The purpose of this paper is to deal with some recent results in the Statistical Dynamics of Control systems, especially with those, connected with the use of the concept of the power spectral density of a random process.
The choice of spectral densities for the description of stationary random processes in a linear control system with constant parameters is founded mainly on the relatively simple relations:
(1)
(2)
where
F (
jω) is the frequency characteristic of the quadripole considered. S
xx (ω), S
yy (ω) are power spectral densities respectively of the input and of the output random processes, S
xy (ω) is the power cross spectral density of the input and output random processes of the quadripole. This paper presents a new algorithm of the mean square error of a servomechanism caused by random processes. The mean-square error of a simple and a multidimensional servomechanism has been computed using this algorithm. A new instrument, the Orthogonal Analyzer of random processes with Laguerre function modulators, has been developed to make the computation of the mean-square error of control systems caused by a random process.
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