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Volume 6, Issue 1
Displaying 1-13 of 13 articles from this issue
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Yasuyuki FUNAHASHI, Kahei NAKAMURA1970 Volume 6 Issue 1 Pages 1-8
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe optimal pursuit problem and a variant of the final value control problem being set in the Hilbert space are considered in this paper, and these two problems are solved in the same framework using the orthogonal projection. The product space is constructed from, input (control) and output (or state) spaces, the norm of which coincides with the performance index itself. The operator relating input to output (state) is represented by its graph in the product space. Then the optimal control is obtained as the orthogonal projection of the desired output (state) onto the graph. The orthogonal projection method shows that even for the improper systems, such as differentiator, the optimal pursuit problem is worthwhile to be considered and its unique optimal control exists. This method offers the optimal control in the explicit form. The computational procedure for obtaining the optimal control is straightforward and then can be easily performed.View full abstractDownload PDF (912K) -
Noriyuki MATSUBARA, Ichiro SUGIURA1970 Volume 6 Issue 1 Pages 9-17
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIt has been known that there are many systems that have the same optimal feedback control law and the same solution of the Hamilton-Jacobe partial differential equation as ones that given optimal control systems have.
In this paper, if the situation stated above happens among systems, they are called to be “equivalent”, and when the optimal feedback control laws coincidence happens, they are called to be “subequivalent”. Thus the equivalent or subequivalent condition is thoroughly studied and sought.
For example, the necessary and sufficient conditions for equivalence between such two systems as,
x=f(x, u, t)J=∫tft0L(x, u, t)dt
and,
x=f*(x, u, t)J=∫tft0{L(x, u, t)+M(x, t)}dt
is obtained, and the sufficient condition for subequivalence between such two systems as,
x=f(x, u, t)J=∫tft0L(x, u, t)dt
and,
x=f*(x, u, t)J=∫tft0L*(x, u, t)dt
is also obtained.
By using these conditions, equivalent or subequivalent classes of optimal control systems can be generated. This paper demonstrates to be able to extend the well-known linear regulator system to a broder class of the system.View full abstractDownload PDF (1064K) -
Fuhito MIYAKE1970 Volume 6 Issue 1 Pages 18-23
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSA new detecting method and an optical element realizing the method are invented for the non-contact precise detection of positions of contours of opaque bodies. The method is applied to a barometer to detect the position of the mercury surfaces.
The principle of detection of this method is to catch the instant of disappearance of light in a dark field of view. This method has not the weaknesses which the usual sighting ring has intrinsically, that is, the disadvantages of penumbra, of diffraction of light, of double focussing and of finite aperture of sighting elements, and of dazzling light remaining in the field of view.
The optical element named Complex Slit is a set of slits composed of a triangurar slit and a rectangular one, the component slits being fixed opposite to each other with sufficient spacing on a rigid body. The summit point of the triangular slit and the summit side of the rectangular one form the detecting plane. When the Complex Slit is driven so that the detecting plane approaches an object placed between the component slits, a triangular spot of light is formed by the silhouettes of the slits and that of the object. A sighting element follows to be kept in the extention of the detecting plane. While the approach proceeds, the sighting element observes that the light spot becomes smaller and smaller and then disappears. The position where the spot of light just disappears is adopted as the detecting point. The precision of detection of this method by unaided eye is proved to be several micrometres in terms of standard deviation, and the personal errors to be of the same order.
A self-calibrating type precision barometer with four Complex Slits is manufactured on trial, whose precision is proved to be about twelve micrometres.View full abstractDownload PDF (2640K) -
Zenta IWAI1970 Volume 6 Issue 1 Pages 24-29
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn the design of control systems it is often necessary to construct estimates of state-variables which are not available by direct measurement. If the system is linear, its state vector can be approximately reconstructed by building an observer which is itself a linear system driven by the available outputs and inputs of a plant.
In this paper it is shown that the design of an observer for an n-th order plant with p available outputs can be reduced to the design of p separate observers for single-output subsystems under some conditions. This result is based on a canonical form developed in Lemmal and the theorem obtained by J.J. Bongiorno and D.C. Youla. The use of observers for indirect control systems is discussed. It is olse shown that if the nonlinear element φ(σ) contained in the indirect control system satisfies the Lipschitz condition, then the observer can be used without loss of absolute stability.View full abstractDownload PDF (686K) -
Eiju MATSUMOTO, Yoshinori NAGATOMO, Masato YAMAMOTO1970 Volume 6 Issue 1 Pages 30-38
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn the process instrumentation field, conventional low level amplifiers are employing modulated carrier type DC amplifier. On the other hand, in these days, very low drift monolithic linear integrated circuits become available.
In this paper some application techniques of linear integrated circuit to 10mV DC level direct coupled amplifiers are considered.
From the theoretical analysis of non-inverting current output amplifier, thermal drift and input noise make ultimate limitation to the input signal level.
Three kinds of circuits are presented.
(i) μA 702 equiralent device applied with tiny component oven using transistor collector power dissipation as heating source.
(ii) Configuration with temperature controlled chip integrated circuit μA 727.
(iii) Configuration with dual transistor of equal VBE operation as preamplifier of integrated circuit.
From the experimental results, (i) has wide applications to field mount mV/mA converters.
(ii) has troubles of reliability and long term drift characteristics that limit the usefulness of thermal chip control. (iii) offers the most excellent low level drift characteristics and stability than the others, and has a possibility of 3mV DC input amplifier.View full abstractDownload PDF (2380K) -
Koichi IINOYA, Nobutoshi TANAKA, Matsuhiro KIMURA1970 Volume 6 Issue 1 Pages 39-44
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe concentration method for flow rate measurement is substantially distinct from other methods. It is often used to measure flow rate of water through a water-turbine of power stations, but few reports of measuring gas flow rate by the concentration method have been published. Some experimental results of flow rate measurement of air by this method is herein presented. The flow rate of air is obtained by measuring both injection rate of inert gas and inert gas concentration of mixed gas, and then substituting these values into eq. (1) or (2).
The accuracy of this method depends on whether the inert gas is perfectly mixed or not. In other words, after injected inert gas is mixed with the main flow through a mixing part, the inert gas concentration must be uniform over a sampling plane normal to the direction of flow. In this work, it is examined how long distance from an elbow is required in order to attain a stable concentration profile, when an elbow is used as a mixing part and the flow rate of air is 0.5 to 1.5m3/min. in 11/2, 2, 21/2 and 3 inches standard gas pipes.
Consequently, the stable concentration profile is attained at about 80cm downstream from an elbow, and its distance does not depend on both the main flow rate of air and the pipe diameter. The accuracy of this method using an elbow is within ±1%. The dispersion of measured values is within ±2% in this work. In spite of some insufficient results, this work may be the knowledge to measure gas flow rate by the concentration method.View full abstractDownload PDF (761K) -
Kimio KANAI1970 Volume 6 Issue 1 Pages 45-53
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSWhen optimal control law of system which is described by linear partial differential equations is found, its Riccati equation becomes usually non-linear partial differential equation. Since the optimal feedback gain is the solution of the infinite dimensional Riccati equation or Riccati type partial differential equation, exact solution can not be solved and it is impossible to construct closed-loop system analytically. In this paper, the computational problems associated with the numerical solutions of a linear diffusion process are treated and finite approximation taking N divisions can be shown to be solved and then by increasing the number of division, the solution to the exact feedback gain is approached, and might be shown to be considered as optimal feedback gain in terms of distributed parameter systems. Moreover, infinity of state variables and control might be estimated using those results from practical standpoint. While it is natural to consider that accuracy increases according to the number of division in such an above method, the resulting controller will become complex.
The accuracy of a finite difference solution to a partial differential equation in terms of the convergence of the difference scheme is discussed. Those problems are concluded numerically with the aid of performance criterion's convergence that this procedure produces results within acceptable engineering accuracy.View full abstractDownload PDF (4106K) -
Kin-ichi KOMIYA1970 Volume 6 Issue 1 Pages 54-58
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSWhen the turbulence is detected at two points along the flow direction, the fluid transit time may be equal to the delay time which makes the cross-correlation function of the turbulence maximum. Therefore the flow velocity is determined by this transit time and distance between two detecting points. An analytical expression of the cross-correlation function of the turbulence is derived under the following assumptions.
The behaviour of the fluid particles is the same as that of a random walk. The displacements of the fluid particles due to diffusion corresponding to the longitudinal and transverse velocity fluctuations are not correlated. The auto-correlation function of turbulence is expressed approximately e-ατ2, where α is a constant and τ is delay time.
In a series of experiment the turbulence of air flow is detected by hot-wire anemometers at two points on the center axis of a circular pipe. Comparing with experimental results and theoretical expression, decay and half-width of the cross-correlation functions are discussed.
Transit times which are determined by this correlation method and those by Pitot-tube velocity meter are compared, and those values are coincidented with each other under the ordinary conditions.View full abstractDownload PDF (544K) -
Takashi SATO, Masanori MORIYA, Atsunobu ICHIKAWA1970 Volume 6 Issue 1 Pages 59-67
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn this paper, the conceipt of one-way interacting control of linear multivariable systems is proposed and its general design procedure is studied. The control system is called “one-way interacting”, when its closed loop transfer matrix is a triangular one.
Both the transfer function approach and the state space approach are employed to analyze the system, and the necessary and sufficient conditions for the one-way interacting control are given.
The merit of this system is that more parameters can be used to design its controllers than the conventional non-interacting control system. It is also pointed out the characteristic equation of the stability criteria can be calculated for each controlled variable independently.
A comparative example illustrates that one-way interacting control works better with simpler controllers than the non-interacting ones.View full abstractDownload PDF (943K) -
Tomoaki MORINAGA1970 Volume 6 Issue 1 Pages 68-73
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSPressure reducing valve is the most widely used self-operating regulator, but its characteristics do not seems to be revealed clearly in publications. It has a intrinsic drawback, that is, the reduction of offset by means of increasing gain cannot be attained without increasing its instability because of its proportional control mode. It often oscillates abruptly, and the oscillation occurs in most cases, if the friction caused by the pressure-sealing O-ring is removed. But the friction causes at the same time the dead zone and hysterisis. Therefore, the desirable thing is the reducing valve, which causes small offset and at the same time has a good stability without friction.
Dynamics of a direct-operated pressure reducing valve is analysed here linearly, and the stability conditions are derived and simplified by neglecting very small terms. The simplified stability condition indicates the improving policy of the valve characteristics, that consists of the reduction of mass of the moving parts, the increase of resistance of the port which introduces output pressure into the diaphragm chamber, and the increase of the damping factor of the moving parts.
Experimental data show well the tendency predicted by the analysis.View full abstractDownload PDF (774K) -
Takeshi SAITO1970 Volume 6 Issue 1 Pages 74-80
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn the identification problem of linear dynamical systems whose states can not be measured directly, the estimated values of parameters do not always converge to the true ones. One of the reasons is that the system considered is not a minimal machine and that there exist systems which are equivalent to the original systems. In this connection, p-stochastic equivalence and stochastic equivalence of dynamical systems are defined and its necessary-sufficient conditions are obtained for linear dynamical systems.
On the other hand, an algorithm of identification of linear dynamical systems using random test input and a least mean square type stochastic approximation is derived and in this algorithm, some conditions by which parameters of the system are identified uniquely are discussed with relation to the conditions of stochastic equivalence.View full abstractDownload PDF (717K) -
Seiji TSUCHIYA1970 Volume 6 Issue 1 Pages 81-88
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper describes a method to construct the logical circuit based on the fail-safe concept. As the actual device to realize the fail-safe three valued logic, C-type fail-safe logical circuits are developed by the author, the key component of which is fail-safe threshold logical operational oscillator composed of resistors and semiconductors.
In these circuits the truth values 1, 0 and 1/2 correspond to the voltages +V, -V(|V|>|E|, ±E: threshold voltage) and v(|E|≥|v|≥0), respectively. The logical functions are expanded in the canonical forms and the logical circuits to form a complemental system by themselves are completed by the use of fundamental elements.
Because the fundamental circuits for this system can be easily integrated, a highly reliable fail-safe three-valued logic system is considered to be obtained.
In the system using C-type fail-safe logical circuits, the output signal carries not only logical information but also the checking signal. If the voltage corresponding to either 1 or 0 appears at the output, it means that there is no failure in the circuits and that the system is normally operating. Therefore, no special device is needed to check the system.View full abstractDownload PDF (1518K) -
Hajime MAEDA, Masao IKEDA, Shinzo KODAMA1970 Volume 6 Issue 1 Pages 89-95
Published: 1970
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe object of this paper is to extend the sufficient condition for the stability of feedback systems with backlash by using the Passivity Theorem of Zames. It is assumed that the feedback loop consists of an asymptotically linear, monotone nondecreasing nonlinearity, a linear time-invariant system consisting of an integrator and a strictly stable subsystem characterized by the impulse response, and a transducer with backlash.
The stability criterion for the freedback system is of the form
Re[(α+Z(iω))(H(iω)+1/k)]≥δ>0, 0≤ω<∞
where H(iω) is the frequency response of the linear subsystem, k is the incremental gain of the nonlinearity, α is a nonnegative number, and z(t), the inverse Fourier transform of Z(iω), satisfies the conditions: z(t)≥0, z(t)≤0, z(t)≥0, t≥0.
When the asymptotic linearity restriction on the nonlinearity is removed, he stability criterion is of the form
Re[H(iω)+1/k]≥δ>0, 0≤ω<∞
An example is given to compare these criteria with the well-known criteria.View full abstractDownload PDF (793K)
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