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Hitoshi TAKATA
1979 Volume 15 Issue 4 Pages
415-421
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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This paper presents a new method of linearization by augmenting state variables in a Taylor expansion for a nonlinear differential or difference equation which describes nonlinear systems. Regarding every polynomial of the state variable (
x) up to the
N-th order as a new state variable, an augmented vector (
X) is introduced. The vector's dynamic equation which associates with the original nonlinear equation is expanded in a Taylor series truncated at the
N-th order with respect to
x so that a linear dynamic equation of
X is obtained. It has been proved that the approximation error by using the resulting linear equation is on the (
N+1)-th order of an infinitesimal.
This paper also proposes a nonlinear observer based on the aforementioned method of linearization for nonlinear systems. The nonlinear observer includes an extended linear observer and a 2nd-order observer as special cases.
The numerical results indicate that both the linearization and the observer given here perform better than the ordinary linearization and observer.
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Kousuke KUMAMARU, Katsuhiko KIBE, Katsuhiro INOUE
1979 Volume 15 Issue 4 Pages
422-428
Published: August 30, 1979
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In this paper, a recognition-identification method is proposed for the nonlinear systems of which the dynamics have unknown pattern variations. Such systems are formulated by considering the parameters in the system configuration as unknown jump parameters, and the identification problem can be reduced to the estimation problem of the augmented system containing these parameters in the state vector.
Using the parallel processing of extended Kalman filter and the generalized likelihood ratio test based on the state observations, we can effectively detect the time at which a parameter jumps, recognize the parameter, estimate the parameter and, of course, estimate the state. Especially in our method, a sensitive filter algorithm and an iterative scheme are used in an extended Kalman filter to improve the estimation accuracy of the jump quantities.
This method is developed from the failuer detection method considered by C. N. Shen, A. S. Willsky, et al. for linear systems. We apply their method to nonlinear systems. This method may be applicable also to the system with more varieties of patterns than those of the jump type by introducing the multi-hypotheses. Satisfactory results are obtained in the numerical study for the 2nd order system with a jump type pole and jump type gain parameters.
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Takashi AMEMIYA
1979 Volume 15 Issue 4 Pages
429-435
Published: August 30, 1979
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The object of this paper is to extend the condition presented in the previous paper for the stability of the equilibrium point of the generalized Volterra equations. In the previous paper, we proved that if the vector function describing the growth rate of species is an
M-function and if the invariant set of this function is not bounded for any variable and contains the original point then the equilibrium point is globaly asymptotically stable.
In this paper characteristics of
M-functions and of more general skew-decreasing functions are studied. It is proved that for the global asymptotic stability of the equilibrium point of the generalized Volterra equation to be an
M-function for the growth-rate function is a sufficient condition without any serious restriction.
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Yasuhiko TAKAHARA
1979 Volume 15 Issue 4 Pages
436-442
Published: August 30, 1979
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This paper is concerned with a category theoretic treatment of the realization theory of a basic linear system. In order to make a categorical problem of the realization we introduced two categories, the category of basic linear functional systems
BLFS and that of basic linear dynamical systems
BLDS, in addition to the category of basic linear systems
BLS defined in another paper. The
BLFS corresponds to a class of so-called“experiments”and is formulated as a category by extracting conditions when an experiment can be modeled into a basic linear system. The
BLDS corresponds to a class of state space representations of basic linear systems and, similarly, their essential properties are extracted to be formulated as a category. Based on these categories, it was shown that two functors, a realization functor
F1:
BLFS→BLS and a representation functor
F2:
BLS→BLDS exist. It was also shown that
F1 and
F2 yield a universal and a co-universal map with respect to their corresponding forgetful functors
G1:
BLS→BLFS and
G2:
BLDS→BLS, respectively and that those maps correspond to categorical representations of controllability and observability. Finally, a category theoretic meaning of a minimum realization of a basic linear system is discussed.
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Yasumichi HASEGAWA, Tsuyoshi MATSUO
1979 Volume 15 Issue 4 Pages
443-450
Published: August 30, 1979
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We have established in (1) the realization theory of discrete-time linear representation systems (l.r.s.). The main theorems say that for any input response map
a∈F(Ω, Y), there exist at least two canonical (quasi-reachable and distinguishable) l.r.s. with the behavior
a, and if σ
1 and σ
2 are two canonical realizations of
a, there exists a unique isomorphic linear representation system morphism
T: σ
1→σ
2, where Ω is the concatenation monoid of a set
U of input values and
Y is a set of output values which is a linear space over a field
K.
In this paper, we investigate details of finite-dimensional l.r.s. (f.l.r.s.). A necessary and sufficient condition of the quasi-reachability [distinguishability] of a finite-dimensional linear
U-action with an initial state [a linear readout map] is given. There are given representation theorems of isomorphic classes of canonical f.l.r.s.. In an isomorphic classes of canonical f.l.r.s., there exists at least one strongly quasi-reachable [strongly distinguishable] f.l.r.s.. A necessary and sufficient condition for the input response map
a∈F(Ω, Y) to be the behavior of a finite-dimensional l.r.s. is given.
When the set
U of input values is finite, the preceding results are rewritten in a more practical form as follows.
In an isomorphic class of canonical f.l.r.s., there exists a unique quasi-reachable [distinguishable] standard canonical system.
The following conditions are equivalent: (1) an input response map
a∈F(Ω, K) is the behavior of a f.l.r.s., (2) the rank of the infinite Hankel matrix H
a is finite and (3)
a is rational. A procedure to obtain the quasi-reachable standard canonical system from an input response map
a∈F(Ω, K) is given.
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Naoya KAWASAKI, Etsujiro SHIMEMURA
1979 Volume 15 Issue 4 Pages
451-457
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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In this paper, a method of constructing a linear state feedback law for a linear control system is proposed. This method yields a state feedback law by which all poles of the closed loop system are located in such area that is desired for the good response of the closed loop system as well as for its stability. The advantage of this method lies in its easiness in calculating a feedback gain. It is only necessary to solve a nonlinear algebraic matrix equation for once. When the eigenvalues of an original system matrix are known, it is readily possible to locate the poles of the closed loop system by this method without calculating eigenvalues of the closed loop system matrix. Therefore no iteration is required before one gets a satisfactory result, whereas a usual optimal regulator problem needs iterations to locate the poles of the closed loop system in the desired area. This method is also especially powerful for a high dimensional system to which the pole assignment method is too complicated to apply.
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Masaya TANUMA
1979 Volume 15 Issue 4 Pages
458-465
Published: August 30, 1979
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A model reference adaptive system for a linear system with transport delay is newly designed by using Lyapunov's stability theory. The process to be studied in this paper, consists of a linear lumped parameter system having unknown variations in parameters and a plug flow process having unknown variations in reaction coefficients. A reference model is described by time invariant ordinary differential equations and partial differential equations.
In order to study adaptive control law, the author introduces a error equation which can describe the difference between process and reference model. The problem of designing the adaptive control system can be formulated as that of determining the stable control law for this error system with transport delay.
For this error system with transport delay, a Lyapunov's functional is assumed. Then, the adaptive control equations that can make the time derivative of the Lyapunov's functional negative-definite, are derived. The proposed adaptive control is a feedback control of state variable errors about transport delay process as well as errors about the lumped parameter process. Stable control gains for adaptive controller can be obtained by solving the partial differential equations of a Lyapunov's type.
From the simulation results for a scalar system with transport delay, it is found that the proposed adaptive control system can adapt the process to the reference model in the presence of variations in the reaction coefficient of the transport delay as well as in the parameters of the lumped process.
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Tadashi KONDO, Hiroyuki TAMURA
1979 Volume 15 Issue 4 Pages
466-471
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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In this paper, a revised GMDH (Group Method of Data Handling) algorithm, which automatically selects optimal intermediate polynomials instead of partial polynomials in each selection layer, is developed. In the previous GMDH algorithms, the partial polynomials, in which the intermediate variables are the input variables in each selection layer, have been estimated and accumulated in the multilayered structure. So, in general, it is difficult to identify exactly the physically meaningful structure between the input and the output variables. The revised GMDH algorithm in this paper generates optimal intermediate polynomials in each selection layer, which express the direct relationship between the input and the output variables, so as to minimize the Akaike's Information Criterion (AIC) evaluated by using all the data. Therefore, the physically meaningful structure can be identified when the characteristics of the system are well reflected in the data. The revised GMDH algorithm is applied to the input-output data observed in a simple kinematic system, and we try to discover the Newton's second law. The result obtained is compared with that obtained by the previous GMDH algorithm of using partial polynomials.
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Nariyasu MINAMIDE
1979 Volume 15 Issue 4 Pages
472-477
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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In the present paper, filtering, prediction and smoothing problems are investigated in a unified manner by introducing a function space description. To these estimation problems, a unified expression for the mean square error is first obtained with the help of linear operators. An original problem of finding a linear minimum mean square error estimator is then reduced to a dual problem of finding an optimal element in a Hilbert space that minimizes a quadratic form associated with the mean square error. By solving this optimization problem, a Wiener-Hopf equation in the function space description is derived.
To each of these filtering, prediction and smoothing problems, the corresponding explicit expressions of this dual problem and of a Wiener-Hopf equation in the function space description are obtained. It is shown that a linear optimal regulator is dual to a filtering problem (or to a prediction problem), while a linear optimal regulator with a jump condition on the state variable is dual to a smoothing problem. The basic results of an estimation problem reported earlier are derived in a simple and perspective manner by solving these dual optimization problems.
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Yoshifumi SUNAHARA, Akira OHSUMI, Yuichi DANJO
1979 Volume 15 Issue 4 Pages
478-485
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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The purpose of this paper is to present a signal detection approach where the signal to be detected is corrupted by a colored random noise whose statistics are unknown.
First, the problem of identifying the unknown noise statistics is solved by computing the likelihood-ratio functions under the
a priori assumption that the unknown noise covariance has one of the preassigned forms. Secondly, the detection procedure is given based on the identification of noise statistics by using the likelihood-ratio concept. The latter half of this paper is devoted to present an application of the general theory to practical problems in the case where preassigned signals are contaminated by a real observed random noise with unknown noise statistics. Results of computer experiments are shown to demonstrate the feasibility of the proposed method.
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Minoru INAMURA, Hiromichi TOYOTA, Kazunori UEDA, Takashi OOMORI, Sadao ...
1979 Volume 15 Issue 4 Pages
486-491
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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Remotely sensed multispectral images are analyzed by the methods of maximum likelihood, Euclidean minimum distance and correlation etc. But a new fast analyzing method is searched because the processing speed of the conventional is slow.
This paper describes the multispectral image processing by means of a binary decision tree. To appreciate the ability of the image analysis, the efficiency of the binary decision tree is compared with the efficiency of the maximum likelihood method under the same conditions.
As a result, the processing speed of the binary decision tree was shown to be twenty times as fast as that of the maximum likelihood with a nine-classes six-features classification. Moreover, the processing time of the binary decision tree method does not increase even if the number of the features increses. This property is another strong point of the binary decision tree. On the contrary, the processing time of the maximum likelihood method is in proportion to the square of the number of selected features. On the other hand, the classification accuracy of the binary decision tree was about equal to that of the maximum likelihood method.
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Mamoru KAWAHARA, Ken-ichi TAKI
1979 Volume 15 Issue 4 Pages
492-497
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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This paper describes the highly accurate and widely applicable tracking control system which guides a welding torch along the line of a joint. The control system includes a servomechanism, an optical image sensor and an image processing apparatus. The optical sensor consists of a He-Ne gas laser and a solid-state image sensor, and detects the cross section pattern of a welding groove using the Light-Sectioning Technique. The image processor is all but a micro-computer and processes the visual information obtained by the image sensor, and then estimates the position of the welding groove center using the statistical estimation method. The estimated data are the output of the processor and are used as reference of the servomechanism. The data are stored at the same time in the Memory because they may be used again as an objective value of tracking control according to demand.
This tracking control method has been applied to the penstock welding apparatus and to confirm its practical usefulness.
A summary of the results is shown below.
(1) The sensor mentioned in this paper is suitable for remote detection, and so has advantage. For example, the sensor is not consumed by contact and avoid of damage due to welding heat.
(2) The detection is made with a high accuracy using a micro-computer and relying on the method of statistical inference.
(3) The accuracy of the measurement can be determined arbitrarily by adjusting the magnification of the image sensor's optical system. For example, under the condition in which the image sensor views 50×50mm
2 area on the steel surface, the maximum detection error is 0.22mm and the maximum tracking error is 0.34mm.
(4) This tracking control method is applicable for every groove shape and also applicable for the monitoring of a bead shape, and the measurement of a gap between two steel plates, the measurement of a flatness offset between two surfaces.
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Fumio MIYAZAKI, Suguru ARIMOTO
1979 Volume 15 Issue 4 Pages
498-504
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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In the last decade, a number of papers studying from the control theoretical viewpoint the stability and optimization of the walking pattern for biped locomotion systems have been published. Various dynamic models for the biped locomotion have been proposed, but most of them represent only a partial feature of the motion. To express fully both functional and morphological features of the motion, it is necessary to adopt a model with many degrees of freedom. However, such models of a high degree are not adequate for the analysis.
To dissolve such an antinomy, this paper proposes a new method of analyzing the biped locomotion system by the use of singular perturbation. It is shown that if the body mass is sufficiently larger than the leg mass the original biped motion can be represented by two divided modes, a fast mode and a slow mode, owing to the singular perturbation technique. The slow mode corresponds to the angular momentum equation about the center of gravity in regard to the fixed point. The fast mode which decays away rapidly under some conditions represents the fast phenomena of the biped locomotion. Based on this fact, a control algorithm for tracking the trajectory of the motion is presented. Finally, a control law of stabilizing the periodic locomotion (gait stability) is suggested by considering only the slow mode.
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Kazuo TANIE, Susumu TACHI, Kiyoshi KOMORIYA, Minoru ABE
1979 Volume 15 Issue 4 Pages
505-512
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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In this paper, in order to develop the spatial electrocutaneous communication system with minimum size of hardware, fundamental experiments were performed to provide with various locations on the skin a continuously variable sensation by utilizing the phantom sensation. Two sets of electrodes were located on the skin just above the biceps brachii and stimuli were presented to each electrodes either simultaneously or with time delay. The effect of relative magnitudes and time delay on the phantom sensation was experimentally studied. The following results were obtained. (1) The magnitude-difference cue was found more distinct than the temporal-difference cue. The phantom sensation caused by a magnitude-difference cue becomes less clear as the energy level becomes high (above 40erg/channel), and as the interval of pulse stimuli becomes short (under 50ms). (2) The relation between the mental location of the relative magnitude phantom sensation and the ratio of the magnitude of stimuli
E0/E1, in which
E0 and
E1 are the energy levels of stimuli simultaneously presented to adjacent locations respectively, is linear, and does not depend on the stimulus energy level (
E0+E1) except in the vicinity of each electrode, where the relation depends on the energy level. (3) The just noticeable difference (
jnd) of mental location has a maximum value at the central position between the two electrodes and a minimum value at the neighborhoods of the electrodes. The maximum information transmission rate calculated from
jnd of mental location depends on the distance
d between the two electrodes and ranges from 2.0 to 3.0 bits for
d between 50 and 150mm. (4) The advantages of employing the technique of the phantom sensation are that it can reduce the number of electrodes required for spatial electrocutaneous stimulation and also that it can distribute stimuli more densely without the restriction of electrode sizes.
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Hikaru MATSUMIYA, Makoto KIMURA
1979 Volume 15 Issue 4 Pages
513-518
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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A two-dimensional incompressible turbulent jet issuing nearly parallel to a side-wall of finite length develops the pattern of either a reattaching flow or a separated flow. When the side-wall is long enough, the jet reattaches naturally to the wall. The jet is thought to be unstable and separate, if the wall is considerably short. In the present paper, an analytical model is discussed. The calculated results for steady phenomena of a wall-reattaching jet show good agreement with experiments. Experimental observations showed even if the wall length is shorter than the offset distance, the separated jet can be forced to reattach to the side-wall by an instantaneous control flow and be kept stable. Therefore, from the viewpoint of controlling flow direction or flow state, three regions along the wall, length are defined as follows: (I) Natural reattaching region-when the side-wall is long enough, the jet reattaches naturally to the wall. (II) Bistable region-in a certain section of the wall length, both the separated flow and the forced reattaching flow are possible, either of which is selectively chosen by a control flow and kept stable. (III) Separated region-the jet never reattaches, if the wall is very short. These three regions are distinctively divided by two lines; a natural reattachment limit line and a forced reattachment limit one. It was confirmed that Reynolds number has no influence either on the overall flow pattern, or on the detailed construction of the flow.
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Jun NAKAZOE, Masao HOTTA, Zen-uemon ABE
1979 Volume 15 Issue 4 Pages
519-525
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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The noise and drift set a limit of lowest input voltage of a DC amplifier. To decrease the effects of noise and drift, a suitable modulating amplifier is used instead of a direct coupled amplifier.
The advantages of the 2nd harmonic type of Magnetic Modulator for this porpose have been discussed by Williams and Noble in 1950. Afterwards, the authors proposed the ultra low noise Magnetic Modulator used Ferrite core which has the smallest value of 2.6×10
-6A/m referring to the input noise of Magnetic Modulator.
In this paper, we attempt to apply the ultra low noise Magnetic Modulator to a DC amplifier which has an input impedance as low as several hundred ohms or less and discuss theoretically the limitation on the low input voltage due to noise and drift on the modulator core, and find that the input drift voltage of the DC amplifier using the Magnetic Modulator can be held at 5×10
-9V/hr, when the source impedance of this DC amplifier is 5 ohm. And more, to consider the limitation for a small signal on DC amplifier, we compare ours with other types of DC amplifier which are incorporating mechanical choppers, semiconductor choppers and so on.
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Osamu SENDA, Teruko INAMATSU
1979 Volume 15 Issue 4 Pages
526-531
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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A simple and sensitive transducer making use of a vibrating glass tube was applied for detecting the small difference of density between water samples.
The glass tube of about 10cm long filled with a sample of about 1cm
3 is vibrated electromagnetically in its bending mode and the variation of the vibration frequency due to the difference of density of water in the tube is detected. For compensating the effect of temperature variation, a pair of vibrating tubes are used together and the density of a water sample is compared with that of standard water.
The procedure of measurement is as follows. The standard water is poured into one of the vibrators and the sample into another, the vibration period of each vibrator is measured with an electric counter, then the difference of density between the standard water and the sample water can be calculated from the difference in period.
It has been confirmed that the density can be compared with a better precision than 1ppm only by controlling the room temperature at (20±0.5)°C.
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Tsutomu WADA, Akira SHIMIZU, Minoru TAKAGI
1979 Volume 15 Issue 4 Pages
532-538
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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In a fluidic circuit, it is desired that each device holds a proper characteristic independent of another device. It is known that a vent in control channel would be useful for that purpose. Although this type of problem has been investigated by some workers, the results are still insufficient to design an optimum control channel.
Then, we investigate experimentally the problem on a large scale model of control channel with various vents. The main factors investigated are as follows: (1) the one-way transmissibility and the independency of signals, (2) the power transmissibility from the input nozzle to the control duct, (3) the switching characteristics with respect to the input port, (4) the time-lag of signal transmission, and (5) the comparison of three types of control channels with four input ports. And the relationships between these factors and the geometries of control channel are made clear. The results can serve the purpose of the design of an optimum control channel.
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Fumio MATSUDA, Minoru UEDA
1979 Volume 15 Issue 4 Pages
539-544
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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A new method to automatically measure thermal diffusivity incorporating analogue computer technique in the previously used pulse method is explained.
In the pulse method, a high-intensity heat pulse such as a laser pulse is absorbed in the front surface of a thermally insulated specimen, and the resulting temperature rise at the rear surface is measured by a thermocouple and recorded with an oscilloscope and a camera. The thermal diffusivity is calculated from the specimen thickness and the time lapse required for the rear surface temperature to reach one-half of the maximum value. This time lapse is determined by the graph of time V.S. temperature of the rear surface.
We propose the new system to decide the thermal diffusivity without a graph or calculation. The fundamental principle of it is the same as the above mentioned measuring method except that an analogue computer is led into the system and the temperature of the rear surface is sampled twice after the heat pulse absorption. The time interval between the two samplings, is fixed and the sampled values are held in an analogue memory device. The ratio of the temperature of the 1st sample to that of the 2nd sample must be different when the thermal diffusivity varies. The variation of the ratio of the two samples is simulated in the analogue computer with the variable of the thermal diffusivity. By this simulation the value of the thermal diffusivity of the tested specimen is decided when the simulated ratio of two sample temperatures is equal to the measured ratio on the specimen.
The simulator is composed of integrators, comparators, multipliers, sample-holders and a thermal diffusivity indicator. With this new system the thermal diffusivity is determined with the accuracy of ±10%.
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Constructing a Utility Function Based on the Concept of Convex Dependence
Hiroyuki TAMURA, Yutaka NAKAMURA
1979 Volume 15 Issue 4 Pages
545-548
Published: August 30, 1979
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Firstly, we point out that the two attributes, pollution and consumption, are not mutually utility independent, and therefore, an additive or multiplicative utility function is not appropriate for analyzing the trade-off between pollution and consumption. We, then, show a methodology for constructing a two-attribute utility function for pollution and consumption based on the concept of convex dependence which is a new extended concept of the Keeney's utility independence.
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Toshiyuki KITAMORI
1979 Volume 15 Issue 4 Pages
549-555
Published: August 30, 1979
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In this paper a unified method is developed which enables one to design control systems of various types in the situation that the dynamic characteristics of the controlled process are not known perfectly.
The control system to be designed is to satisfy the following specifications:
(a) It has zero steady-state error.
(b) It has adequate damping characteristics.
(c) (a) and (b) satisfied, it has a shortest rise-time.
For the design, a sequence of parameters is found suitable to represent the dynamics of an element or a system. The sequence is equivalent to that of moments of the impulse response in the sense of I. F. S. (independency from the successors) which plays a fundamental role in the development.
The specifications above are also reorganized into a sequence of conditions on the parameters of the control system to be designed.
Owing to the I. F. S., any truncated sequences of conditions and parameters give rise to a formula to design a compensator and/or a controller based upon partial knowledge about the controlled process. The formula has a kind of matching property, so that the simpler control mode calls for as less the number of controlled process parameters known.
Formulas for the PID and the I-PD control schemes are derived, and some results are demonstrated in step response curves, which show the effectiveness of the method. For an overdamped process, the response speed increases as the number of controller parameters, whereas the damping characteristics remain unchanged. Even for an unstable process, a satisfactory control system is brought about when a sufficient number of controller parameters are employed.
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Naoya KAWASAKI, Etsujiro SHIMEMURA
1979 Volume 15 Issue 4 Pages
556-557
Published: August 30, 1979
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Eiichi BAMBA
1979 Volume 15 Issue 4 Pages
558-559
Published: August 30, 1979
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Shunshiro OONISHI, Shinya KATO, Konosuke AKITA
1979 Volume 15 Issue 4 Pages
560-561
Published: August 30, 1979
Released on J-STAGE: March 27, 2009
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