• Transactions on Control, Automation and Systems Engineering
• /
• 제3권3호
• /
• pp.164-169
• /
• 2001

This paper considers the problem of robust stabilization and disturbance attenuation for a class of uncertain singularly perturbed systems with norm-bounded nonlinear uncertainties. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed-loop system for all $\varepsilon$$\in$(0, $\infty$). Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed.

• Journal of Electrical Engineering and information Science
• /
• 제1권2호
• /
• pp.33-38
• /
• 1996

In this paper, we present a robust H\ulcorner control design method for parameter uncertain systems that have delay in both state and control input. Through a certain algebraic Riccati inequality approach, a state feedback controller is obtained. The proposed state feedback controller stabilizes parameter uncertain delay systems and guarantees disturbance attenuation within a prescribed level. An illustrative example is given to demonstrate the results of the proposed method.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
• /
• pp.60-63
• /
• 1996

This study deals with the nonlinear H$_{\infty}$ control problem of linear system using nonlinear weight. Generally the solvable condition of nonlinear H$_{\infty}$ control problem is given by the Hamilton Jacobi equality or inequality, but it is very difficult to solve. In this study, some constraints of nonlinear weight reduce the solvable condition to linear Riccati equation. Some examples of the control system design using nonlinear weight are shown.n.

• 제어로봇시스템학회논문지
• /
• 제2권1호
• /
• pp.1-4
• /
• 1996

This paper presents a state feedback $H^{\infty}$ controller design method for linear systems with delayed states and inputs. We derive a sufficient condition that the closed-loop system is asymptotically stable for all time-delays and that the $H^{\infty}$-norm of the closed-loop transfer function is less than or equal to some prescribed level $\gamma$. And we propose a sufficient condition for the existence of a state feedback $H^{\infty}$ controller using a form of linear matrix inequality(LMI). Furthermore, we show that the state feedback $H^{\infty}$ controllers can be obtained from solutions satisfying LMI.

• International Journal of Precision Engineering and Manufacturing
• /
• 제3권4호
• /
• pp.78-86
• /
• 2002

In this paper, LMI (Linear Matrix Inequality) based on H$\_$$\infty$/ controller for a lire of sight (LOS) stabilization system. It shows that the proposed controller has more excellent stabilization performance than that of the conventional PI-Lead controller. An H$\_$$\infty$/ control has been also applied to the system for reducing modeling errors and the settling time of the system. The LMI-based H$\_$$\infty$/ controller design is more practical in view of reducing a run-time than Riccati-based H$\_$$\infty$/ controller. This H$\_$$\infty$/ controller is available not only to decrease the gain in PI-Lead control, but also to compensate the identifications for the various uncertain parameters. Therefore, this paper, shows that the proposed LMI-based H$\_$$\infty$/ controller had good disturbance attenuation and reference input tracking performance compared with the control performance of the conventional controller under any real disturbances.

• 제어로봇시스템학회논문지
• /
• 제3권1호
• /
• pp.1-8
• /
• 1997

In order to reject the steady-state tracking error, it is common to introduce integral compensators in servosystems for constant reference signals. However, if the mathematical model of the plant is exact and no disturbance input exists, the integral compensation is not necessary. From this point of view, a two-degree-of-freedom(2DOF) servosystem has been proposed, in which the integral compensation is effective only when there is a modeling error or a disturbance input. The present paper considers robust stability of this 2DOF servosystem incorporating an observer to the structured and unstructured uncertainties of the controlled plant. A robust stability condition is obtained using Riccati inequality, which is written in a linear matrix inequality (LMI) and independent of the gain of the integral compensator. This result impies that if the plant uncertainty is in the allowable set defined by the LMI condition, a high-gain integral compensation can be carried preserving robust stability to accelerate the tracking response.

• 융합신호처리학회논문지
• /
• 제3권2호
• /
• pp.76-82
• /
• 2002

본 연구는 유연한 로봇팔의 선단 위치를 제어하기 위한 강인한 제어기의 설계하고 이것의 효과를 실험을 통하여 확인하는 데 있다. 이를 위해 먼저 유연한 로봇팔의 모델링을 Lagrange 방정식을 이용하여 수행하여 시스템의 수식모델을 구한 뒤, 이 모델을 기본으로 하는 강인한 제어기의 설계를 LMI(Linear Matrix Inequality)을 적용한 H$_{\infty}$이론을 도입하여 수행한다. 이 과정에서 로봇팔의 선단부하 변경으로 인한 시스템 파라미터의 변동을 플랜트가 가지는 불확실성 영역으로 간주하여 이를 설계에 적극적으로 반영함으로서 결과적으로 플랜트의 파라미터 변동에 강인한 제어기를 구현하고 이것의 유효성을 실험을 통하여 확인한다. .실험을 통하여 확인한다. .

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
• /
• pp.135-140
• /
• 1998

The concept of dissipativity and passivity are of interest to us from a theoretical as well as a practical point of view. It is well known that the Riccati equation is derived from the dissipation inequality which expresses the fact that the system is dissipative; the energy stored inside the system doesn't exceed the amount of supply which flows into the system. The pencil model is regarded as a representation based on behavioral approach introduced by J.C. Willems. It has first order in the internal variable and zeroth order in the external variable. In general, any matrix pencil is transformed into a canonical form which is consist of several kind of sub-pencils, One of them has row full rank for $^\forall S\;\in\;\mathds{C}\;\bigcup{\infty}$, we call it under-determined mode of the model. In our opinion, most important properties of dynamical system lay in the mode. According to the properties of canonical form for pencil, it is shown that the storage function which characterizes the dissipativity of the system can be written as a LMI for the under-determined mode, if the system doesn't include impulse mode.

• International Journal of Control, Automation, and Systems
• /
• 제1권1호
• /
• pp.11-18
• /
• 2003

The parametric approaches to sliding mode design are newly proposed for the class of multivariable systems. Our approach is based on an explicit formula for representing all the slid-ing modes using the Lyapunov matrices of full order. By manipulating Lyapunov matrices, the sliding modes which satisfy the design criteria such as the quadratic performance optimization and robust stability to parametric uncertainty, etc., can be easily obtained. The proposed ap-proach enables us to adopt a variety of Lyapunov- (or Riccati-) based approaches to the sliding mode design. Applications to the quadratic performance optimization problem, uncertain systems, systems with uncertain state delay, and the pole-clustering problem are discussed.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1997년도 하계학술대회 논문집 F
• /
• pp.2196-2199
• /
• 1997

In the industrial motor drive system, a shaft torsional vibration is often generated when a motor and a load are connected with a flexible shaft. This paper treats the vibration suppression control of such a system. In this paper, a control system design method using Linear Matrix Inequality (LMI), which is a tool for control design that replaces or complements Lyapunov-Riccati equations, is provided and a $H_{\infty}$ speed controller for a induction motor by LMI is proposed. In the $H_{\infty}$ speed controller, weights are used to satisfy tracking and disturbance rejection. Experimental results show the validity of the proposed $H_{\infty}$ speed controller by LMI, and this controller is compared with the state feedback controller.