First, the source of the birth and development of control theory
Great realistic demand is the source of the birth and development of control theory. Although this is obvious, we still use three typical examples to illustrate it.
The first famous example is the steam engine invented by Watt. 1782, Watt invented its "core technology": using the feedback of centrifugal governor to control the speed of steam engine, which made the steam engine widely used and became the main symbol of British industrial revolution.
1868, British physicist Maxwell published On Regulator, which described the motion state of the governor with differential equation for the first time, derived the differential equation of the regulator, and linearized it near the equilibrium point, pointing out that stability depends on whether the root of the characteristic equation has negative real part. Maxwell was the first "control theorist" in history. How to judge the stability of polynomials according to their coefficients is an important content of control theory, such as Routh-leonid hurwicz criterion and Haritonov theorem.
The second famous example is the feedback amplifier. Because the electric signal decreases gradually with the increase of transmission distance, it needs to be amplified by an amplifier to continue transmission, and the nonlinearity of the amplifier often leads to the straightening of the signal. Amplifiers amplify noise and distortion while amplifying signals. The negative feedback amplifier invented by H.S.Black in 1930s made great contribution to long-distance communication. The research on the stability of anti-health amplifier gave birth to Nyquist-Bode-Evans and other famous frequency domain analysis and design methods.
The third famous example is the filter. During World War II, in order to solve the problems of air defense fire control and radar noise filtering, Wiener proposed and defined the filtering problem, and established the Wiener filtering theory of stationary random numbers.
Later, Kalman filter theory based on state space description broke through the limitations of Wiener filter theory to a great extent, and was widely used in aerospace, communication, signal processing and many other fields, and had a far-reaching impact. So far, filtering theory (especially nonlinear filtering theory) is still an important research topic in control theory and other fields.
Second, the key to promote the development of control theory
As we all know, the development of control theory closely depends on the application of mathematical methods, and even in turn can promote the development of mathematics itself. When summing up his research experience, Kalman once said: "First of all, what should we do? It has the correct physical meaning, and then it is all mathematics. " This sentence is very reasonable.
From the control discipline itself, it has rich scientific connotation and unique research problems. Although the proper application of mathematical theory and the innovation of mathematical methods are very important, whether the theoretical results have important control scientific significance is the most critical. Therefore, it should be the most important innovation to put forward original basic concepts and problems and create viable control methods.
For example, Kalman, the founder of modern cybernetics, put forward some important concepts such as state space method, controllability and energy view. The concept of "robustness" put forward by Zames, the founder of control.