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Volume 14 (1978)
- Issue 6 Pages 613-
- Issue 5 Pages 479-
- Issue 4 Pages 347-
- Issue 3 Pages 217-
- Issue 2 Pages 107-
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Volume 14, Issue 6
Displaying 1-23 of 23 articles from this issue
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Eiji KONDO1978 Volume 14 Issue 6 Pages 613-619
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper considers the problem of designing a linear functional filter (L. F. F.) to estimate a linear function of the state variables of a linear stochastic system, for the purpose of implementing a feedback control law.
The L. F. F. is a linear unbiased filter, and is generally of lower order than the Kalman-Bucy filter. It is shown here that, when the L. F. F. is used in the standard LQG control problem, separation property is established for the cost and the stability. For the steady-state case, the minimal order, canonical forms and the optimal design are obtained by a single L. F. F. which estimates a scalar-valued linear function of the state. Finally, an illustrative example is given to show the effectiveness of the L. F. F..View full abstractDownload PDF (783K) -
Hisato KOBAYASHI, Etsujiro SHIMEMURA1978 Volume 14 Issue 6 Pages 620-625
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper deals with a state observer for a bilinear system. The estimation error of the proposed observer converges to zero independently of the input. It is shown that the existence problem of a state observer reduces to a stability problem of a type of bilinear system. Using the results of the present authors on such a stability problem, the design procedure of this observer is presented. Similar results for the minimal order observer are also derived and it is shown that if a full order observer can be designed for a given bilinear system, the minimal order observer can be designed. For the single input system, a simpler design procedure of the minimal order observer is derived. Furthermore for a class of systems which do not satisfy the existence condition of the observer, it is shown that the observer can also be designed for a restricted class of inputs.View full abstractDownload PDF (713K) -
Daisaku HIRATA, Hajime MAEDA, Shinzo KODAMA1978 Volume 14 Issue 6 Pages 626-632
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper discusses the asymptotic behaviors of a class of nonlinear compartmental systems. The system treated here is a nonlinear reciprocal compartmental system for which the flow of a certain material between compartments depends only on the difference of the amounts of the material in the compartments. The specific problem considered here is the derivation of mathematical conditions which guarantee the following properties of systems: the nonnegativeness, the asymptotic stability, and the nonoscillatory property of solutions.
The compartmental system under consideration is a special class of nonlinear reciprocal RC networks. We introduce a Lyapunov function which corresponds, from the circuit theoretical point of view, to an electric energy stored in nonlinear capacitances and discuss the global asymptotic stability. Necessary and sufficient conditions for the global asymptotic stability are established for open systems. For closed systems, necessary and sufficient conditions with which the solutions approach asymptotically the unique steady state are given.
In this paper we also consider a class of nonreciprocal compartmental systems, which describe the dynamics of pharmacokinetics, and give a mild condition which guarantees the nonoscillatory property of solutions. Under this condition we give several necessary and sufficient conditions for global asymptotic stability, boundedness of solutions, and uniqueness of the steady state of solutions.View full abstractDownload PDF (925K) -
Hiroo YAMAURA, Kazuo OCHIAI, Kazuhide NAKAJI1978 Volume 14 Issue 6 Pages 633-639
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSNecessary and sufficient conditions for singular control problems to be optimal are presented for the case where the system has n states and n-2 control variables. For the second and third order control systems, one of the authors has proposed the so-colled selection rules based on the geometrical property of the sufficient conditions. The purposes of this paper are to extend the author's methods to multi-input control systems and to show that, including the case of selection rules, the sufficient conditions derived here are at the same time necessary ones.
First, the given system is transformed, so that mathematically one of the state variables has a role as the independent variable, while the n-2 derivatives act as control variables. The necessary conditions for the existence of the singular controls are derived from the first variation to this new system. Next, the second variation is calculated. By definition of a new perturbation the variational system can be transformed into a homogeneous one, whose solution vanishes for all times, while the second variation is reduced to take a quadratic form with only control perturbations. Thus the necessary and sufficient conditions can be obtained. Finally, the relation between these conditions and the selection rules are discussed. To derive the selection rules, a pair of necessary and sufficient conditions which are equivalent to each other must be obtained. And it becomes clear that it is realizable only in the case of n=3.View full abstractDownload PDF (869K) -
Takashi AMEMIYA, Yasuhiro TAKEUCHI, Hidekatsu TOKUMARU1978 Volume 14 Issue 6 Pages 640-645
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper discusses the stability of a positive equilibrium point with respect to a strictly positive orthant of solutions of the generalized Volterra equation
dxi/dt=-xifi(x) i=1, …, n
which has been used to describe physical, biophysical, chemical or biochemical systems. The population dynamics among interacting biological species and the reaction dynamics in some chemical or biochemical processes are two specific examples.
When f(x)=b+Ax, a sufficient condition for a positive equilibrium point x*=-A-1b to be stable is that A is an M-matrix. The authors show that this sufficient condition can be extended for a nonlinear f(x). It is proved that f(x) is an M-function when f(x) is nonlinear with respect to x.View full abstractDownload PDF (718K) -
Takahiko MORI, Masami ITO1978 Volume 14 Issue 6 Pages 646-651
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper considers the relation between the steady-state error of a feedback system and the open-loop transfer function matrix, and presents a new algorithm for determining the steady-state characteristics of a feedback system from the open-loop transfer function matrix. This algorithm is much simpler than the ones given in the earlier studies [2], [5]. The steady-state characteristics of the system are also considered for the case where its parameters change slightly.View full abstractDownload PDF (796K) -
Yoshifumi SUNAHARA, Akira OHSUMI, Yoshio MOGAMI1978 Volume 14 Issue 6 Pages 652-658
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe purpose of this paper is to present a method for finding the optimal allocation of sensors for state estimation of linear distributed parameter systems. This method is based on the criterion that the error covariance associated with the state estimate becomes minimal with respect to the allocation of the sensors.
A theorem is established, giving the sufficient condition for optimizing the allocation of sensors to make minimal the error covariance approximated by a modal expansion. The remainder of this paper is devoted to illustrate important phases of the general theory of the optimal measurement allocation problem. To do this, several examples are demonstrated, including extensive discussions on the mutual relation between the optimal allocation and the dynamics of sensors.View full abstractDownload PDF (827K) -
Yoshifumi SUNAHARA, Shin-ichi AIHARA, Fumio KOJIMA, Katsumi IKEDA1978 Volume 14 Issue 6 Pages 659-666
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe purpose of this paper is to find the optimal boundary control for distributed parameter systems with stochastic parameters under noisy boundary observations.
First, with background knowledge of functional analysis, the mathematical model of both the system dynamics and the boundary observation mechanism is formulated, giving the statistics of stochastic parameters by white Gaussian process.
Secondly, the optimal boundary control for the quadratic cost functional is derived by using the stochastic maximum principle.
Finally, an illustrative example is shown for the purpose of supporting the theoretical aspect developed here.View full abstractDownload PDF (926K) -
Toshihiro KOBAYASHI1978 Volume 14 Issue 6 Pages 667-672
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn this paper we study questions regarding controllability of a distributed parameter system in the case of discrete-time controls. We present the necessary and sufficient conditions for controllability. For the systems with finite-dimensional control functions, we also investigate the relations between a discrete-time control system and a continuous-time control system from the controllability point of view. We show that the distributed systems will never be N-step controllable for any finite N. Moreover we give the set whose elements are attainable by means of N-step controls.View full abstractDownload PDF (657K) -
Tetsuzo TANINO, Yoshikazu SAWARAGI1978 Volume 14 Issue 6 Pages 673-678
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn this paper, a dual problem in a wide sense is defined for a convex programming problem with multiple objective functions and the relationship between the primal problem and the dual problem is made clear.
All nondominated solutions with respect to the preference order specified by a convex cone in the objective function space are considered to be solutions of the original multiobjective programming problem.
First, it is shown that saddle points in an extended sense of the vector-valued Lagrangian provide solutions to the primal problem. Next, the primal problem is imbedded into a family of perturbed problems and a point-to-set map called perturbation map is defined as a map which gives optimal value sets of those problems. The meaning of the multiplier vector is made clear by the geometric study of the graph of this perturbation map. Furthermore, a class of problems called stable are defined by the perturbation map and their properties are investigated.
Finally, a point-to-set map called dual map is defined over the dual variable space by a minimal point set of the vector-valued Lagrangian of the primal problem. The dual problem in a wide sense is presented through this map. The relationship between the solutions of these two problems is given as a weak duality theorem and, moreover, it is shown for stable problems that there exists a solution of the dual problem corresponding to each solution of the primal problem (strong duality theorem).View full abstractDownload PDF (883K) -
Toshiyuki INAGAKI, Koichi INOUE, Hajime AKASHI1978 Volume 14 Issue 6 Pages 679-684
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper presents a new formulation of an optimal reliability design problem for a system under changing environment, where the system components have time-dependent reliability. Our optimization problem is of a nonlinear mixed-integer program and its solution determines simultaneously an optimal reliability allocation and an optimal preventive maintenance schedule. A computationally economical method of solution is presented on the basis of a nonlinear programming algorithm. By use of an illustrative example, the importance of our formulation is shown in comparison with other two formulations.View full abstractDownload PDF (730K) -
Kageo AKIZUKI, Masato TAJIMA1978 Volume 14 Issue 6 Pages 685-692
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn this paper, we are concerned with the existence of a periodic solution of a weakly nonlinear stochastic system with periodic coefficients (Intensity of nonlinearity is expressed by a parameter ε>0). Here the term “periodic” means that every finite dimensional distribution function of the solution process is periodic in t.
We prove the existence of a periodic solution along two different approaches under the condition that the characteristic exponents of the corresponding linear system have negative real parts.
At first, we give a proof by actually constructing a periodic solution, where the successive approximation procedure is adopted. Techniques used there are similar to the ones of A. Ja. Dorogovcev 2) or of H. Bunke 3), but some properties of a Wiener process are incorporated in the proof as essential parts. At the same time, we give a sufficient condition in terms of the range of a parameter ε>0, under which there exists a periodic solution.
Next, we construct a periodic solution according to I. Vrkoc 4), but in this time, we exclusively deal with distribution functions of the process. First, we show that solutions of the original system are uniformly exponentially stable in the quadratic mean for sufficiently small ε>0. Under this stability condition, it is shown that distribution functions of the process which are sampled at every T-time, where T is a period of coefficients, converge. Let the limit distribution be F*. Then the distribution after one period of the solution process with the initial distribution F* is also given by F*. In this way, we can prove the existence of a periodic solution again.View full abstractDownload PDF (877K) -
Tadashi ISHIHARA, Ken-ichi ABE, Hiroshi TAKEDA1978 Volume 14 Issue 6 Pages 693-698
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe optimal control problem of linear stochastic systems with unknown parameters is essentially nonlinear, so that an explicit solution of dynamic programming is not available. Thus, various suboptimal approaches have been suggested in treating this class of problems.
In this paper, a suboptimal algorithm based on the use of the open-loop-feedback-optimal (OLFO) method is derived on the assumption that unknown parameters take finite values. It is shown that the resulting control system consists of
1) an optimal state-parameter estimator formed by the parallel operation of Kalman filters;
2) an, OLFO adaptive feedback gain which is computed on-line based on the a posteriori probabilities of unknown parameters.
The OLFO algorithm is compared with existing algorithms by using the Monte Carlo method. The results are summarized as follows.
1) In the average performance, the OLFO control is a little superior to others for stable systems but inferior for unstable systems.
2) For the both stable and unstable systems, the standard deviation of the performance of the OLFO control is smaller than that of others.
3) The convergence rate of the a posteriori probabilities of unknown parameters is primarily dependent on the stability of the system rather than the choice of the algorithm. For unstable systems, the convergence rate is faster than that of stable systems.View full abstractDownload PDF (763K) -
Yoji UMETANI, Takashi OZAWA1978 Volume 14 Issue 6 Pages 699-705
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper deals with discriminating textural patterns of geometrically dot-arrayed figures by means of optical Fourier's transform.
A set of original patterns, which have idealized regularity and homogeneity as texture, is defined as that of categories to be recognized. In order to extract the parameter of feature, both the elementary shape of the pattern and the array of the element are introduced. A fundamental theory to recognize the input textural pattern as one of the category patterns is derived premising optical Fourier transform. Some experiments are carried out using an optical set-up by which the Fraunhofer diffraction of the input pattern is obtained. The input patterns used in the experiment are such that they are fluctuating as a whole pattern around a regular array fixed in the space. The experiments show that the method proposed in this paper is so effective that so much fluctuated textural patterns as being visually difficult to recognize are clearly recognizable.View full abstractDownload PDF (2463K) -
Masaru UCHIYAMA1978 Volume 14 Issue 6 Pages 706-712
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSHigh-speed motion of a mechanical arm is necessary to speed up a job done by the arm. In high speed, however, the desired trajectory of motion of the arm cannot be obtained simply by applying the trajectory function to the servo system as the reference function because the time lag in the servo system is not negligible.
A solution to this problem is to apply dynamically compensating computed torques to the servo system. By this method, however, for increasing the accuracy of the mathematical model of the arm necessary to compute the compensating torques, a very large effort would be required. To avoid this difficulty, an alternative method of correcting the reference function by trial will be useful. Repeating a proper process of trial and correction, the reference function which realizes the desired pattern of trajectory may be obtained.
In this paper, correcting algorithm of a reference function for this method is investigated theoretically from the standpoint of stability or convergency of the process of trial and correction, and a stable correcting algorithm is obtained. Through the experiment using a mechanical arm of six degrees of freedom controlled by a digital computer, it is confirmed that the process of trial and correction by this algorithm is stable and the response of the servo system converges rapidly to the desired pattern of trajectory.View full abstractDownload PDF (1299K) -
Masatake SHIRAISHI, Tomoaki MORINAGA1978 Volume 14 Issue 6 Pages 713-718
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis report deals with a control of NC lathe by feedback of workpiece dimension which is measured with the method reported previously by the authors.
The outer surface of a workpiece being machined is continuously monitored to determine its instantaneous size by the measuring apparatus during operation and the tool rest is automatically moved in the direction to eliminate the error. As a consequence, a high dimensional accuracy is obtained by this feedback control for not only the workpiece with constant diameter but also the workpiece with a curved profile. Moreover with this control method, there is no need to perform the conventional complicated calculations in programming to compensate the error caused by the finite cutter radius.
Total errors are suppressed within the range corresponding to ± one feed pulse by this control.View full abstractDownload PDF (873K) -
Keiichiro MIYATA, Hideo HANAFUSA1978 Volume 14 Issue 6 Pages 719-724
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn this paper, to clarify the random switching mechanism of an attached jet, characteristics of velocity fluctuations of the attached jet are investigated experimentally by using a large scale fluidic model. The relation between turbulence and random switching is made clear.
The turbulence intensities of an attached jet and a free jet were measured. For the attached jet, the power spectrums and the probability densities of velocity fluctuations were also measured.
Based on the experimental results, velocity fluctuations near the half width of the velocity profile of the attached jet, which is equilibrium with the control flow, are considered as stationary normal random oscillations and the random switching model is given.
Values of model parameters are estimated from the experimental results and the distribution parameters of switching delays are calculated. This calculation agrees with the experimental results of switching delays in the random switching process. Thus the validity of the random swishing model based on the randomness of velocity fluctuations is confirmed.View full abstractDownload PDF (831K) -
Fumio HARASHIMA, Haruo NAITO1978 Volume 14 Issue 6 Pages 725-731
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSCurrent source inverter-fed synchronous motors, hereafter we call them commutatorless motors, have come into a wide use in industry as variable speed drives. They can be controlled to give a good to give a good performance as DC motors can and are easy to be maintained as AC motors are.
When this system is used as a variable speed drive, it is important to consider dynamic characteristics as well as steady state ones.
When we consider dynamic characteristics of variable speed drives, two kinds of dynamics should be taken into consideration; one is the electrical dynamics and the other is the electromechanical dynamics. Since a response in electrical dynamics is much faster than that of electromechanical ones, these two dynamics can be discriminated one from another. The electro-mechanical dynamics can be easily obtained from the torque-speed curve of the motor and the torque characteristics of the load. On the other hand, the electrical dynamics can not be easily obtained, since it involves complicated electrical phenomena. However, the electrical dynamics is a very important factor when a high performance of control characteristics like that of DC drives is required of commutatorless motors.
In this paper, first, the transfer function models of commutatorless motors are obtained mainly from the view point of the electrical dynamics and the transfer function model including the electro-mechanical dynamics is discussed later. The models have been derived on the basis of the average behaviours which are represented by continuous dynamic equations. The phenomena during commutation periods are considered to be equivalent with average voltage drops in the circuits. The adequacy of the transfer models has been confirmed by both simulation and experimental results.
The effects of motor parameter on the performance characteristics of the system are also discussed.View full abstractDownload PDF (939K) -
Tsutomu YOKOZUKA1978 Volume 14 Issue 6 Pages 732-738
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSA Consideration of transient torque characteristics is of special importance for cases where induction motors are started and stopped frequently or continuously, since under such conditions a quick response is often required. The required response is such that sometimes a full speed rotor must come to a dead stop in less than one revolution. In this paper we obtain the computing methods (1) transient braking torque performance under dc excited conditions (2) transient accelerating torque characteristics under conditions of suddenly applied ac voltage.
Based on the methods, we investigate the effects of the rotor resistance and rotor speed on the transient dc braking torque characteristics, the relation between time lag of dc braking torque and parameters, the effects of switching time and rotor resistance on the transient accelerating torque characteristics when an ac voltage is suddenly applied.View full abstractDownload PDF (1519K) -
Iwao MORISHITA1978 Volume 14 Issue 6 Pages 739-744
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn the automatic operation of travelling cranes the velocity of a trolley must be controlled so that the swing of its grab just vanishes when the trolley has arrived at a goal position. This paper describes a new control algorithm for such a grab-swing elimination. In this control algorithm the total travelling distance is divided into halves. In the first half, the trolley may be run with any velocity pattern and a program control scheme is employed. The swing angle of the grab and the actual velocity of the trolley are measured and stored into a data memory in the controller. In the latter half, both the trolley velocity and the grab swing-angle are controlled with a linear feedback control scheme. The stored data are read out from the data memory in the“last-in first-out”mode and used as the reference signals. This algorithm has been implemented on a microcomputer and used to control a crane model of 1m high and 2.5m long. The maximum swing angle remained at the goal position was ±3 degrees.View full abstractDownload PDF (679K) -
Kiyotaka SHIMIZU, Eitaro AIYOSHI1978 Volume 14 Issue 6 Pages 745-746
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSDownload PDF (311K) -
Eiji TOBA, Tsutomu AONUMA, Masao SAWAJI1978 Volume 14 Issue 6 Pages 747-748
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSDownload PDF (372K) -
Takashi SEKIGUCHI, Noboru UNNO1978 Volume 14 Issue 6 Pages 749-750
Published: December 30, 1978
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSDownload PDF (267K)
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