This paper derives an explicit solution of bilinear systems from the work of Wei and Norman about the solutions of homogeneous linear differential equations. This solution is based on the canonical basis of the Lie algebras spanned by the coefficient matrices, which are supposed to be solvable. The main achievement of this paper is an algorithm to compute these canonical basis.
The explicit solution then follows directly by a standard procedure from the results of Wei and Norman. The solution of bilinear systems is applied to the controllability of bilinear systems.

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Petri net with external inputs and outputs is proposed in this paper to represent the control of event-driven systems. Several fundamental problems arise for the design and analysis of the control system, when a Petri net is subject to the external inputs and outputs. Among these, the free-firing, the observability and the controllability are of crucial importance.
Major results of the analysis of free-firing are:
-a Petri net is firee-firing for any initial state, any external input place set and any control input seqence if and only if it is conflict-free.
-any Petri net can be made free-firing for any initial state by choosing properly the external input place set and the input control sequence.
Analysis of the controllability of the conflict-free Petri net in this study gives the necessary and sufficient condition for the reachability of the net. The condition leads to the method to determine the external input place set and the control input which bring the net from the initial state to the target state.

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In this report, we discussed the weight control of hopper by using a microcomputer. As for the control algorithm, we used the “LQ Control” method.
In the previous report, we applied “Finite Time Settling Control” to the hopper system, but this time, a conspicious jump in the manipulated variable occurred for the step reference input change. Therefore we investigated the application of so-called “LQ Control” method to avoid the jump.
To determine a proper weighting matrices in the quadratic performance function is one of the important problems in the LQ control method.
In view of the situation that the response waves of the system for the step reference input and step disturbance input are influenced by a pole assignment of closed loop system, we investigated the effect of value of the weighting matrices on the pole assignment. Furthermore the characteristics of the process handling granules and powder have been influenced by the environment conditions such as temparature and humidity, then we studied the closed loop behavior under the parameter mismaching between plant and observer model occurring due to the environment conditions.
The following results became clear.
1) If we use “LQ Control” method as for the control algorithms, the response waves show a good behaviour with an increase in the value of W_1x, and with a decrease in the value of W_3x, but when W_1x is made too larger, the response wave results in an alternating behaviour and become oscillatory.
2) Relation the weighting matrices W_x between pole assignment is shown obviously, and it is possible to calculate a value of W_x based on the arbitary desired pole assignment.
3) We indicated the condition that does not remain a steady state error for the disturbance input and modeling error, and then we could show the practical constructure of processes.

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To make a minimum time position control of DC-motor with saturated limitation on driving force, one drive-change-position at which a driving force changes from positive maximum to negative maximum must be determined.
In our studies, an on-line algorithm for determining a drive-changing-position without any off-line calculation and an identification algorithm for identifying a system constant by learning driving, were developed. The minimum time position control of DC-motor by these algorithms has the following properties.
1) Any off-line calculation for determining a drive-changing-position is not necessary.
2) Any estimation for inertia load of a controlled target is not necessary.
3) Proposed algorithms can be easily programmed on an assembling language of a micro-computer.
4) System constants are identified by a few learning driving so that they are not necessary to measure beforehand.
Proposed algorithms were programmed on the assembleing language of z-80 CPU, and the minimum time position control of DC-motor was performed, from the results of which it was turned out that after the system constant were identified by one or two learning driving, the drive-changing-position was determined almost precisely with on-line calculation.

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This paper proposes new method to synthesize a robust speed control system for a separately-excited direct current motor system which attains maximum efficiency on the basis of an improved optimal regulator theory. In this method, the ratio of the armature current and the field current giving the maximum efficicncy of the DC motor system is analytically derived, and the error term for the current ratio is included in a quadratic performance index, together with the speed error term and the difference term of the control input variable. Therefore, the error term for the current ratio is strictly zero at the steady state, and the speed of transient response is arbitrary controlled to some extent by selecting the weights of the performance index. Then the control system which realized both the good response and the optimal ratio for the current giving the optimal efficiency with guaranteeing zero steady state error, is obtained in the systematic design procedure.
In experimental results, good speed response is obtained. Also, considerable improvements on the efficiency at the steady state are obtained, compared with usual control method, in which only the armature impressed voltage is controlled while the field impressed voltage is kept constant, especially at the light load condition.

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This paper is concerned with the state estimation problem for stochastic distributed parameter systems with a semi-permeable wall under noisy boundary observation mechanism.
The distributed parameter system with a random coefficient and a semi-permeable wall is formulated as the stochastic variational inequality. Studying the existence and uniqueness of the solution to the stochastic variational inequality by applying the method of penalization, the state estimator dynamics is proposed with the evaluation of the mean square estimation error.
Finally for the purpose of supporting the theoretical aspects developed here, an illustrative example is shown including results of digital simulation experiments.

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A method in designing a function observer for linear systems with unknown inputs is presented in this paper. Some properties of the function observer are also discussed. If the system with unknown inputs is right invertible, the minimal order is uniquely determined and all poles of the observer are specified as a part of invariant zeroes. When the system is not right invertible, the minimal order can not be determined. However, the design procedure presented here is based on the usual algorithm for the system without unknown inputs, so that it gives the relatively lower order function observer even if system is not right invertible.

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In this paper, a design method of optimal feedforward compensator provided for disturbance input is proposed. Firstly, disturbance input is assumed to be uncorrelated stochastic process. The design is based on system impulse responses and consists of minimizing the mean square weighted values of outputs and control inputs. The optimal compensator, which is FIR (Finite Impulse Response) filter, is obtained by solving a normal equation. The normal eqution can be solved by fast recursive order up date algorithm, so called LWR algorithm. The method is extended to the case of colored noise disturbance and step disturbance. Simulation results show the effectiveness of the proposed method.

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This paper presents a design method of model reference adaptive control system (MRACS) for single-input single-output linear continuous-time plants with inaccessible disturbance input.
A disturbance model, which is defined by a polynomial with respect to time multiplied by an exponential term, is introduced as an approximation of actual disturbance and a composite system is given by accommodating the disturbance model to the plant. Then the composite system parameters are represented by the linear conbination of the unknown plan parameters. In the proposed scheme, the indirect MRACS is design for the composite system. The global stability of the overall adaptive system is proved in the same way as the method shown by Goodwin et al..
A numerical example is given to illustrated the effectiveness of the proposed method.

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“Dynamic Mass-Measurement System of Displacement and Velocity Sensing-Type” (DMS-DV) consists of a spring scale, a microcomputer, and displacement and velocity sensors. In the system, to obtain the mass value of the goods very quickly in comparison with a conventional spring scale, the displacement and velocity data of the goods-plate of spring scale are data-processed in real-time by means of the software on mincrocomputer.
It also is an example of the software-oriented approaches based on the dynamic measurement method to meet the two contradictory requirements, “Quickness” and “Precision”.
The feasibility of the DMS-DV has already been confirmed through the theoretical analysis, the computer simulation and the experiment using the test system.
This paper describes the software which plays an important role in the utility of the DMS-DV.
Firstly, the modified version of a dynamic mass-estimation algorithm has been presented to shorten a measurement time. Secondly, the software system has been supplemented to the DMS-DV to support its operation and to meet “Usability” as well as the above two requirements.
In case of the previous algorithm, accuracy of the measured value depends on the displacement data rather than on the velocity data. So smoothing of the velocity data by software and its positive utilization have made the present algorithm possible to shorten the measurement time within 2/3 of that which is achieved by means of the previous algorithm.
Moreover, the DMS-DV has become usable by means of the software system to support the determination, management, and renewal of the parameters and conditions for execusion of the algorithm, and to assist the record and storage of the measured value.

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This paper describes an optical fiber droplet sizer which can measure 0.1∼12μm diameter particles.
The measuring principle of this sizes is the forward scattering method. First, laser light is irradiated on many particles, and the scattered light intensity pattern by the particles are measured. Second, the intensity pattern is inverted to the particle size distribution using Eq. (1),
I(θ)=∫i(D, θ)n(D)dD (1)
where I(θ) is the measured light intensity pattern, i(D, θ) is the light intensity scattered by one particle, n(D) is the particle size distribution, D is the particle diameter and θ is the scattering angle.
A conventional particle sizer based on this method could not measure particles smaller than 5μm diameter. The following improvements were made in the optical fiber droplet sizer.
(1) i(D, θ) based on the Mie theory was used. The Mie theory is applicable to spherical particle of all sizes.
(2) The measuring range of the scattered light intensity pattern was extended using optical fibers.
The above two improvements extended the lower limit of the measurable particle size range.
(3) In the inversion from the scattered light intensity pattern to the particle size distribution, the Logarithmic Constrained Inversion Method proposed by the author was used. In this method, equation (2) is directly solved for n(D).
log I(θ)=log[∫i(D, θ)n(D)dD] (2)
The feature of this method is that any form of distribution (even bimodal distribution) can be determined without a prior assumption of the size distribution form.
In order to test the performace of the optical fiber droplet sizer, 0.1∼12μm average diameter Polystyrene particles were measured. The test results showed close agreements between measured size distributions and actual size distributions.
Finally, it is shown that the scattered light intensity pattern can be measured accurately without the effect of multiscattering if the transmission ratio is larger than 50%.

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Since an ever-unrevealed shortcoming in dynamics was reported for phase-locked loops, two alternative arrangements have been proposed. This paper describes another novel configuration without a seperate phase comparator, making use of the linear time-voltage characteristics of ramp waves inside VCO's. In addition to requiring fewer circuit components, normalizing the loop gain can yield time-optimal responses without overshoots. Other features include the normal FM detection capability and unconstrained input for time-optimal operations. Implementation requires less than 10 IC's, providing the operating frequency range of 0.01Hz to 100kHz. A prototype demonstrated the above advantages.

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Recently, techniques of acquiring 3-D information at high speed and with accuracy have been pursued with increasing demands for advanced and sophisticated tasks that a robot has to carry out.
A new approach to simultaneously measure 3-D position and orientation of robot environments is proposed in this paper. The 3-D sensor consists of a camera using a position sensitive device (PSD) and multiple LEDs attached to robotic devices such as a robot's hand and a teaching device.
Their 3-D position and orientation are calculated based on both 2-D coordinate values of the LEDs in an image plane of the camera and geometrical relationships among 3-D positions of the LEDs.
The 3-D sensor has advantages of simple system configuration and real-time response for reliably acquiring 3-D information of robotic devices.
Experimental results of applications using the 3-D sensor are presented. They are as follows: (1) visual detection of robot's hand position and orientation, (2) teaching of robot paths by a 3-D teaching device.
They show the feasibility of applying the 3-D sensor to these kinds of robotic tasks. Finally, future subjects and extensions of the 3-D sensor are discussed.

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The present paper is concerned with a mathematical model analysis of the femoropatellar joint in human knee, taking into accunt the articular surface geometry and the mechanical properties of ligament and muscle.
Study on load bearing characteristics of human knee joint is one of the main subjects awaiting solution in orthopaedic surgery, and various experimental research works are having been performed in relative fields.
Notwithstanding the above, such characteristics have not been elucidated yet, because we can scarcely obtain fragmentary results, in actual fact, considering the difficulties in circumspect experimental works.
On the other hand, we may say that the composing a mathematical model of knee joint is effectual for quantitative analysis in respect that any arbitrary conditions can be settled upon easy by parametric alteration of input data, and various results can be inferred successively through mathematical model analysis.
The author has already deduced the curved surface equation to express the entire femorotibial articular surfaces mathematically through the application of computer aided designing theory.
In the present study, besides the similar equation was adopted to femoropatellar articular surfaces, a three-dimensional model of the relevant joint was composed, taking into account the mechanical properties of ligament and muscle. Then, the contact points trajectries between femoropatellar surfaces, the three-dimensional behavior of patella, and the like were tracked, according as the knee flection proceeds.

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