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## Transactions of the Institute of Systems, Control and Information Engineers Vol. 4 (1991), No. 6

• ### Studies on the Controlled Path Integrals-I. Structure Algorithm

pp. 207-215

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First, it is shown that the output of the control system with statespace description can be expressed by the integral of completely integrable differential 1-form along the controlled path of the system, which is named as the “controlled path integral”.
Adopting the controlled path integrals as the outputs, we construct the “Structure Algorithm” for the nonlinear system defined on a differentiable manifold M with a vector field X=X0+u1X1+…+umXm, control inputs ui (i=1, …, m), and outputs Yk=∫ωk (X) dt (k=1, …, l), where the differential 1-forms ωk are not necessarily completely integrable. Coefficients of linear dependence of differential forms are assumed to be C-functions defined on M. If the coefficients are constant around a point, we can derive a feedback control law which linearizes the input output relations of the system in an appropriate neighborhood of the point. Moreover, in order to calculate the feedback law, we can dispense with the local coordinates system, if the global coordinates describing the dynamic behaviour of the system are available.
Since the performance index of the optimal control can be also expressed by the controlled path integral, we recommend the controlled path integrals of differential forms and more general tensors for the study of control systems.
• ### A Design of Adaptive Observer to Estimate Periodic Unknown Disturbances

pp. 216-225

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An adaptive observer to estimate deterministic periodic disturbances in servo systems is proposed. The observer in this paper uses a sinusoidal wave model as a disturbance model, which includes frequencies as unknown parameters. The adaptive observer identifies frequencies of the disturbance model, then estimates the disturbance. This paper gives a simple condition of the observability of the disturbance. It also gives a simple scheme to calculate the linear model for the frequency identification. The proposed method to estimate the disturbance is straightforward and it does not require to calculate a transfer matrix for the observable canonical form. This scheme and the method are obtained by taking account of the restricted structure of disturbance models. The results of disturbance estimation in two examples are shown. These estimations are obtained from simulated data and experimental data of the repeated movement of the 5th axis of a manipulator.
• ### A Representing Method of Cartographic Information Data Using Verbal Representation

pp. 226-234

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We present a method for representing the 3D surfaces using the verbal representation, which human beings use for representation of topography. This method has advantages for representing relation of mountains and valleys. And the verbal representation gives human beings a concept of shapes through a small amount of information which is represented by symbols. It is expected that the verbalizing of the shape will make it possible to represent a shape features which is hard to be represented by contour lines. That is why the verbalizing is one of symbolizing methods of the shape. Therefore, an intelligent processing, such as inference, abstraction and so on, is executed on a computer.
In this paper, the words used for a topographical representation in the cartography are discussed. Next, the words used for the verbal representation are defined in 3D space. And the method is applied to a topographic map for representing a feature of the topography in a different way from the contour lines. Finally, we present a representing method of cartographic information data using the verbal representation.
• ### On-line Diagnosis Technique for Electro-Hydraulic Servo Dynamics of Rolling Mills Based on Parameter Estimation

pp. 235-244

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This paper deals with a condition diagnosis technique to maintain a dynamic performance of electro-hydraulic servo system and to assure thickness accuracy.
The diagnosis technique has following two features. One is to estimate the parameters of servo dynamics during rolling without specified input signals for testing. The other is to diagnose the degradation trend of the servo system and carry out the predictive maintenance based on the on-line monitoring of the estimated parameters, such as the resonant frequency and the damping coefficient.
For the plate rolling, the servo signals at biting condition are used, because these signals have high frequency components enough for the estimation. The parameters are estimated such that the frequency characteristics of the model is optimally matched to the actual data. On the other hand, servo data at steady state rolling is used for the strip rolling. The parameters are calculated recursively by the least square estimation.
These methods have been successfully applied to the actual rolling and the thickness variation caused by the servo degradation can be reduced by servo gain adjustment according to the estimated parameters.
• ### Implementation of Model Following Control for Nonlinear Discrete-Time Systems by CMAC

pp. 245-251

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This paper discusses a design method of “neural controller” which achieves the model following control for a SISO nonlinear discrete-time system. If the system dynamics is completely known, the model following control law can be derived as a nonlinear function of input-output sequence via the nonlinear control theory. Under reasonable assumptions, a neural network CMAC-Cerebellar Model Arithmetic Computer-is able to learn both the uncertain nonlinear dynamics of the system and the nonlinear function which yields the model following controller. Moreover, in order to improve the accuracy and the speed of learning, the data presented to the CMAC are transformed by the difference method or the correlation method. It is shown by computer simulations that our method works well and the correlation method is better than the difference method.
• ### The Improvement of Adaptive Observer's Convergency with the Prediction of Parameter Errors

pp. 252-253

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