WALSH 함수 단일항 전개를 이용한 선형 시변계의 최적제어

朴俊勳 忠州大學校 1996 한국교통대학교 논문집 Vol.31 No.2

When modern control techniques are used in the design of control systems for dynamic processes, a feedback law often results which requires availability of the whole state of the plant. For time varying systems, the optimal control is generated by a feedback law of the form u??(t) = -K(t)x(t). The time varying optimal control vector u??(t) and feedback gains K(t) are computed from the solution of nonlinear matrix Riccati differential equation. But the design apporach taken in this paper is to replace the optimal control vector u??(t) and gains K(t) with their approximate values which are generated using a single-term of Walsh series approach. The method is illustrated by an example.

WALSH 함수를 이용한 비선형계의 파라메터 추정에 관한 연구

朴俊勳 忠州大學校 1995 한국교통대학교 논문집 Vol.30 No.2

This paper deals with a parameter estimation of non-linear systems using Walsh functions which are important analytical tools for control theory and signal processing . Concern with this thesis, a method for the state estimation of bilinear systems, one of the non-linear systems, using Walsh transforms is devised, and the simulation results are compared with Runge-Kutta method. Compared with other conventional method, the simulation results with simpler computation are ascertained by using the method presented here. Accordingly the results approach to the original functions.

BPF를 이용한 비선형 대규모 시스템의 부시스뎀 최적화

朴俊勳 忠州大學校 1998 한국교통대학교 논문집 Vol.33 No.2

This paper presents a method for sub-system optimal control of large scale nonlinear systems based on the idea of orthogonal approximation. In this paper block pulse functions(BPF) are chosen as the orthogonal set. BPF have become increasingly attractive recently, due to the convenience and simplicity of related computations. The method gives piecewise constant solutions with minimal meansquare-error. And this paper also addresses a hierarchical recursive algorithms. Finally, a suitable example is given to illustrate the algorithms.

대규모 비선형 시스템의 새로운 계층별 최적제어

박준훈,김종부,Park, Joon-Hoon,Kim, Jong-Boo 대한전자공학회 1999 電子工學會論文誌-T Vol.t36 No.2

대규모 시스템 제어와 관련하여 몇 개의 부시스템으로 분할하여 처리하는 계층별 제어이론이 많이 연구되어 왔으며 특히 치수가 높은 대규모 비선형 시스템의 경우에 고차의 비선형 미분방정식을 동시에 적분을 해야하고 많은 계산량을 필요로 하므로 해를 구하기가 어려운 문제가 있다. 1980년대 Singh과 Hassan은 상호예측 알고리즘(two level prediction algorithm)을 제시한바 있고 이 방법은 비선형 대규모 시스템의 최적제어에 효과적이나 시스템 행렬 Q, R, S, H에 따라 제한된 최적화 구간에서만 성립되는 등 최적화 구간의 길이와 수렴성 여부가 행렬 값에 영향을 받는 알고리즘상의 단점이 있다. 본 연구에서는 수렴조건으로부터 평가함수에 구속조건(quadratic penalty term)을 부여하지 않는 새로운 개선된 알고리즘을 제시 적용하여 시스템 행렬 결정을 위한 과정 없이 수렴속도의 향상과 함께 최적의 수렴성 및 최적화 구간을 얻도록 했다. 분할된 비선형 시스템의 최적제어를 위해서는, 대수 반복연산만으로 2점 경계치 문제(two point boundary value problem)를 해결함으로써 기존의 수치 해석법에 비해 연산이 간단한 블록펄스 변환 방법을 사용해서 처리했다. This paper presents a new possibility of calculating optimal control for large scale which consist of non-linear dynamic sub-systems using two level hierarchical structures method. And the proposed method is based on the idea of block pulse transformation to simplify the algorithm and its calculation. This algorithm used an expansion around the equilibrium point of the system to fix the second and higher order terms. These terms are compensated for iteratively at the second level by providing a prediction for the states and controls which form of a part of the higher order terms. In this new approach the quadratic penalty terms are not used in the cost function. This allows convergence over a longer time horizon and also provides faster convergence. And the method is applied to the problem of optimization of the synchronous machine. Results show that the new approach is superior to conventional numerical method or other previous algorithm.

대규모 비선형 시스템의 계층별 최적제어

朴俊勳 충주대 산업과학기술연구소 1999 産業科學論文集 Vol.7 No.1

This paper presents an algorithm for hierarchical optimal control of large scale nonlinear systems based on the idea of orthogonal approximation. In this paper block pulse functions(BPF) are chosen as the orthogonal set. This algorithm used an expansion around the equilibrium point of the system to fix the second and higher order terms. These terms are compensated for iteratively at the second level by providing a prediction for the states and controls which form of a part of the higher order terms. The method gives piecewise constant solutions with minimal mean-square-error. And this paper also addresses a hierarchical recursive algorithms. Finally, a suitable example is given to illustrate the algorithms using BPF transformations.

STWF를 이용한 비선형 시스템 최적제어 알고리즘

박준훈 忠州大學校 2002 한국교통대학교 논문집 Vol.37 No.3

This paper presents an optimal control algorithm for non-linear systems using singl term Walsh functions method. And the proposed method is based on the idea of Walsh functions transformation to simplify the algorithm and its calculation. And this paper used the method proposed by J. P. Matuszewski for adaptive optimal control scheme. And the method is applied to the problem of optimization of the Van der Pol equation. Results show that suggested algorithm is superior to conventional numerical method or other previous algorithms.

適應形 接近 方法에 依한 線形 時變係의 最適制御에 關한 硏究

朴俊勳 충주대학교 1992 한국교통대학교 논문집 Vol.26 No.-

This paper presents an adaptive approach method for optimal control of linear time-varing (LTV) systems. The theory of optimal control of linear systems with quadratic performance index is well known and firmly established. But the solutions of stae equation and Riccati differential equation are usually quite difficult. For solving these problems, the adaptive approach scheme is proposed and block pulse transformation is used. In this way, the states in the A(t) and B(t) matirces are considered constant at the present value ti and an optimal cotrol is determined by integrating the matrix Riccati equation backward from final time to present time. The method proposed in this paper is simple and computationally advantageous. And viability of the this method is established with simulation results for apporpriate examples.

마이크로프로세서를 利用한 高速 WALSH 變換器 具現

朴俊勳 忠州大學校 1994 한국교통대학교 논문집 Vol.29 No.2

Walsh function and transform are important analytical tools for control theory and signal processing and have wide applications in those fields, expecially in the field of digital co-mmunications. There is a need for a fast Walsh transformer in order to realize certain applications. So this paper presents a microprocessor based design and implementation method of fast Walsh transformer for a signal processing. An input data of a processor are directly reordered and transmitted to the data storage. And then, the fourier coefficients are determined as the combination of the Walsh coefficients by the Walsh-Fourier mutual conversion algorithm described in this paper.

STWF를 이용한 비선형계 해석에 관한 연구

朴俊勳 충주대 산업과학기술연구소 1997 産業科學論文集 Vol.5 No.-

This paper deals with a analysis of non-linear systems using single term Walsh functions (STWF) which are important analytical tools for control theory. For this thesis, the STWF method which is more useful than conventional WF and its applications is introduced. Vail der Pol equation is one of the non-linear systems. So this equation is analyzed by the single term Walsh functions transformation method. And compared with conventional WF method, the method presented in this paper is more simple and accurate for a analysis of non-linear systems. Accordingly the results apporach to the original functions.

마이크로프로세서를 利用한 WALSH 函數 發生器 具現에 關한 硏究

朴俊勳 忠州大學校 1993 한국교통대학교 논문집 Vol.28 No.-

Walsh function and transform are important analytical tools for control theory and signal processing and have wide applications in those fields, especially in the field of digital communications. There is a need for a walsh function generator in order to realize certain applications. And a number of different designs are known. But design and implementation of such a generator through hardware logic may give rise to orthogonality error. To further develop Walsh function generator which gets rid of othogonality error, this paper presents a microprocessor based design and implementation method.