The composite-system type analysis is generally acknowledged to be useful for a stability study of large-scale systems. However, in many cases it is highly difficult to construct Lyapunov functions for subsystems with best parameters. In this paper a method to construct Lyapunov functions of the subsystems suited for the composite-system analysis based on the frequency-domain stability condition is given. For that purpose we first extend the Lyapunov stability theorem of composite systems and then show that Lyapunov functions of subsystems which satisfy all the conditions of the above extended theorem exist if the L₂-stability condition given in the frequency domain is satisfied. In the proof of the last statement, a method to construct the Lyapunov functions of subsystems is included. Using this result it is easy to construct a Lyapunov function of the whole system.

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Optimum night temperature control for the leaf-vegetables. Recently the importance of stable and efficient production in agriculture is pointed out, many green houses are built and the plant factory is in actual operation. The optimum growth of the plants by the regulation of the environment is very important. The air temperature control at night is economically more profitable than that in the day time. Therefore, the effect of an optimum night temperature control is considered in this paper. The experimented vegetable is lettuce, grown by the hydroponic culture in the growth chamber, and the dry-weight is selected as the plant character.
The dry-weight of the plant decreases by the respiration at night. But the water in the body of the leaves is necessary for the photosynthesis in the next day. Therefore the optimum night temperature must be determined by the balance of the respiration and the water absorption. The relationship between the water weight change of plant and the night temperature was examined by the plant weighing apparatus. The photosynthetic rate was measured by the mass-spectrometer and the dry-weight change in the daytime is described by the mean light intensity, the mean temperature, the total weight and the total-weight/dry-weight ratio (η) in the daytime.
From these results, the optimum night temperature, at which the dry-weight change from the beginning of the night to the end of the next daytime is maximum, was calculated with the maximum principle.
The result obtained is summarized as follows.
If either (1) or (2) is satisfied, the night temperature should be raised initially and lowered rapidly at the end.
(1) In the next day, the light intensity is high, the temperature is suitable, and the total weight of plant is light.
(2) In the present day, the diurnal humidity is low and the light is high.
This night temperature control is a predict control and the optimum temperature depends on the weather of the next day. It is expected that the plant growth with the temperature controlled by this method is over 10% faster than with the fixed temperature.

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In this paper synthesis of low sensitivity optimal feedback configuration for distributed parameter systems is discussed.
First, sensitivity functions and their equations of optimal feedback configuration are defind and derived for the two types of system parameter variations; i. e., the ordinary system parameter variation and the variation of initial conditions.
Secondly, a quadratic performance index is defined for the sensitivity functions. The gradient function is derived for the feedback compensating operator which needs only the output signals of the plant concerned. Thus, a generalized gradient method can be applied to this problem.
Thirdly, the dynamical model for the main problem is given by a set of linear partial differential equations which are reduced to equivalent infinite dimensional ordinary differential equations.
Finally, the theory discussed above is applied to a modal control system.

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Conventional state regulators which are optimal with respect to a quadratic performance index are proportional controllers, and therefore do not, in general, perform satisfactorilly in the presence of constant disturbances. In this paper, a method to design an optimal regulator incorporating integral feedback control functions for a linear system with transport delay is presented.
The problem is formulated as that of minimizing a quadratic performance index containing new state variables which are integrals of the output variables. The problem is solved by the conventional regulator theory for a system with time lags.
The developed optimal regulator possesses the function of a proportional feedback control and of an integral feedback control. The proportional control can improve response and stability by using the state variables in the transport delay process as well as state variables in the lumped parameter process. The integral control can eliminate offset errors in the output variables.
Simulation results show that the proposed control system is superior to the conventional optimal regulators in the presence of steady disturbances.

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The pole assignment problem in multivariable delay systems is investigated. The delays may be lumped or distributed, and contained in the state and the input. Delay operators are introduced so that the study can be made within an algebraic framework. Sufficient conditions are found and a method for obtaining feedback matrices is proposed based on the algorithm used for delay-free systems. The study of pole assignable structures is also done and two types of structures are found.

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This paper presents a method of determining the optimal feedback gains of a PI control for multivariable linear systems. The control law considered here is an output feedback, and the cost performance index is a quadratic type one which does not contain the integration of the output error or the time derivative of the input. The necessary condition which minimizes the cost performance index is given by the nonlinear simultaneous matrix equations which can be solved by the gradient technique.
This method is based on the fact that, in the steady state, the input u_s is related to the integration of the output error, z_s, as u_s=G₁z_s, where G₁ is the feedback gain matrix of the integral action. Using this relation, we can obtain the feedback gains of the integral action without modifying the cost performance index as mentioned above.
In this method we need not be concerned with the complex problem of obtaining the relationship between the output overshoot and the weighting matrix of the integrated output error or of the derivative of the input. An illustrative example is given.

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A singular perturbation method may be classified as a sub-optimum method of linear regulators. In the previous paper, it was proposed to adopt the repeated perturbation method with plural parameters in order to decrese the calculational labor. But the method applied only in problems of a limited scope, because the existence conditions had not been fully known.
In the present paper, certain conditions for the existence of the sub-optimal solution are derived and utilized to enlarge the number of problems solvable by this method. These conditions are simpler than those given by Kokotovic et al.. The design procedure developed in this paper is also easier than conventional ones, because the suboptimal solution is obtained by the decomposition of a high-order problem into several low-order problems whose solutions are obtained independently.

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This paper is concerned with a min-max problem for decision-making under uncertainty that excludes even stochastic information. A min-max solution is sought for the problem that a function to be maximized with respect to the maximizer's variables is to be minimized with respect to the minimizer's variables. The solution is rational in the sense that the minimizer makes an optimal decision against the worst case that might be chosen by the opponent (the maximizer).
First we present a necessary condition and a computational method for the min-max problem in which the minimizer and the maximizer are constrained separately. This condition is stated in a form like that of Kuhn-Tucker's Theorem and is closely related to the subgradients of a Lagrangian. The proposed computational method is based on a relaxation procedure. We next study the min-max problem of the minimizer and the maximizer subject to unseparated constraint. It is shown that the results obtained for the separated case can be applied for the unseparat ed one by the use of duality theory.

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The purpose of this paper is to derive the filtering equations for the continuous-time linear stochastic systems with completely unknown disturbance. For the discrete-time system, the filter is already well-known as the information filter. However, since the covariance matrix of the estimate error approaches infinity as the time step tends to zero, the discrete to continuous time limit fails to yield the general solution. Recently Mehra found the solution for the continuous-time Fisher model by an ingenious time-limiting procedure from the corresponding discrete-time filter.
In this paper the lower order filtering equations are derived by a direct procedure, rather than by a time-limiting procedure. Two different methods are attempted to derive the filtering equations. The first method is based on the partition of the state into two components; one is affected by completely unknown disturbance and the other is not. Since the only latter component is estimable, the lower order filter can be easily obtained by the direct application of the standard filtering theory. The alternate method attempted here is to let the input covariance matrix go to infinity. Thus the filter is obtained as the limiting form of the standard continuous-time Kalman filter. Then the equivalence of two filters derived from the respective approaches is examined. To facilitate the development, however, a steady state version of the solution is given for a time invariant linear model. The investigation of the stability of the filter is included.

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This paper is concerned with an operating method which controls the position and orientation of a tool attached to a manipulator hand to translate and rotate at constant velocity.
We propose an operating equation in which the time dependent term is treated as a discrete variable, while it is treated as the continuous variable in the conventional path control-methods. The equation is composed of a transformation matrix, T_h(0) of the hand at t=0 and two constant matrices, P(T) and R(T) which represent the translation and rotation. At t=nT, the transformation matrix, T_h(nT) is represented as follows.
T_h(nT)={P(T)}ⁿT_h{R(T)}ⁿ.
The above equation has a simple form and is proved effective to shorten the calculation time.
Finally, by applying it to control a manipulator with six degrees of freedom, some problems of numerical interpolation are discussed.

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This blackbody is manufactured to be a standard radiator for calibration of the infrared radiation thermometers with a large field angle, the multi-spectral scanner for the remote sensing, etc.
The plane blackbody is made of an aluminium plate which has a radiating area of 200mm×400mm. The radiant face of the plate is covered tightly with quadrate pyramids of which the top angle is 60°, the length of aside line on the base is 1mm and the slopes are covered with a black oxide film, to obtain an effective emissivity greater than 0.99. The temperature of the blackbody is controlled by water at a constant temperature circulating from an outer tube and is maintained at a set temperature in the range from 0°C to 50°C.
The effective emissivity and the distribution of the luminance temperature have been estimated by the use of infrared radiation thermometer of which the range of the measurement wavelength is from 8μm to 14μm and the resolution of the temperature is 0.01K, to compare the manufactured plane blackbody with the standard blackbody having the accuracy of ±0.01K. On the basis of these results of measurement, the effective emissivity of the plane blackbody was estimated to be 0.992±0.001 when the surface is dry and 0.994±0.001 when wet.
By the use of the plane blackbody, if the luminance temperature corrected in terms of the emissivity, the infrared radiation thermometer shall be calibrated with the accuracy better than ±0.2K.

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In the measurement of dielectric constant and dissipation factor of sheet specimens, the unparallelism of specimen surfaces causes errors in the measurement. This paper describes these errors for the Q meter, reactance variation, varying gap, liquid immersion, and varying gap immersion methods. The errors vary much with the method employed. The errors with the varying gap method are less than those with the Q meter and reactance variation methods, and the errors with the liquid immersion and varying gap immersion methods are much less and usually negligibly small. The results shown in this paper will be a guide in choosing a measuring method and in specifying the required condition of specimen surfaces to be measured by the method.

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Most analyzers of air pollution must be calibrated by the standard gas which is a mixture of the pollutant gas and the diluent gas with known concentration. Usually the mixed gas is prepared in a gas cylinder and the concentration of the pollutant gas is determined by the mass measuring method as it is fed into the cylinder. But it is known that the concentration changes in the cylinder, especially in the case of low concentration, because the gases are absorbed by a cylinder wall. In such a case, the flow measuring method is used for the preparation.
Before being put to use, the standard gas mixed by the flow measuring method must be confirmed that it is homogeneous. In this experiment, nitric monoxide (NO) is choson as the pollutant gas. The mixed gas is taken by a sampling probe at various positions of the tube and the distribution of NO concentration is measured by the chemiluminescence NO analyzer. It is shown that the distribution and the homogenizing process agree well with the prediction by the diffusion equation. According to the result, a length of about 5m is necessary for the tube to make the variation coefficient of the concentration distribution less than 10^-3 when the flow rate is 10⁴cm³·min^-1, and the required length dose not depend on the diameter of the tube.
Since the use of such a long tube is not advisable for preventing adsorption, several types of mixers are produced and their effects are experimentally evaluated. As a mixer for the flow measuring method, a higher efficiency of mixing is required, and at the same time, a lower pressure loss and a smaller fluctuation of the flow rate. By the present investigation, “twisting plate type” of mixer is found to have the best characteristics.

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An optical particle counter which can detect submicron particulates in the range of 0.1-10μm individually is applied to the measurement of atmospheric suspended particles. The purposes of this measurement are to determine the particle size distribution of the suspended particle in the atmosphere and to examine correlation between the particle number concentration and the polynuclear aromatic hydrocarbon (PAH) content in the atmosphere.
We measured concentration of exhaust dusts from automobiles, of dusts in high-way tunnels, and of suspended particles in a large city (in a field experiment). At the same time, PAH was collected by using an Anderson and an ordinary high volume air sampler.
As a result, at a high confidence level above 0.95 we found a close correlation between the particle concentration and the PAH content in the atmosphere. It is clarified that this optical counter can be available for in situ measurement of the environmental pollution by miscellaneous particulates.
Finally, we believe that this instrument can be applied to the monitoring of PAH in cities, where the primary pollution comes from the automobile exhaust.

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A fluidic one-shot-multivibrator is composed of a wall attatchment element and a delay element. To analyse and design such fluidic digital circuit, we must know its transient behavior. But, the method for analyzing it taking into account both the static and dynamic characteristics of the wall attachment element has not yet been well-established.
The purpose of this paper is to propose a method for analyzihg the transient behavior of such a circuit by the computerized method of characteristics. We investigate the method for estimating the boundary conditions and the switching delay time of a wall attachment element for a ramp control input. Based on the results of estimation, we calculate the transient response and the output pulse width of an one-shot-multivibrator, and compare them with the experimental ones.
As a result, the following is concluded.
1) The method of characteristics is very useful for analyzing the transient behavior of the complex fluidic circuit with branches, having nonlinear or varying boundary conditions, and so on.
2) The switching delay time of a wall attachment element depends on the rising of the control input. And the time required for the element to be switched after the control port pressure reaches its static switching level is nearly inversely proportional to the time derivative of a control port pressure at its static switching level.
3) When the static and dynamic characteristics of the wall attachment elements that constitute an one-shot-multivibrator are given, we can calculate with sufficient accuracy the output pulse width of the curcuit with any restrictor and capacitor by the above method.

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Described in this paper, is a switching device based on a pneumatic amplifier with a positive feedback system. Two sets of bellows are located on the same axis in an enclosure, and divide it into three chambers. A nozzle is put on a movable end of one of the sets of bellows and faces the movable closed end of the other. The nozzle is pneumatically connected to a constant pressure source through an orifice provided in the fixed end of the former bellows, and its back pressure is used as the output of the device. The positive pulsating pressure introduced in the latter bellows serves as the input signal for setting the device and keeps the output pressure at a high level by the positive feedback action of the former bellows. The pressure within the enclosure serves as the input signal for resetting the device and causes the output pressure to fall off by compressing the both sets of bellows. Negative pulsating pressure can be also applicable as the input signals, where the pressure within the enclosure serves as the set signal and the pressure in the latter bellows as the reset signal. Experiments were conducted with an apparatus made on trial. The conditions of setting or resetting the device and the dynamical behavior were discussed using the results.

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In the DDC System, an analog signal is simulated by digital signals with a zero-order hold circuit. But its sampling period is rather short compared with the time constant of the process. From the point of view of the effective utilization of the controller or the computer, it is desirable to make the sampling period large. This can be done by using the controller which produces the repeated pattern control signal.
In this paper, a method is proposed to obtain the repeated pattern signal by sampling the impulse response of the process. By virtue of the repeated pattern signal, the system's output settles within several sampling periods. An acutual controller generating the pattern control signal is produced. It is found from the experimental results of this controller that the proposed method works satisfactorily in a practical system.

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This paper presents a simple method to calculate the critical stepping rate of a variable reluctance stepping motor, of which the rotor is made up of mild steel cores. The stepping rate is a very important design parameter of a motor of this type.
In this analysis, a critical stepping rate is determined by equating the average torque generated in the coils in one stationary cycle to the external load torque. Here the Fourier series expansion of the normalized current and voltage in a phase is employed to calculate the average normalized torque. As a result, an algebraic equation for coefficients in Fourier expansion of a normalized phase current is derived. The average normalized torque is iteratively calculated for various switching electrical angles so that it is maximized, since it depends on the switching electrical angle with respect to the equilibrium angular position and the rotor normalized velocity.
It can be said, in comparison with the exact numerical solutions of the system equations of a stepping motor with 2 phase or 1-2 phase excitation, that at most the second or third term of Fourier series expansion will be needed to approximate the motor dynamics used to determine the critical stepping rate.

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This paper investigates a control problem of a jib-crane to transfer a load from an initial position to an objective position:
1) suppressing a swing at the final time, and
2) making the traveling time as short as possible, under assumptions that:
a) the length of the rope is kept constant, and that
b) a control pattern is bang-bang type with two or four switchings.
A θ (angle of elevation)-control problem is investigated first and then, the results are extended to a θ-φ (angles of elevation and rotation)-control problem.
The control strategies can be realized by a use of microcomputer. A computer simulation and an experimental study using a crane simulator and micro-computer are included to illustrate the control strategies.

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In the control of a crane system (for example, an ore unloader), the following requirements must, be satisfied.
(1) The traversing time of the trolley must be reduced as much as possible.
(2) The swing of the grab must be stopped at the end point.
For these requirements, we divide the traversing interval into three parts, that is, the accelerating interval, the interval of constant speed and the decelerating interval.
In the interval of constant speed, the trolley runs at the maximum speed under a condition that the grab has no swing, and in the other intervals, the traversing time is minimized by the minimum principle.
Assuming that the rope length is constant, we show a table by which an optimal switching time can be achieved. The utility of the proposed scheme is demonstrated by using a model of the crane system.
Alsop et al. proposed a similar control scheme, but the traversing time was not optimized.

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The present paper presents multiobjective programming models, to evaluate a policy to increase electric power supply capacity, with special emphasis on the interaction between the energy development and the social siting concern. Following a linear difference capacity balance model, a social impreference measure is firstly introduced to provide decision makers with quantified social concern mainly about the environmental problems around the electric power plant site. Presupposing a shortage of electric energy, a multiobjective programming capacity expansion model KOM-[I] is then developed under cost restriction to analyze the trade-off between the energy supply and the social concern in the expansion policy decision, while another model KOM-[II] is also formulated as a multiobjective program to evaluate the trade-off between the cost and the social concern under electric demand restriction. The special feature of the models is the introduction of the social siting concern through a social impreference measure into the siting (environmental) phase of the policy decision. Simulation studies by applying the Surrogate Worth Trade-off Method are illustrated.

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