Optimum Second-Order Control Systems with Stationary Random Inputs

Abstract

In this paper, the author intends to decide the characteristics of optimum control systems with stationary random inputs. To get useful data for actual design of optimum control systems, the author calculates mean square error values (M. S. E.) of second order systems. For input power density spectra, three typical types are chosen as follows:
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The results of these calculations are put into order on many graphs. From these, we can find many important things as given in the following:
(1) To decrease M. S. E., natural frequency of control system must be decided far larger than input frequency band.
(2) In general, the smaller value of damping ratio ζ of control system brings, the larger M. S. E. but when ζ is somewhat large, deviation from the minimum M. S. E. is small.
(3) When the input power density-spectrum is of type 1 or type 3 and the above Item 1 is satisfied, the optimum damping ratio is in the same value as that of minimizing the integrated square error value of step input.
Taking into consideration the above Item 3, relations between transient characteristics and the above characteristics are investigated.
These results and graphs are believed to be useful for designs of control systems with stationary random inputs.