Many practical position control systems have been developed up to now. When the load varies, however, an ordinary feedback control system does not perform satisfactorily.
In this paper, we consider a position control system subject to inertia load variation. An adaptive control of the system with unknown load variation is studied.
1) We determine optimal values of parameters to minimize the performance index with respect to load variation.
2) We design a self-adjusting control system which adjusts its own parameters by measuring the inertia load when the inertia load is constant but unknown before measurement.
3) We design a control system which takes into account the angular acceleration term in addition to PID control and compensates a variation of inertia load through a positive feedback loop when the unknown inertia load varies with time.
The results obtained by digital simulation suggest that the designed control systems are satisfactory for practical use. The simulation also comfirms the requirements to realize an optimal performance.

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There are several methods to solve the minimum-time (or the minimum-stage) problem of discrete systems with the bounded control. Most of these methods are concerned with the computation of the reachable region in some sense. In the computation of the reachable region, as the dimension of the system increases, the computer program becomes more complex and the amount of the computation increases exponentially (since, for example, the number of the corners of the n-dimensional polyhedron in Euclidian space increases exponentially).
This paper analyzes the relation between the optimal solution for the quadratic performance index and the minimum-time solution which minimizes the control cost. Using this relation, the suboptimal solution of the minimum-time problem and its computation algorithms are given. Although the solution is suboptimal, the solutions of several examples are all sufficiently close to the optimal solutions. This method is thought to be applicable without difficulty for multi-input systems.

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This paper deals with a differential, two-person zero-sum game. It is assumed that the system is linear including time-delay, the payoff function is quadratic, and the players are given perfect information. The mathematical model of system with time-delay is formulated as a coupling of lumped parameter subsystem and distributed parameter subsystem imbedding time-delay elements.
Three different problems, a hitting game, a settling game in the restricted sense and a (general) settling game, are formulated, depending on the form of evaluating the terminal miss. In the hitting game, only the finite dimensional state of the lumped parameter subsystem is evaluated at the terminal time. In the settling game in the restricted sense and in the settling game, only the infinite dimensional state of the distributed parameter subsystem and the state of the system, respectively, are evaluated at the terminal time.
A transformation is defined, which transforms the original problem to the problem of a finite dimensional system. An optimal strategy and a value of game are derived in the transformed problem by a dynamic programming method. The results are then rewritten in terms of the original problem. The settling game is considered as an extension of the hitting game and of the settling game in the restricted sense and is solved according to the results derived from the latter two games.
In the settling game, one of the conditions for existence of a saddle point is that saddle points of the hitting game and of the settling game in the restricted sense exist. The conditions for existence of the saddle point and for controllability on each player are related to each other in the hitting game, but are not related directly in the settling game in the restricted sense and in the settling game.

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This paper is concerned with a design of control systems when the specifications of the systems' elements are subjected to random variations from their nominal values. We discuss how far the variations in the characteristics of the elements affect the performance of the overall system, and conversely how accurate each element should be in order that the performance of the overall system may be in the specified allowance. A design of an instrument servo system is presented to illustrate the proposed procedure.

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The problem considered is the recursive estimation of state variables for linear dynamic systems with nonlinear sensors. The criterion employed for estimation is the maximum likelihood method. As is well-known, the usual approach to obtain optimal estimators for nonlinear systems leads to nonrecursive estimation schemes in which the entire data previously obtained must be used to update the estimate whenever new data become available. In general, the time required to compute the new estimate increases as the number of measurements increases and the problem of growing memories arises. In order to avoid the above difficulties, various approximation methods have been proposed to obtain recursive estimation schemes, in which only the fresh data are used to update the estimate.
The approach employed in this paper is quite different from those obtained up to the present. First, the special case is considered for which the problem is transformed to the equivalent linear problem. The optimal recursive estimator is obtained. The results are naturally extended for general cases to obtain a simple recursive scheme which has a strong resemblance to Kalman filter.
The estimation scheme obtained is applied to two cases (the first is for the device with saturation and the second for the device with insensitive zone). The numerical results are given.

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This paper describes a method to measure the dynamic characteristics of nonlinear systems with 2-level inputs whose topological structures are unknown. For this purpose a functional model is proposed and expanded into a series of orthogonal functions, in order to simplify the process of measurement. The dynamic characteristics of a nonlinear system is represented in terms of the coefficients of the expansion series. A special test signal m(t) is proposed so that the terms of the expansion series become orthogonal to one another. The signal m(t) is generated by slightly modifying the well-known m sequences. An error function is defined which is an integral squared error between the response of the system and that of the model when the, signal m(t) is applied.
Assuming the order of the model-the number of the terms of the expansion series-to be known, the coefficients are determined so as to minimize this error function. Whether or not the assumed order of the model is adequate is tested by the normalized minimum value of the error function. Making use of the properties of the signal m(t), the coefficients are obtained from a certain correlation function between then input and output. It is not necessary to modify the onceobtained coefficients even if the order of the model is increased. The minimum value of the error function is also obtainable by using these coefficients without computing the response of the model. Several application results are presented.
.It is also shown that this method is theoretically applicable to nonlinear systems with multilevel inputs.

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This paper deals with a simple method to delay analog signals using PWM technique and its application to a sampled-data controller. One unit circuit by which PWM signals are delayed for one sampling period consists of two monostable multivibrators and a few logic circuits. The output signals of the delay circuit are the same PWM signals as the input signals. Therefore, the delayed time of several sampling periods can be obtained by connecting the corresponding number of unit circuits in series. As the sampled-data controller requires many delayed signals at every sampling period successively, this delay circuit will be suitable for the controller. It is possible to keep the fluctuation of this delay circuit satisfactorily small, for the fluctuation depends only on the stability of monostable multivibrators.

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The magnetic field of the electromagnetic flowmeter practically in use now is usually uniform. This type of flowmeter can measure any flow rate very accurately as long as the velocity distribution of flow is axially symmetrical. However, sensitivity of this flowmeter varies very greatly by the velocity distribution of flow if the flow velocity is axially non-symmetrical.
In this paper, the measurement errors of flow in the 90° bend of pipes are discussed both theoretically and experimentally.
The following results are obtained.
1) The measurement error due to an axially non-symmetrical flow can be reduced by using the probes with appropriate magnetic field distribution.
For example, the 45° A probe explained in the text is one of the best probes for the measurement of axially non-symmetrical flow.
2) The measurment error greatly depends on the setting angle. The measurement error of axially non-symmetrical flow by the uniform magnetic field probe is usually very great, but it can be greatly reduced by making the setting angle 60°. Each probe has its best angle.

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The gasflowmeter with throttling device is theoretically based upon Bernoulli's theorem. This flowmeter enables us not only to know the volume flow rate of gas by measuring temperature difference between two cross sections, but also to know the mass flow rate of gas by measuring pressure difference and temperature difference.
The apparatus used in the experiments is a Venturi tube with ratio 0.071 in area and with convergence angle of 20 degrees and divergence angle of 8.4 degrees. The experimental results, in the region of Reynolds number 2.5×10³∼19.2×10³, show that the discharge coefficient for volume flow rate is 1.4×2.1 and the discharge coefficient for mass flow rate is 0.08∼0.12.

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The differential pressure transducer developed by the authors is very simple in construction and extremely sensitive, with a minimum span of 1mm H₂O producing an output signal of 1.5mV, even without an amplifier. Its dynamic characteristics are flat in the range betweem 0 and 15Hz.
This transducer consists of two principal assemblies:
(1) Deflection-balance assembly-consists of a casing and a slightly tightened, vertical, thin diaphragm (0.013mm thick, made of polyvinyl fluoride) which divides the casing into two symmetrical pressure chambers. There are 16 prestressed, horizontal, unbonded strain gauge filaments (8 filaments on each side of the diaphragm), which are each connected to the center of the diaphragm by means of a diaphragm disk and to the casing wall.
(2) Electrical assembly-consists of a 4-arm active Wheatstone bridge (cach arm containing 4 series-connected filaments on the side of the diaphragm), its power supply, and output terminals.
Differential pressure causes positive strain in the filaments on the side of higher pressure and negative strain on the other side. Consequently mV output is proportional to the differential pressure. Displacement of the diaphragm is as slight as 0.015mm at a differential pressure of 2.5mm H₂O which serves to demonstrate its fine dynamic characteristics.
This transducer contains a temporary field checking system and can be assembled into a portable instrument, including an indicator or recorder.

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This paper deals with the compensation of a force-feedback pneumatic servovalve.
As pneumatic fluid has higher compressibility and lower viscosity than hydraulic fluid, the natural frequencies and the damping ratios of a pneumatic circuit are lower and smaller respectively than those of a hydraulic circuit. Therefore, the frequency characteristics of a pneumatic circuit have a sharp resonance at a very low frequency comparing with those of a hydraulic circuit. So, by the mere increase of the supply pressure of a force-feedback servovalve, we cannot expect much improvement of its performance because of the sharp resonances of the pneumatic circuit.
For a great improvement of a force-feedback Servovalve, it is necessary not only to increase the supply pressure but also to give some compensation to the resonant pneumatic circuits in order to give suitable dampings.
Here, the tank-resistance compensation method suggested by J.L. Shearer is compared with the compensation spring method tried by the author. As a result, it is verified that the both methods are useful for the compensation of a force-feedback servovalve. Comparing the two methods, it can be said that the spring gives a quicker response and a wider bandwidth to a force-feedback servovalve than the tank-resistance. At 10kg·cm^-2 of supply pressure, the bandwidth of the force-feedback servovalve used in this experiment is 70Hz with the tank-resistance compensation, while 190Hz with the spring compensation.
Furthermore, a greater improvement of the performance of a force-feedback servovalve is obtained by using the tank-resistance compensation along with the spring compensation. It is proved, in this case, that the widest stable region of a force-feedback servovalve is obtained when ω_n^*T_ta nearly equals unity, where ω_n^* is the resonance frequency of the pneumatic preamplifier of the force-feedback servovalve and T_ta is the time constant determined from the tank volume and the resistance.
The effect of the dimensions and parameters of a forcefeedback servovalve upon its stable region is described.

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Hydrostatic weighing method is often used in the precision measurement of solid density. The accuracy of the measurement is limited by the uncertainty in determining the volume of the solid sample.
In this work, a substitution method in balance weighing is introduced in order to eliminate the major sources of error in volumetric measurement. A hydrostatic balance is modified so that the weights can be changed without seperating the knives from the corresponding bearing planes of the balance beam. Also the devices for remote operations and observations are incorporated.
The results obtained are as follows:
1) The method presented here makes it possible to repeat the volumetric measurement in a short interval without an accurate control of temperature of water and as the result the precision and efficiency of the measurement are greatly improved.
2) The change of surface tension on the suspension wire is largely decreased and the reproducibility of the surface tension is estimated to be ±0.04mg with confidence coefficient of 95%.
3) By using the value of water density in Chappuis table, the precisions of determining the volume and the density are estimated to be ±7×10^-5cm³ and ±4×10^-6g/cm³ respectively, with confidence coefficient of 95%, for a weight of 1kg made of stainless steel whose volume is 127cm³.

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The authors propose a new method of non-contact speed measurement. They call it the “model method”, because it is based on the idea of transfer function parameter estimation using a dynamic model.
The irregular pattern on the surface of a long moving object (so called web) is observed through two detectors placed separately along the direction of the movement. The signal from the upper stream detector is supplied to a dead time model, and its dead time is automatically adjusted so as to minimize the mean square error between the model output and the down stream detected signal. Consequently, the model dead time coincides with the time required for the movement of the web between the two detection points, and indicates the object speed.
Similarity of the proposed method to the correlation method, in which the model dead time is adjusted on the maximum correlation criterion, is shown. A further comparison with the correlation method demonstrates the practical advantages of the model method as follows. First, variance in the measured value of speed is suppressed in a short averaging time by using the model method, and theoretically, it can be decreased to zero. This is not the case with the correlation method. Secondly, while the use of imperfect differentiator in the correlation method biases the measured value of speed, the model method is free from such a problem and therefore adaptable in a wide range of speed and for a variety of irregularities.
These results are theoretically derived and confirmed in a simulation and in a speed measurement experiment with a prototype measurement system. From the features mentioned above, the proposed method is considered to have the possibility of practical application in industry.

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