If we could realize a power variable resistor of which resistance can be varied at will, we would have many applications of it in the field of control and measurement.
For this purpose, a mechanical variable resistor is not adequate in its response and available power. The thyristor variable resistor to be mentioned here is a power variable resistor in which the equivalent resistance between two terminals is varied by means of controlling thyristor switches. Owing to the use of thyristors, we can expect the variable resistor to have a fast response as compared with mechanical ones.
In this paper, we describe the thyristor variable resistor circuit using choppers and constant resistor element. This circuit can be used in both DC and AC systems. From the circuit analyses, we obtain the equivalent resistance and its practical variable range. Furthermore we give an example of thyristor gate control circuit to get the linear characteristics. Next we give the design criterion of the filter that absorbs the variation of the load current occurred by the switching. Lastly we exhibit the experimental circuit which has the variable range from 10 to 100Ω and the rate current 10A. We obtained satisfactory test results.

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It is well known that a commutatorless motor is constructed with a 180°-type three-phase thyristor inverter, a synchronous motor and a phase angle detector.
In this paper, we propose a method to analyze this commutatorless motor, using the “state transition method”. This method enables us to analyze the characteristics of a commutatorless motor directly in time domain. We can analyze by this method, not only the stationary characteristics of a commutatorless motor, but also the transient characteristics when the input voltage changes instantaneously.
We also show that the power factor of a commutatorless motor can be optimized by the regulation of the field current in the same manner as done with a synchronous motor.
An experiment is performed with a 1kW class commutatorless motor. The experimental results of the starting torque, the input and output current wave forms of the inverter and the curves of phase characteristics agree well with the theoretical results by the analysis mentioned above.

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One of the effects which cause error in attenuation measurement of ultrasonic pulses transmitted in a specimen from a piezoelectric transducer is beam divergence. H. Seki, et al. and A.E. Lord, Jr., have derived approximated formulas of sound pressure by using Bessel's functions and evaluated this effect in the case where a circular transmitter and a similar receiver are set coaxially on a parallel specimen.
In order to extend the evaluation of error due to beam divergence in other cases, a method of numerical integration to calculate particle velocity and to integrate it in the receiving area is formulated so as to fit the computations on a digital computer, and the apparent attenuation when the circular receiver is not coaxial with the transmitter is calculated. Then the attenuation of pulsed 2 and 5MHz signals travelling in a parallel steel specimen of 76mm in thickness, is measured by means of X-cut quartz transducers of 20mm in diameter, changing their relative positions, and the result shows a good agreement of ±1.5dB with the numerical computations.

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A method is described for measuring carbon monoxide in gases using a small galvanic cell oxygen meter. The Hopcalite catalyst is employed for the oxidation catalyst of carbon monoxide.
As a measuring gas containing carbon monoxide and oxygen comes in contact with the surface of the catalyst, carbon monoxide is oxidized by the reaction 2CO+O₂→2CO₂. Since oxygen required for the oxidation of carbon monoxide is supplied from the gas, the oxygen content in the gas is decreased by the oxidation reaction of carbon monoxide. Therefore, the content of carbon monoxide in the gas can be determined from the difference in oxygen contents measured before and after the oxidation reaction of carbon monoxide.
The catalyst is packed in a tube of 1.5cm diameter and 10cm long, and the measuring gas is passed through the tube. In order to check whether or not carbon monoxide is oxidized completely in the catalytic tube, the temperature distribution in the catalyst layer is measured. It is found that as the concentration of carbon monoxide is increased the temperature near the entrance of the catalytic tube rises, but becomes equal to the room temperature in the region more than 6∼7cm away from the entrance.
The experimental data obtained for carbon monoxide standard gases and exhaust gases of motorcar are presented. The method mentioned above is very simple and workable with a small amount of the sample gas. It is a special advantage of this method that the oxygen content is simultaneousely known with the carbon monoxide content.

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A winding or bushing type power transformer has heretofore been used for the purpose of measuring (monitoring) high voltages.
A method of measuring the high voltage by means of electro-optical effect has also been proposed. Such method makes use of Pockel's effect or Kerr's effect. The present article relates to study on the fundamental characteristics in case of measuring high voltages with the aid of the electro-optical Kerr's effect.
The present article first shows the experimental results of the temperature characteristic, polarization characteristic, insulation breaking characteristic etc, of nitrobenzene filled in a Kerr cell and then shows the results of measurement obtained by applying DC-high voltage, AC-high voltage or high frequency high voltage to the Kerr cell.
In practice, various matters have to be taken into consideration, particularly the fact that the degree of purity of the nitrobenzene is a very large factor in succeeding in measurement by this method.
The range of measurement may be extended by increasing the gap formed between the electrodes of the Kerr cell. The linearity of the measuring range is good. The present method is easier in applying voltages and more advantageous as an apparatus for measuring the high voltage than the conventional method with the aid of Pockel's effect which makes use of solids (ADP, KDP etc).

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This paper describes the design principle and the construction of a simple average response computer which uses a wire delay line memory as an accumulator. A series of rectangular pulses or the maximum-length binary sequence is used for an input signal to the measured system. In the case of the maximum-length binary sequence input, the response of the system is computed and summed up into the accumulator by making use of a fast m-sequence signal which is synchronized with the cycle time of the delay line. The computed response consists of the increments of the step response of the system within the sampling interval. The minimum sampling interval of this device is 40μs.
The rms errors of the averaged response are analyzed under the condition that the noise is additive and the system is linear. The rms error obtained with the rectangular pulse input is compared with that obtained with the m-sequence input. It is concluded that the m-sequence input is extremely effective from the point of view of the measuring time when the noise level of the system is high and the amplitude of the input signal is restricted within some limit. An experimental example which shows the effectiveness of the m-sequence signal input is also presented.

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Several models have been developed for attached flow in fluidic logic elements, but these are compared or verified by the experiments only at the attached points. In the design problem of fluidic devices, on the other hand, the location of the jet centerline, rather than that of the attached point, is indispensable. Here emerge the necessary steps of measurement or more particularly visualization of the centerline of the attached flow and of comparison with the models.
In this study, experiments are performed to determine the radius of curvature of the jet centerline and to find the impact point length which is the distance from the offset wall to the crosspoint of the fictitious centerline and the side wall. The visualization of jet centerline is accomplished by Schlieren photography using CO₂ gas as the main jet for the model devices of offset (D/b)=2∼10 and wall angle (α)=0°∼45°.
According to the results of visualization, the jet centerline may be approximated by a circular arc. The impact point is determined and compared with the computed value based on the theory of Levin and Manion, Perry, etc. And a new table of effective spread parameters is proposed. The new table is more practical than the contemporary tables because it defines the location of centerline more accurately. The values of spread parameter in this table differ from those proposed by Levin et al. and change widely around 7.67. This fact may insist on the necessity of a new model of attached flow.

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In order to observe the air jet flow in a small scale fluidic element, possibilities of application of several optical methods were investigated, e.g. the double-diffraction Schlieren method, the sensitive color Schlieren method, the moiré fringe sharpening and multiplication methods, the Mach-Zehnder interference method, the multiple beam interference method, the Twyman interference method and the differential interferometry. The double-diffraction Schlieren method is suited to observe the curvature of jet center-line and the attaching point of jet to the wall of an element. The moiré fringe sharpening and multiplication methods are useful to observe sensitively the gradient of static pressure as fringe displacement, but their weak point is that the image near the wall is a little blurred by the interference between the diffraction beam at the wall of a fluitlic element and that of the grid of moiré. They are primarily of line system and measure a phase gradient. Therefore, they are not subjected to the vibration induced by a compressor. The Mach-Zehnder interference method, the multiple beam interference method and the Twyman interference method are useful to observe an optical phase which corresponds to the static pressure. By using the multiple beam interference method, the fringe is sharpened and its displacement is doubled. But in this method the distance between the two mirrors is limited by the walk off effect and by a phase error, so it is suited to observe the flow of a small scale fluitlic element. The Twyman interference method can also achieve a twofold multiplication of fringe displacement without the limitation on the distance between mirrors, so it is suitable to observe the flow of a large one. When the cover glasses of a fluidic element contain some distortions, the new improved differential interferometry is useful to exclude the effect of distortion and to take the fringe displacement induced only by the air jet flow. Those interference methods are easily subjected to vibration. To prevent this, all mirrors which are related with optical interference are firmly combined to one frame.
Using these methods, the effects of offset, splitter position and splitter form on the jet were studied. Their experimental data were compared with those calculated by using a compressible model.

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This paper describes a high speed digital servo system which is used mainly as servo drives in numerical control systems.
A direct current servo system, when a quick response is required, often requests both position and velocity detectors. Resolvers and direct current tacho-generators are widely used for them. The former has an upper speed limit, and so gears are put between the detector and the motor shaft. As a result, a high performance cannot be expected because of the dead zone of the gears. Also these detectors have mechanical brushes for the transmission of electrical signals so that many troubles occur from non-working contact of brushes.
An optical detector is developed for non-contact measurement of position and velocity. Quantization errors due to quantized position and velocity signals in the servo loop are evaluated and the upper bounds of the errors are shown as a function of the damping coefficient of the linear system. The experimental results of the servo system with the quantized position and velocity detectors are given.
A pulse-drive servo system which is a digital servo system containing only switching elements in the circuit is proposed. The servo system is completely free from hunting due to the variation of system characteristics because the circuit is constructed with logical elements. The functional descriptions and the experimental results of the system are given.

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This paper is concerned with the control of neutron flux distribution by the finite number of control rods with the constraint on the reactor period. The control aim is to shift the initial neutron flux distribution to the desired flux distribution in a given time. The iteration scheme is proposed in order to obtain the solution of the problem. This method is composed of two processes: in the process A, the control function α_k(t) is determined so as to minimize the performance index J_k=||Φ_{d, k}(x, t)-Lα_k(t)-L_IΦ_I(x)||², in the process B, the distribution function Φ_{d, k+1}(x, t) is determined so as to minimize J'_k+1=||Φ_{d, k+1}(x, t)-Lα_k(t)-L_IΦ_I(x)||², where L is an operator which transforms a function of t into a function of t and x, and L_I is an operator which transforms an initial flux distribution into a function of t and x. These two processes are iterated until a sequence of [J_k] converges.
An example is given to show the effectiveness of the proposed method and the possibility of this control scheme.

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For the analytical approach to optimization problems of the distributed parameter systems, it is advantageous to use the methods of the functional analysis. This means that we at first transform the partial differential equations, which describe the state of the system with distributed parameters, into the ordinary differential equations in the function space and solve the optimization problems, and then we transform again the results obtained above into the partial differential equations and we obtain the optimum solutions for the distributed parameter systems described by the partial differential equations.
In this paper, we define in the infinite dimensional space the stochastic integral of Stratonovich type, which is useful for the modeling of the physical processes in the finite dimensional space, and we shall discuss the convergence and other properties of the integral. Furthermore, using these results, we can derive the nonlinear filter in the infinite dimensional space, under such a criterion as the unbiased and least square estimation. As a special application of the above, we shall derive the optimal filter for the linear distributed parameter systems with the state dependent noise, moreover we shall discuss the moment equations required for this case.

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There are many engineering problems which are reduced to the mathematical programming problem. The constraints and/or the objective function established are sometimes subjected to errors due to experiments or estimations, and thus are probabilistic in nature. In such a case, a stochastic approach must be adopted to make the program realistic by treating the constraints and/or the objective function as random variables. Thus we set up the problems 1) to minimize the expected value of the objective function under the chance-constraints on the constraints and 2) to minimize the expected value of the objective function under the chance-constraint on the objective function as well as on the constraints.
The constraints and the objective function are random variables, the distributions of which are not predetermined. Thus, the chance-constraints are not to be calculated directly. In this paper, a new approach is employed to transform the chance-constraints into the equivalent deterministic nonlinear constraints. Validity of this transformation is proved by using Tchebychev inequality. A possible algorithm to solve the problems is proposed and numerical examples are also provided to illustrate the given method.

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The authors apply the classical variation principle to the analysis of singular solution problem in second order systems in relation to the switching function of the bang-bang control. The necessary condition derived from the first variation indicates the first derivative of the switching function should vanish, and the coordinate function gained through this process is conveniently used in discussing the second variation which leads to the sufficient condition. It is shown the sufficient condition for the true minimum may easily be described by the selection rule graphically represented. Also the transition condition between the singular and the bang-bang trajectories is clearly given through the analysis of the discontinuity of the second derivative of the switching function. As the result, it is found that the true optimum trajectory is attainable without numerically computing the values of performance index for comparison.

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To construct an optimal state regulator for a nonlinear system with quadratic performance index, several approximation methods are investigated, namely, the perturbation method, the method of instantaneous linearization, and the method of parameter optimization.
The perturbation method or the ε-parameter method, previously established by the present authors, is briefly outlined and some practical difficulties are remarked. The method of instantaneous linearization, proposed by Pearson, is based on the idea to use a technique similar to that for linear systems. This idea much simplifies the calculation. However, the best possible solution can not necessarily be obtained, because of the arbitrariness in the system description. In order to correct this serious shortcoming, the present paper proposes to use a parameter optimization technique jointly. According to the idea, the nonlinear system is represented by a linearized state-dependent model which contains a set of adjustable parameters. Secondly the values of these parameters are determined so as to minimize the performance index by the gradient method.
Three examples attached illustrate and compare the perturbation method and the method of instantaneous linearization improved by parameter optimization technique. In the first and the third examples which permit the exactly optimal control, the applications of the two methods are examined analytically, while in the second example the results of numerical calculations are compared.

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The optimal control of linear time-invariant systems relative to time-multiplied quadratic performance indices is discussed. The problem is posed with an additional constraint that the control vector is a linear time-invariant function of the output vector rather than of the state vector. The degree of optimality assigning a physically meaningful measure of the “quality” of control systems which are not optimal is proposed and applied to this problem.
The necessary condition for minimizing matrix of feedback gains is obtained in the form of algebraic equations. The second and fourth order systems are examined in detail as examples.

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This paper treats the method for designing the time optimal steering system that minimizes the steering time to turn a ship to an assigned angle. When this problem is synthesized by using the state space, the state vector representing the magnitude of the steering angle is bounded because the steering angle is limited in both of a magnitude and a rate. The general solution of this is obtained by using the maximum principle and the jump-condition, but, this problem is considered as a special case of that in the bounded state space. In this paper, applying the result of J.Y.S. Luh, the simple method to find the minimum time optimal control is shown, using this, the minimum time closed-loop controller is designed for the following steering system of ships;Td²θ/dt²+dθ/dt=Kδwhere θ is a turning angle, δ is a rudder angle, T is a constant which represents the quickness of response of ships, and K is a constant which represents the turning quality. Also, a simulation is tried using a digital computer and it is shown that this method can be applied to realize the optimal steering device in any ships.

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A linear time optimal control system subjected to random noise needs a control law which is optimal on the whole state space. But in many cases the control law for the state which is very far from the initial and terminal states has very little significance in the probabilistic sense. Therefore in the above stated situation practically we can use a suboptimal control law which vanishes except on a bounded region of the state space. Then with a certain probability the state point goes into the region where no control is given and the system cannot be controlled.
When the deterministic linear time optimal control system is used accepting white Gaussian noise, an evaluation of this probability is given.
The time when the state point reaches a neighborhood of the target point is a random variable. We give a bound for the expectation of it.

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