Compared with the case of linear systems, there seems to be some vagueness in the observability concept of nonlinear systems. That is, the “observability” of the nonlinear systems can not be defined without fixing the input. For such a reason, Brockett introduced the concept of distinguishability instead of observability in the study of bilinear systems. In this paper, the distinguishability for some generalized bilinear systems is defined and the concept of the indistinguishable manifold is introduced. Then it is shown that the tangent bundle of the indistinguishable manifold exhibits an invariant property very similar to the unobservable subspace of the linear systems. In practice, it will be almost impossible to calculate the one parameter group of the vector field, so it seems necessary to establish some feasible method for the observation. In this paper, the method which utilizes the higher order derivatives of the output is proposed. Then, for some class of systems, it is shown that if the system is distinguishable, it is distinguishable by differentiation.

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This paper defines [σ1, σ2, …, σp] integral left invertibility which is a generalization of L-integral left invertibility given by Sain and Massey. A necessary and sufficient condition is obtained for the existence of a [σ1, σ2, …, σp] integral left inverse system of a linear time-invariant dynamical system. And a constructing algorithm of a [σ1, σ2, …, σp] integral left inverse system for suitable {σ1, σ2, …, σp} such that the system is integral left invertible is presented. Furthermore, the integrator decoupling problems of multivariable systems having the number of inputs more than that of outputs are considered as an application of the discussion about the left inverse system. A necessary and sufficient condition for the integrator decoupling by special state feedback is presented.

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This paper deals with the problems of observability and the feedback stabilization of distributed systems of the hyperbolic type. The necessary and sufficient condition for observability is derived. It is proved that the feedback system becomes asymptotically stable under the observability condition.

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This paper deals with the optimal control problem (regulator problem) of stochastic systems described by stochastic functional differential equations.
This problem has not been solved completely even in the deterministic case if the system is linear but includes delay terms. A stochastic version of this problem is very complicated because the solution of stochastic functional differential equations is not a Markov process with values in Euclidean space. This paper consists of the following parts, namely, the formulation of the problem, the functional equation to be satisfied by optimal control, the optimal control problem of linear systems with delay, and the construction of an approximately optimal control for the linear systems with a small delay term.
When the system is linear, a sufficient condition for the existence of an admissible control is also given. Specially, for the optimal control problem of the systems described by linear stochastic delay-differential equations with the quadratic performance criterion, we get a set of differential equations which the gains of the optimal control have to satisfy. We show that these equations can be reduced to a set of a nonlinear integro-differential equation of Volterra type and an algebraic matrix equation.
Moreover, it is shown that if the delay term of the systems is sufficiently small, we can successively integrate the set of differential equations.

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This paper presents a method of identification for multivariable linear dynamical systems. An observable canonical form is used in this method. Generally speaking, in such a canonical representation an input-output relation can be defined in the form of the smallest number of parameters. Therefore in the case of identification the number of parameters to estimate becomes small.
This method consists of the part of Markov parameter estimation and the part of minimal realization: the parameters of an impulse response matrix which are obtained from the state equations are estimated through the least mean-square type stochastic approximation algorithm, and an observable canonical form which is controllable is derived from the formerly estimated matrix.
The proposed method has the advantage that any type of input sequence can be used for identification and that few properties of both system and observation noises need to be known.
In this paper, we deduce some equations to obtain the parameters of an observable canonical form from an impulse response matrix and also show the condition to obtain unique solutions in this case.

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This paper describes the theoretical and numerical aspects of the multiplier method in nonlinear programming problems. The theoretical results indicate that a local solution for the original problem and the corresponding Lagrange multipliers are found by solving the dual problem.
The convergence rate of the multiplier method is governed mainly by the iterative scheme of Lagrange multipliers for solving the dual problem. In this paper we present a class of the updating algorithm of Lagrange multipliers which employs quasi-Newton methods to accelerate convergence of the multiplier method.
Several different algorithmes are available as quasi-Newton methods. The quasi-Newton method that involves no accurate line search is applied in this paper, since this method requires fewer number of evaluating the dual function than other methods which make use of the accurate line search. Numerical results show that this algorithm is superior to the usual multiplier method.

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Obviously a random process that may be considered as strictly stationary seldom exists in practical random phenomena such as urban noises. Especially, the road traffic noise always exhibits, the nonstationary property in a long time interval, because of the temporal changes of social or urban environment. In addition to such an essential cause, taking into consideration the extensiveness of collected noise data in a long time interval (for example, observed by an automatically recording sound-level meter), the complexity of statistical treatment involved and the capacity of digital computer, we are inevitably requited to use observed data skillfully with computer for the prediction and/or estimation problem of state variables in a nonstationary urban noise.
In this paper, concerning the actual road traffic noise with many different types of level distributions, a new trial of statistical treatment to estimate the noise level distribution in a Long time interval on the basis of an information of noise level statistics (with high degree of experimental reliability) in a short time interval is firstly considered from the theoretical view-point. That is, the above estimation technique is mainly founded on the use of the newly established probability expression in the form of statistical expansion series. The expression has an arbitrary number of nonstationary-parameters to be universally available for arbitrary nonstationary forms of the traffic noise fluctuation over a long period of time. More explicitly, in this unified expression, the stationary term is taken in the first term and many nonstationary factors are reflected successively in the second and higher order expansion terms. Two explicit, expressions of level distributions over a long time interval on the basis of level distribution over a short time interval are derived. This is a special application of the above general theory. In the derivatibn, two fundamental and typical viewpoints of modeling an actual random time series are pointed out. One is to regard the time series as multiplicable, and the other is to rigard it as additive. Finally, the validity of the above estimation theory is experimentally confirmed by applying it to data of actually measured road traffic noise. The experimental result is in good agreement with the theory.

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The purpose of this paper is to present sufficient conditions for the stochastic observability of nonlinear systems under randomly interrupted observations.
First, the observation mechanism with interrupted data is modeled by introducing the Poisson process. Then both the finite time stochastic observability and the asymptotically stochastic observability are defined. Finally, by using a Lyapunov-type function, theorems giving sufficient conditions are presented and the stochastic convergence of the estimator is examined.
For the purpose of supporting the theoretical development here, results of simulation studies are also given.

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A new method for generating pseudo-Gaussian signals by use of a weighted m-sequence is proposed. This method utilizes the central limit theorem and the uniform distribution property of the weighted m-sequence signal. M-tuples obtained from an m-sequence which is generated by an n-stage shift register are weighted and summed up to obtain pseudo-Gaussian signals, where M≤n.
Skewness and kurtosis of the signal thus obtained are theoretically calculated and it is shown that when the number of M-tuples which are summed becomes large, the skewness and the kurtosis approach to those of the Gaussian signal, provided M is suitably chosen.
Digital simulations are carried out and it is shown that the signal obtained remains Gaussian after it passes through a low pass filter having a time constant of even fifty times as much as the clock period of the signal.
A simple pseudo-Gaussian signal generator of analog type is also proposed which consists of a shift register, a summing amplifier, a first order filter and a sample-hold circuit.
Three types of statistical tests are carried out for those signals obtainned in digital simulations and from the analog type signal generator to see how good they fit to a Gaussian distribution (skewness, kurtosis, x² test). These tests show that the signals are considered to be Gaussian under the 0.01 significance level.

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This paper describes the mathematical model of a manipulator and the software servo that controls the manipulator in a task-oriented coordinate system. A motion of the manipulator is decomposed into the six components of task-oriented coordinates, each of which is independently controlled as virtual manipulator freedom. The servoing method makes us free from the physical manipulator mechanism and enables us to control the manipulator in any task-oriented coordinate system. It reduces the complexity of description and execution of manipulations, especially in the case of partially constrained motions.

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Two methods have been devised for making shipboard scales which can be used on a swaying base: the first is to use two simple levers and the second is to employ several levers which are connected mechanically by rods or flat springs.
In this paper, the statics of complex lever systems is dealt with theoretically. A quantity κi is introduced and defined by the equation
φi=κiφ
where φi is the tilt angle of the i-th lever when the standard lever deviates through the angle φ, κ represents the “tilt angle coefficient of the lever” or briefly “lever coefficient”.
By employing κ, the complex lever system can be treated as if it contained only one lever. Then several conditions can be derived for the case of mass weighing on an inclined plane, i.e., “slopeproof conditions”.
In the following paper, experimental results which agree well with the above theory will be presented.

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In a conventional NC machine, the tool carriage is positioned according to a tape command, but it has no feedback mechanism from the tool edge.
In cutting operation, sufficient dimensional accuracy can not be obtained by positioning control alone of the tool carriage because of the tool wear or the thermal expansion of the tool and the workpiece. Therefore it will be necessary to maintain the accuracy of workpiece dimensions during operation. For realization of this dimensional control, a reliable and inexpensive detector is required in order to measure the workpiece dimensions continuously and accurately in operation.
The measuring apparatus reported here is realized by the use of a laser tube, photoconductive cells and optical systems. The experimental characteristics of this apparatus is satisfactory and the effective results are obtained in the application of the dimensional control to an NC machine lathe.

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One of the causes of decreasing the analog input accuracy of the process control computer is the common mode voltage induced commonly on a pair of signal lines. The common mode voltage is converted to the normal mode voltage (appearing as the differential voltage between a pair of signal lines) by the influence of the unbalance resistance existing in the pair of signal lines and the leakage impedance between the signal lines and the ground when there are open scanner switches in parallel with the input signal lines.
The normal mode voltage is superposed on the signal voltage and causes an error.
The normal mode voltage, if converted at the signal source side from the input scanner, can be eliminated by a low pass filter, if converted at the amplifier side from the input scanner, cannot effectively be eliminated by the low pass filter.
In this paper, the relation between the common mode voltage and the input accuracy is discussed, in view of the following three points.
1) Referring to the equations for the conversion of the common mode voltage into the normal mode voltage, the double mixed shielding method is introduced, which is effective for decreasing the common mode voltage with the electro-magnetic shield by the method of two points' earth shielding.
The double mixed shielding method is also effective for making large the common mode rejection ratio with only electrostatic shield by the method of one point earth shielding.
2) The block switches' effect for the common mode rejection ratio and the optimum number of block switches is discussed. (The block switch is inserted in series with the specified number of scanner switches.)
3) The design method for the amplifier's settling time is discussed, in view of the relation between the scanning speed and the settling time, and between the induced noise rejection by clock pulse and the settling time.

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The effusion method was originally designed by Bunsen and improved later by Schilling for determining gas density. It has been widely used for over a century because of its relatively simple setup.
It has been, however, generally recognized that the method has a fairly large error of uncertain sources.
This paper discusses the error of the method due to dynamic causes and describes an improved method to avoid the error.
Experiments show that the improved method yields more accurate gas specific gravity with an error reduced nearly to 0.5 percents which is similar to the result obtained by a weighing method.

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This study has been performed from the point of view of designing a fluidic sonic oscillator. First, we experimentally and theoretically investigate the oscillation mechanism and the reattached jet switching in the oscillator. Next, on the basis of the investigations mentioned above, we formulate the condition for sonic oscillation.
The results obtained can be summarized as follows:
1) In a so-called sonic oscillator, the oscillation is classified into two modes. These depend upon the geometric parameters of the device and the supply pressure of the main jet. The sonic oscillation occurs when the supply pressure becomes higher than a certain level.
2) The analytical model satisfactorily describes the jet switching in the oscillator and the condition for sonic oscillation. Therefore, we can theoretically predict the geometric parameters and the supply pressure to cause the sonic oscillation.

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This report treats of the improvements of the fluidic PID controller operated with PWM signals one of the authors reported previously. The main points of improvements are the use of the new saw-tooth wave form for PWM and the use of the delay line composed of logical circuits instead of the propagation lag of pressure wave.
The analog signal is converted into PWM signal by the fluidic comparator and the sawtooth pressure wave whose rear side is used for the modulation. The obtained PWM signal is delayed by one period and two periods by the delay line. Analog PID control modes are obtained by a differential type algorithm between the original signal and the delayed signals, and by the demodulation with capacities. There are no interferences among three control modes.
The delay line consists of fluidic logical circuits and monostable multi-vibrators composed of an impulse generator and constant time hold circuits. Factors affecting the performance of the delay line are discussed here.

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This paper deals with the step response of throat-terminated pneumatic transmission lines. Analytical and experimental results are presented to show the reflection behaviour from a throat at the end of a line, and also to prove the dynamic matching technique.
The analysis is performed in the following steps;
(1) The transfer function of throat-terminated transmission lines is expanded in an infinite series in which the terms consist of the product of the reflection coefficient and the transfer function of semi-infinite line.
(2) With the assumption that the reflection coefficient (m) is constant, the step responses of throat-terminated lines based on the three analytical models of pneumatic transmission line, (i.e. lossless line model, linear friction model and Brown's model), are obtained. Then the model comparison is made on the basis of the calculated pressure waveforms for m=±1, ±0.5, 0.
(3) The pressure responses to a step input are calculated by using the Brown's model and the approximate reflection coefficients ma, ma =(RL-Rc)/(Rc+RL), Rc is the characteristic resistance of a line and RL the linearized load resistance due to the static characteristic of pressure-flowrate of a throat.
The experimental results with a positive pressure input are compared with the analytical results based on the Brown's model and ma. The agreement between experiment and calculated results is good. Therefore, it may be concluded that the response waveform of throatterminated lines to a step input can be forecated in the procedure described above and the practical matching condition is RL=Rc.

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This paper is concerned with a method for generating pneumatic pulse trains of various types. The system consists of a rotary disk, two pneumatic sensors, a gear mechanism and an electronic circuit for driving the disk. The disk has fifty holes the centre of which are spaced equally round the circumference near the periphery of the disk. A column is mounted on each hole and a rectangular prism chip is attached on its upper surface. The column is adjusted to make the chip surface take a proper position using a spring and screw assembly, and also is set to rotate about the centre axis so that the long side of the chip can direct to either the centre of the disk (set “on”) or the direction perpendicular to it (set “off”). The pneumatic sensors are composed of a nozzle and an orifice. One of the nozzles is fixed on the base and the other is put on an arm rotatable about the turning axis of the disk, and they are arranged so as to face the outside part of the upper surface of the set “on” chips. The disk is rotated by a motor through a gear train with a speed proportional to an input voltage of an electronic circuit. When the chips set “on” pass through the nozzle counterfaces, pneumatic pulses generate in the pneumatic sensors, but the chips set “off” make the sensors generate no pneumatic pulse. Presetting the angular position of displaceable nozzle, two pneumatic outputs, one of which is lagging to the other in time, can be obtained from the pneumatic sensors by driving the disk. There are three basic pulse series generated by this device: (1) the pulse series of which the amplitude is proportional to a time function, (2) the pulse series of which the pulse interval is set at the standard length multiplied by an integer, and (3) the pulse series of which the pulse intervals are modulated by an electric signal. There are possibly combinations of the above three types.

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Gd-Co films which have uniaxial magnetic anisotropy perpendicular to the film plane are prepared by the rf-sputtering method. The transverse Hall effect and the planar Hall effect are studied with these films. It is found that the extraordinary Hall effect plays a dominant role in the transverse Hall effect in these films. It is also found that the hysteresis loop of the Hall effect corresponds to the M-H loop observed by the Kerr magneto-optic effect. The planar Hall effect is negligibly small compared to the transverse one. The hysteresis loop of the Hall effect varies remarkably its shape with temperature, and the polarity of the Hall voltage is reversed at the compensation temperature. A Gd-Co film can be used as practical Hall effect device considering its high sensitivity to magnetic field. In this paper several applications of the extraordinary Hall effect in Gd-Co sputtered films are also proposed.

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