This paper contains a survey of the method for solving higher characteristic equations by means of root-locus method. We often encounter problems to solve chracteristic equation of higher order in fields of automatic control, vibrations, and others. In general, judgement whether roots of characteristic equations are stable or not, is given by Routh-Hurwitz criterion which designates all roots in left half plane. However, the criterion does not give magnitude of real and imaginary part of roots, and so it is not always so convenient for optimum setting, that is to specify 25% or 1/e damping. Author classifies the root-locus of first, second, third, fourth and fifth order characteristic equation. He also made a nomograph for solving cubic equations. By means of the root-locus method, all roots are plotted in the s-plane, and the damping of system can be found immediately.

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In order to obtain the transient response from the frequency response through the Fourier synthesis, the approximation by square-wave response for indicial response is used. This paper describes the validity and the error of the method by simplified calculation. Rules are given to determine the fundamental frequency and necessary number of odd harmonics for the Fourier synthesis of general low-pass system. A method is given which employs another auxiliary element having a known response. The necessary number of terms of harmonics can be remarkably reduced by this method. Segment type sine-wave potentiometers are used as a Fourier synthesizer. Each one of them generates odd harmonics (order 1-19). Several examples of applications of this synthesizer are given, which shows that the accuracy of its solutions is within 1%.

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Some approaches to the chracteristics of amplidyne generators have ever been per formed in this country. However, most of them are limited in the study of static cha racteristics and indicial responses of the machine without touching to informations as elements of servomechanism. We have experimentally determined many fundamental data of an amplidyne, calculated its time-constants and established its precise block diagram. The frequency response of the machine Was also examined and we found that the amplidyne can be treated as a linear servo element under some limitations in spite of the inherent nonlinear characteristics of magnetic parts. In this paper, we moreover describe some methods of generating low frequency alternating current and explain the apparatus used to measure the amplitude and the phase at low frequency.

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For analysis and design of process control systems, the analogue computer is a powerful tool. The authors, with the special objective for handling process control systems, have constructed an analogue circuit having the following features:(1) Analogue is all electric, so that time constants are determined by RC networks.(2) As the dead time pertains to almost all process control systems, the specially designed tape recording machine is employed as the dead-time generating unit.(3) Each time constant is easily adjustable within the range of several minutes, so if required, actual controller can be readily tested by placing in this analogue circuit. As the control element, model of Leeds & Northrup Co. type electronic controller is employed in this experiment. This paper describes the constructions and dynamic behaviours of each element and illustrates some simple examples solved by this analogue for the sake of examining its accuracy.

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The design of automatic control systems to give “optimum” response has been discussed in terms of “control area”, “square error area”, “weighted control area”, “Mp”, “fundamental damping factor” and so on. However, they are not always applicable to a certain problem. In this paper, more universal design criterion “A* criterion” is proposed. Let
Then, by means of A*-criterion, the most desirable condition of a system is to be obtained by adjusting system parameters to minimize A*. On the right side of Eq (1), the first term means to weight the deviation of response, the second term to weight the deviation of response in the considering time, and the third term to weight the cyclings of response. The comparison of A*-criterion with other criteria is shown with refering to various problems.

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