• 제어로봇시스템학회논문지
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• 제5권6호
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• pp.647-655
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• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

• 제어로봇시스템학회논문지
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• 제1권2호
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• pp.71-77
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• 1995

The control effectiveness and disturbance suppressibility are mainly governed by a left eigenstructure of a system. In this paper, a control algorithm which uses an output feedback eigenstructure assignment scheme is proposed in order that a desired closed-loop system has the specified degree of controllability and/or degree of disturbance suppressibility. To do this, a modal and a gross disturbance suppressibility measures are proposed. A modified version of Hamdan and Nayfeh's modal controllability measure is also presented. The validity and usefulness of the proposed measures and the controller design algorithm are illustrated by designing a controller for a third-order system as an example.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권2호
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• pp.93-105
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• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.399-415
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• 2024

We looked at nonlocal controllability for Hilfer fractional differential equations with almost sectorial operator in this manuscript. We show certain necessary criteria for nonlocal controllability using the measure of noncompactness and the Mönch fixed point theorem. Finally, we provided theoretical and practical applications are given to demonstrate how the abstract results might be applied.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.47-51
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• 1993

A method of finding the optimal actuator location for efficient control of the modes of interest is presented. The proposed approach relies on certain quantitive measure of degree of controllability based on the controllability grammian. This measure proves to be useful for regulating problem of the undamped system and can be extended to cover the tracking problem of the viscous damped system. The example of the uniform cantilever beam is given to verify the effectiveness of the method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.412-419
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• 1993

The transient responses of a linear system having undesired disturbances are dominantly governed by the system's left eigenstructure(eigenvalues/left eigenvectors). In control system design problem of altering the transient response of the system, both the controllability and the disturbance suppressibility, should be considered simultaneously to obtain a robust, effective controller. The controllability of the system may be degraded if the left eigenstructure is chosen to suppress the disturbance, or vice versa. In this paper, first, proposed are a modal disturbance suppressibility measure and an improved version of the modal controllability measure suggested by Hamdan and Nayfeh. Second, a simple and general left eigenstructure assignment scheme, considering both the proposed modal disturbance suppressibility measure and the improved version of modal controllability measure, is suggested. When the previous works are applied to assign the left eigenvectors may differ from the desired ones. But the proposed left eigenstructure assignment scheme makes it possible to achieve the desired colsed-loop eigenvalues exactly, provided the desired left eigenvectors reside in the achievable subspace. In case the desired left eigenvectors do not reside in the achievable subspace, the closed-loop eigenvalues are achieved exactly and the left eigenvectors are assigned to the best possible set of eigenvectors in the least square sense. Finally, a numerical example is included to confirm and demonstrate the usefulness of our propositions and to illustrate the proposed design scheme.

• 한국가스학회지
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• 제3권1호
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• pp.27-32
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• 1999

화학 공정은 그 특성상 비선형성이 크고, 다변수 시스템이며, 그 구조가 복잡하다. 그러나 현재까지 개발된 제어성 평가 방법들은 제어성의 평가 방법이 복잡하고, 평가에 필요한 정보가 설계의 초기 단계에서는 알 수 없는 경우가 많다 따라서 공정 및 공장 설계 과정에서 제어성의 평가 및 향상 단계를 적절하게 도입하기 위해서는 이를 위한 절차에 대한 연구가 필요하다. 초기 설계 단계에서의 정보를 이용하여 제어성을 평가하기 위해서는 공정 구조를 분석하는 것이 가장 효율적이다. 입력 변수와 출력 변수가 얼마나 직접적으로 영향을 주는가를 나타내는 척도로는 상대 차수가 있다. 열교환망 합성에서 상대 차수를 이용한 구조적 제어성 분석 방법이 설계 초기 단계에서 효율적임을 알 수 있었다.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.787-800
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• 2000

In this paper we consider an optimal control system described by n-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem. We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.

• 대한수학회보
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• 제38권1호
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• pp.29-53
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• 2001

This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2008년도 춘계학술대회논문집
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• pp.63-70
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• 2008

In this paper, we propose a bearing redundant coordinates and decoupled PD controller for 5-axes active magnetic bearing system, which consists of two bearing parts such as three-pole hybrid active magnetic bearing for stabilize the radial direction and ring-type permanent magnetic bearing stabilizing in axial and tilting motion. Based on derived system equation with decoupled control scheme, we conduct the modal analysis and measure of modal controllability and observability.