• Proceedings of the KIEE Conference
• /
• 2004.07d
• /
• pp.2239-2241
• /
• 2004

이 논문은 최적 제어 설계방법 중 하나인 LQR 제어기의 과도 상태를 개선하는 방법에 관한 연구이다. 적절한 상태가중행렬과 제어가중행렬을 설정한 후 대수 Riccati 방정식을 풀면 LQR 제어기가 설계된다. 그런데 이 가중행렬은 시행착오 방법을 이용하여 설정하기 때문에 설계된 제어기의 과도 상태를 개선하기 하기가 매우 어렵다. 이러한 문제점을 해결하기 위한 방법으로 closed-loop 근과 가중행렬과의 상관관계를 수학적으로 표현하고, 이를 바탕으로 설계조건을 만족하도록 시스템의 근을 이동시키는 가중행렬을 구하는 방법을 제시한다. 원운동형 도립진자(rotary type inverted pendulum)를 통해 matlab 모의실험으로 그 타당성을 검증한다. 얻어진 결과를 이용하면 원하는 극점을 갖는 LQR 제어기를 체계적으로 설계할 수 있다.

• Proceedings of the IEEK Conference
• /
• 2007.07a
• /
• pp.485-486
• /
• 2007

In this paper, we use Lyapunov equations and functions to consider the linear systems with perturbed system matrices. And we consider that what choice of Lyapunov function V would allow the largest perturbation and still guarantee that V is negative definite. We find that this is determined by testing for the existence of solutions to a related quadratic equation with matrix coefficients and unknowns the so-called matrix Riccati equation.

• Journal of the Korean Society of Marine Environment & Safety
• /
• v.19 no.6
• /
• pp.637-642
• /
• 2013

In this paper, an analysis results of towing force and towing points which are dominating factors to determine the behavior of towed ship are introduced. The towing force and towing points to achive the desired posture and its position of the towed vessel are derived based on simplified dynamics and linearization method. LQR algorithm for posture control is applied to linearized system and numerical simulation is also executed. Force based on COG(cneter of gravity) and gain of controller to achieve desired posture for target vessel are obtained by using Riccati matrix equation and pseudo inverse matrix is applied to analyze the relation between the derived force and its towing point. Based on this analysis method, towing force need to move the towed vessel from its initial position to target position can be calculated. The towing method including towing point and direction is also considered on this method. Finally, the relation between towing force and towing point is confirmed from the analysis and the results can be applied to arrangement of tug boats during salvage works.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1995.04a
• /
• pp.344-349
• /
• 1995

셀구조물은 선박, 항공기, 우주선 등의 산업분야에 자주 사용되는 중요한 구조요소로서, 이에 대한 연구도 공학적 필요성에 의해 많은 연구가 진행되어 왔다. Maddox등의 Rayleigh-Ritz법, Srinivasan and Bobby의 적분방정식 기법, Petyt의 유한요소법, Irie, Henderson등의 전달매트릭스법, 그 외 Webster, Petyt and Deb Nath, Blevins, Srinivasan and Krishnan등에 의해 여러가지 해석방법의 진동해석이 행해져 왔다. 현재 주로 사용되고 있는 매트릭스 구조해석 및 진동해석 방법으로는 유한요소법과 전달매트릭스법을 들 수 있다. 유한요소법은 범용적인 해석 프로그램의 개발은 수월하지만 대규모의 선형 연립방정식의 해법에 귀착되므로, 기억용량이 큰 대형컴퓨터가 필요하고, 반면 전달매트릭스법은 기억용량이 적은 퍼스널컴퓨터로도 계산수행이 가능하나 고차의 고유진동수를 구할 경우나, 중간에 단단한 경탄성지지가 존재할 경우 등에는 수치계산상의 문제점이 지적되고 있다. 이에 대한 대책으로, 상태변수를 바꾸어 넣은 Riccati방법, 각 절점의 기지의 상태변수를 제거하는 Frontal법, 전달매트릭스와 강성매트릭스를 결합시키는 방법 등이 보고 되고 있다. 이에 자자들은 퍼스널컴퓨터 이용에 적합한 고속, 고정도의 구조해석 및 진동해석 기법으로 전달영향계수법을 제안하여, 원판구조물, 사각판구조물, 원통형 셀구조물 등의 여러가지 형상구조물의 자유진동 해석에 적용해서, 종래의 전달매트릭스법에 비해 계산정도 및 계산속도의 양면에서 매우 우수함을 보고한바 있다. 본 연구에서는 동적영향계수의 축차전달에 그 개념을 두고 있는 전달영향계수법을 좀 더 일반화시키고 체계화시키기 위하여 탄성지지를 갖는 셀구조물에 적용하여 자유진동 해석 알고리즘을 정식화한 후, 간단한 모델에 대한 수치실험을 통해서 전달 영향계수법으로 구한 해를 전달매트릭스법의 결과와 비교.검토하여 본 방법의 유용성을 확인하였다.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.31B no.5
• /
• pp.65-72
• /
• 1994

We resolve the suboptimal $\infty$ control problem using (J,J')-lossless coprime factorization by transforming the linear fractional transformation (LFT) into chain scattering description (CSD) in discrete-time systems. The condition transformed LFT into CSD is that the inverse matrix of $P_{21}$ of standard plant exists. But, this paper presents the method of transforming LFT into CSD for 4-block problem in case that the inverse matrix of $P_{21}$ of standard plant does not exist and parameterization of the all suboptimal $\infty$T controllers using (J,J')-lossless coprime factorization. It is shown that this method can resolve the suboptimal $\infty$ control problem solving only two Riccati equations in discrete-time systems.

• Journal of the Institute of Convergence Signal Processing
• /
• v.3 no.2
• /
• pp.76-82
• /
• 2002

The objective of this paper is to design a robust controller for a flexible robot arm manipulator using LMI(Linear Matrix Inequality) theory, and confirm its effectiveness through experimentation. We first describe a modeling Process of the flexible arm in order to get a mathematical model, and then discuss how to approximately obtain the uncertainty of the model for robust control. As to the control system design, we adopt the LMI-based H$_{\infty}$ synthesis algorithm which has the merits of eliminating the regularity restrictions attached to the Riccati-based methods. As a result of this, we can cope with the parameter variation (that is, modeling uncertainty) due to the tip-load variation. Finally we confirm the effectiveness of the controller through experiment and simulation.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.17 no.8
• /
• pp.805-815
• /
• 1992

In this paper, robust decoupling control scheme of miftivarlable systems Is studied. Design methods for Input-Output decoupling systems with robustness against signal failure In arbitrary feedback loop or actuator loop Is suggested based on the Riccati type matrix equation and state feedback, and is simulated In Turbo-Generator systems with B-Input, 2 output. The results of simulation represents the decoupled and stable response against the failure of signal In sensor or actuator loop. However, the system designed by conventional ,it ate feedback shows the unstable response. This method Is applied for robust decoupling control of the complicated multivariable systems.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.6
• /
• pp.1381-1388
• /
• 1993

This paper presents a method for the simultaneous optimal design of structural and control systems. Sensitivities of performance index with respect to structural design variables are analyzed. The structural design variables are optimized to minimize the performance index by use of conjugate gradient method. The method is applied to a half model of an active vehicle suspension system with elastic body moving on a randomly profiled road. The suspension control force of an optimally controlled system in the presence of measurement errors are calculated by use of linear quadratic Gaussian control theory and Kalman filter theory. The performance index contains ride comfort, road holding and working space of suspension. The structural design variables taken are stiffness, daming properties and the position of the suspension system. The random road profile considered as colored noise is shaped from white noise by use of shaping filter. The performance of an optimal simultaneous structure/control system is compared with that of an optimal controlled system.

• Journal of the Korean Institute of Telematics and Electronics S
• /
• v.36S no.7
• /
• pp.50-61
• /
• 1999

\In this paper, we consider the optimal scheduling of detection and tracking parameters in phased array radars to minimize the radar energy required for track maintenance in a cluttered environment. We develop a mathematical model of target detection induced by a search process in phased array radars. In the mathematical development, we take into account the effect of unwanted measurements that may have originated from clutter or false alarms in the detection process. We use and analytic approximation of the modified Riccati equation of the probabilistic data association (PDA) filter to take into account the effect of clutter interference in tracking. Based on the search process and the tracking models, we formulate the optimal scheduling problem into a nonlinear optimal control problem. We solve a constrained nonlinear optimization problem to obtain the solution of the optimal control problem.