was to use negative feedback to improve the linearity and stability of the amplifiers. However, this introduced further stability problems very similar to those encountered in control systems.

The leading telecommunications research establishment in the world was then the Bell Telephone Laboratories just outside New York. The Bell Telephone Company had a critical interest in this problem, in its ambitions to provide transcontinental telephony in America. Two men at the Bell Laboratories, Harry Nyquist and Hendrick Bode were responsible for solving these problems.

Both of them should have received Nobel prizes for their work, but there are no Nobel prizes in Engineering!