In this paper we discuss when a time system can be represented by a canonical form.
The concept of a time system has been introduced as a general abstract model of dynamic systems. Since the model is defined as an input-output (set theoretic) relation, it is so general that it can cover almost all dynamic systems. On the other hand, in modern systems theory most of the arguments and results of dynamic systems are based on their state representation. Hence, it is an interesting problem in general systems theory to find how a general time system can be represented by a state space.
This paper takes the automaton type state representation as a canonical form for dynamic systems and discusses how a state space and the canonical representation can be introduced for a general time system and, hopefully, places a theoretical foundation to the state space approach.

View full abstract

One important and difficult problem in the thermometry of gaseous substances is how to eliminate the error due to radiation.
The purpose of the paper here reported is to construct a thermoelectric thermometer with which the correct temperature of a gas can be obtained by a single measurement regardless of radiation. Two copper-constantan thermopiles are covered with materials of different emissivities. The ratio of the number of couples of the two piles is inversely proportional to the emissivities of the materials.
The error due to radiation is canceled, and the correct temperature of a gas can be obtained by a single measurement. The ratio of emissivities may be estimated experimentally.
Improvements are made for simplification of the equipment and stabilization of the output voltage. The number of couples and reference junctions is considerably reduced.
An improved thermometer of type I is composed of a reflective thermocouple, a reference junction and a set of differential couples.
An improved thermometer of type II is composed of some reflective couples and absorptive couples connected in parallel and a set of compensating differential couples.
The experimental results show that good stability of output voltage and simplification of the setup are obtained fairly well. The error due to radiation is within ±3μV (0.06°C) over the temperature range from 35°C to 45°C. It is recognized that improved thermometers are available for gas temprature measurement.

View full abstract

Turning an He-Ne ring laser (0.6328μm, triangular cavity, one or two D.C. discharge gain tubes) on a rotating table, the beat signal generated by the optical mixing of the clockwise and counter-clockwise laser beams has been observed. Simultaneously, the relation between the angular velocity and the beat frequency has been measured.
It is found that the frequency, waveform, and amplitude of the beat signal are extremely unstable in the region near the lock-in rate, and that the beat frequency has a linear relation to the angular velocity in the region far above the lock-in rate. The beat frequency from a ring laser with one gain tube has a bias from the expected value in the absence of mode-pulling effects by Langmuir flow. It is found that the magnitude of the bias increases monotonically with that of the discharge current in the region of 12-18mA, and to be about 1kHz at 18mA. The direction of the bias depends on that of the discharge current and on that of the ring laser rotation. The possibility of achieving zero bias frequency is experimentally shown using a ring laser with two gain tubes.
An improvement of the ring laser devices is suggested in consideration of the analysis made on the various causes of the noise in the beat signal. The conditions to operate a ring laser as a practical equipment for the precise measurement of the angular velocity are discussed.

View full abstract

This paper presents the design method of an electro-hydraulic type acceleration generator which can reproduce the acceleration of an arbitrary wave form. Because of the attainable lower limit of the mass-spring type vibration pick up (vibrograph or accelerometer), the mechanical vibrations in the low frequency region are usually measured or recorded by an accelerometer. Then an acceleration generator which can reproduce or simulate the environmental conditions of the acceleration which are recorded in service is required in the laboratory test.
In general, compared with the electromagnetic type, the electrohydraulic type vibration machines have advantages in their large output power, large stroke and power efficiency in the low frequency region. But the distortion of the output acceleration wave forms of the electro-hydraulic type vibration machine in present use is very large. So it can not be applied in actual use as an acceleration generator.
In this paper, the fundamental problems of the design of the elements and the systems are shown, and the design method is explained systematically.
The main elements and the construction of the apparatus which is manufactured in this research are similar to those of ordinary electro-hydraulic servosystems. But the ideas of the synthesis of the system are original.
From the results of the experiments, it is shown that the realization of an electrohydraulic type acceleration generator with a large output power is possible.

View full abstract

The applications of the wall attachment fluidic device have become so wide that the establishment of a method for circuit analysis is urgently needed. The dynamic analysis of the circuit with capacitance can hardly be treated graphically and, moreover, in a large amplitude operation, the nonlinearity caused by switching elements prevents us analizing with a linear equivalent circuit such as seen in an analog circuit. Here, an attempt is made to apply the method of parameter representation, which was previously reported by the author, to the dynamic circuit analysis.
First, the element loaded with volume is replaced by a nonlinear resistance, connected by the capacitance. Then its step response is analyzed and expressed by the time constant defined here. Further, an attempt is made to represent in the same way the step response of the circuit in which the input resistance of the next stage is connected parallel to the capacitance.
Now the method of step-response represantation is applied to the capacitance-feedback oscillator, and its characteristics are analyzed. The results become fairly acceptable by taking the dead time, such as the switching time, into consideration. This method might be applicable to the analysis of other systems like a fluidic controller, etc.

View full abstract

This paper aims at clarifying the movement control system of skeletal muscles.
The authors paid attention to the small oscillation (tremor) that is observed in the movement control system and proposed the hypothesis that this small oscillation is caused in the closed loop called the stretch reflex arc consisting of an α motor neuron, a muscle and a muscle spindle.
The experiments on the elbow joint were carried out under the following conditions and the EMG, the EMG envelope, the joint angle and the joint angular velocity were recorded.
a) To maintain a preassigned joint angle precisely under constant torque disturbance.
b) To rotate the elbow joint by a preassigned angle at the highest possible speed.
c) To maintain the integrated value of the joint angle constant precisely.
In these experiments oscillations of the EMG envelope and the joint angle at about 10Hz were observed.
Then the model of the movement control system was proposed, the parameters of a muscle were measured experimentally, and those of a muscle spindle could be determined such that the existing oscillation was explained.
Analog simulation of the movement control system showed good agreement with the results of our experiments.

View full abstract

This paper presents conditions for deterministic identifiability and stochastic identifiability of linear time-invariant systems with mulitiple inputs and outputs. The main difficulty in treating systems with multiple inputs and outputs is that there is not such a simple canonical form as there is for systems with single inputs and outputs. Therefore this paper utilizes the method for the identification of a deterministic system which was given by B. Gopinath and extends it to a stochastic system. The concepts of identifiability in this paper are an extension of those of R.M. Staley and P.C. Yue.

View full abstract

The gradient method for computing the optimal control is usually formulated for a problem in which the final instant is fixed and the final state vector is free. Although the minimum time control problem is the most familiar optimal control problem, it does not belong to the above class of optimal control problems. The usual technique for solving the minimum time control problem is the following. Assume the control time sufficiently shorter than the true (but unknown) minimum control time, and construct the problem to minimize the norm of the final state vector. Then, find the time when the minimum norm just vanishes as the control time is increased little by little. This technique requires some information about the true minimum control time, and moreover is not suitable to deal with the bounded state variable problem. The authors discovered that it is not required to solve the infinite series of optimal control problems, as is done in the ε-method, and that the currently assumed control time is easily determined as shorter or longer than the true minimum control time by solving an optimization problem once with a certain proper value for ε. The true minimum control time is obtained by the interval contraction method. Moreover, a characteristic of the proposed method is that a problem with some kind of bounded state variable as well as a bounded control variable can be dealt with quite easily.

View full abstract

This paper presents a state estimation algorithm of a single variable nonlinear system to which the stochastic approximation is applied.
First, under a weaker condition than any previous one, it is shown that the estimation error by this algorithm converges to zero in the mean square for a disturbance free message process.
Further, it is clarified that, under a still weaker condition, the estimation error variance for a nonlinear message process with a disturbance which may be correlated with a measurement noise has a finite upper bound which is previously given by statistical parameters of a disturbance and a measurement noise, if known.
Finally, some digital simulations for simple nonlinear systems demonstrate that the convergence rate of this algorithm is very fast and that the error variance converges to a smaller value than a theoretical one.

View full abstract

A method is proposed for an approximate construction of the optimal state regulator for an autonomous nonlinear system with a quadratic performance index. The method is based upon the instantaneous linearization technique developed by Pearson. In the method of instantaneous linearization, the nonlinear system is approximated by a state-dependent linear model. The resultant problem is then solved using a technique similar to that for linear systems. However, the solution is not optimal in general because of the arbitrariness of the linearized model. The purpose of the present paper is to correct the serious shortcoming of this method.
First, an optimality condition for the control law obtained by the method of instantaneous linearization is derived. Secondly, by making use of this condition, a systematic procedure is presented to determine a suboptimal feedback control for a second-order system. A minimax algorithm is used to design the linearized model closely approximating the original system within a prescribed region in the state space. The validity of the present method is shown by examining typical examples.

View full abstract

An approximate technique is presented for determining optimal stationary control of a class of nonlinear stochastic systems with a quadratic performance criterion. Since the stochastic nonlinear optimal control problem is in general unsolvable, a kind of approximation technique will be resorted to. The first task is to introduce a statistical equivalent linear system in the sense of second order statistics. Given a nonlinear dynamical system, the method for describing the equivalent linear system is given by using the Gaussian assumption. This can be viewed as an extension of the statistical linearization technique of Booton type, and an advantageous use can be made even for a dynamical system subjected to the state dependent noise. Next the parameter optimization technique is used to determine the sub-optimal control law, using the equivalent system. The paper covers cases both with and without the bounded constraint of control amplitudes. For the unbounded case, the resultant control is linear. A computational algorithm and certain discussions on the statistical linearization technique, which appear to have been neglected previously, are also included. For the bounded case, the resultant control must be nonlinear. Thus the control problem is split into two separate problems: the parameter optimization problem and the inverse problem of linearization. By the parameter optimization, the feedback gain is found to depend on the state covariance, and then the bounded control rule can be determined by using the non-uniqueness of the inverse problem solution.

View full abstract

Two on-line adaptive control methods for minimum-time control of unknown plants are presented. In the methods, the switching surface of the control is represented by a polynomial switching function with hierarchical structure, and the structural parameters are iteratively modified according to the information obtained during the control process. The methods do not need to identify the plant dynamics, and furthermore they can determine the switching surfaces, which approximate the optimal ones well, in comparatively few steps.
Two algorithms, the gradient modification method and the location modification method, are derived for modifying the switching function based upon the state-transition patterns in the state space. They can be called the self-adaptation algorithms, as they require no external instruction for modifying the switching function parameters. The location modification method is simpler and has better adaptivity. This method was applied to many unknown plants under different conditions by a computer simulation technique. Some of the results are given in order to show that the proposed method can realize a quasi-optimal control of high quality for unknown plants. It is also noted that the algorithm has a function to stabilize the control systems.

View full abstract

An automatic flare control system is formulated as an tracking problem, where the desired values of the altitude and rate of descent are specified as exponential functions of time. The resultant optimal closed-loop scheme has a good performance under the variations of the initial conditions such as altitude and rate of descent.
The mass of an aircraft, on the other hand, varies according to the number of passengers and the amount of fuel. So it is necessary to construct an automatic landing system which leads to the sensitivity reduction under the change of mass in the equilibrium flight condition. The optimal feedback system investigated here is implemented using output feedbacks, and the responses of the optimal closed-loop scheme are used as the nominal solution in this configuration.
The proposed methods satisfying the equilibrium flight condition are as follows;
1) a constant approach velocity with the flaps being used to alter the lift coefficient,
2) a constant lift coefficient with the approach velocity being changed so as to satisfy the equilibrium flight condition.
The output feedbacks of the altitude and rate of descent are used in the synthesis examples, and the optimal feedback gains are determined using the steepest descent method to minimize a given sensitivity performance index. It is shown in the digital simulation that the open- and closed-loop schemes are heavily affected by the mass variation in the equilibrium conditions 1) and 2), respectively. The optimal feedback system, however, shows good performances in both cases.

View full abstract

Along with the increase in the share of the total electric power system held by thermal power plants, the increase of capacity of individual units and the trend towards higher steam pressure and temperature are also remarkable. In this situation, the improvement of functions and abilities of the plants like quick startup, shutdown and the safety of operation are becoming much more important. Especially in Japan, problems related to plant startup where a complicated procedure is involved and the system characteristics are not always made clear are being given serious consideration. In this case, the application of a highly efficient computer control system is expected to be the most effective.
The paper deals with the development of a direct digital control (DDC) system for steam turbine startup, which is one of the most important procedures of the thermal power plant operation. The steps and results of the development are as follows.
(1) The optimal scope to be automated by DDC was decided after analyzing the plant operation procedures, and the computer control systems suitable to this control were planned.
(2) The dynamic equations of the systems were derived and the control problems were extracted and analyzed. Then control systems with advanced functions like adaptive control were developed for solving the problems.
(3) The systems were simulated by a digital simulation technique, and the control characteristics of the systems at various operational conditions of a plant were analyzed.
(4) The control systems were applied to an actual plant, and their high performance was demonstrated.
As a result, a realistic turbine startup DDC system was brought to completion, and so safe and long-life operation of turbines can be expected.

View full abstract

This paper presents a new method for precise attitude control of a spinning satellite using CMG (Control Moment Gyro). CMG has been considered to be quite promising for precise attitude control of a satellite with long life. Nevertheless, its application to spin axis control has not been fully studied. The biggest trouble we meet in trying to apply CMG to a spinning satellite is the interaction of the spin of the satellite with that of the CMG rotor. In this paper we avoid this difficulty by considering the control law from the viewpoint of angular momentum. The torque exerted on the satellite under this control law is examined and is shown to be reasonable.
The control law for the desaturation of CMG gimbal angles using the earth's magnetic field is also discussed.
Assuming proper figures for the satellite and CMG dimensions, the procedure for designing system parameters is presented.
Digital simulation for the system is carried out and satisfactory results are obtained.

View full abstract

Most pattern recognition problems may be categorized as parametric and nonparametric ones on the bases of our knowledge concerning the conditional densities of the input patterns. In addition, the learning machines can further be classified into two types, supervised and nonsupervised ones.
This paper presents a mathematical model of a nonsupervised learning machine using a first principal component. Previous works related to the classifying method using the first principal component, such as those by Cooper and Cooper, and Takanuki and Morishita, have led to a nonsupervised classifiers with parametric learning methods.
In this paper, we discuss a nonparametric case. Under the assumption that the patterns of each category are clustered, the separating hyperplane should contain the mean vector Z_s of all patterns used and should be perpendicular to the line governed by the first principal component W_sTX. Therefore, the decision rule is given by decide: X∈{C₁ if W_sX>θ_s C₂ otherwise θ_s=(W_s, Z_s). The learning algorithm employed in the classifier is as follows: {W_k+1'=W_k+a_k{(X_k-Z_k, W_k)(X_k-Z_k)-|X_k-Z_k|²W_k}W_k+1=W_k+1'/|W_k+1'|Z_k+1=Z_k+a_k(X_k-Z_k)θ_k+1=(W_k+1, Z_k+1), where W_k is the weight vector, Z_k is the mean vector and a_k is the correction increment at the k-th iteration.
Also we have made a computer simulation to study the learning performance of the classifier for the Gaussian data. The results of the experimental study show that the probability of error of the classifier proposed is slightly larger than the Bayes' minimum error.

View full abstract