• Structural Engineering and Mechanics
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• v.16 no.3
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• pp.327-340
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• 2003

Variations in system parameters due to uncertainties of parameters may result in system performance deterioration and create system internal stability problems. Uncertainties in structural modeling of structures are often considered to ensure that the control system is robust with respect to response errors. So the uncertain concept plays an important role in the analysis and design of the engineering structures. In this paper, the active control of the intelligent structures with the uncertainties is studied and a new method for analyzing the robustness of systems with the uncertainties is presented. Firstly, the system with uncertain parameters is considered as the perturbation of the system with deterministic parameters. Secondly, the feedback control law is designed on the basis of deterministic system. Thirdly, perturbation analysis and robustness analysis of intelligent structures with uncertainties are discussed when the feedback control law is applied to the original system and perturbed system. Combining the convex model of uncertainties with the finite element method, the analysis theory of the robustness of intelligent structures with the uncertainties can be developed. The description and computation of the robustness of intelligent structures with uncertain parameters is obtained. Finally, a numerical example of the application of the present method is given to show the validity of the method.

• Journal of Advanced Marine Engineering and Technology
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• v.18 no.4
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• pp.102-111
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• 1994

This article deals with the problem of designing a robust algorithm for the motion control of robot manipulator whose nonlinear dynamics contain various uncertainties. To ensure high performance of control system, a model-based feedforward compensation with continuous robust control has been developed. The control structure based on the deterministic approach consists of two parts : the nominal control law is first introduced to stabilize the system without uncertainties, then a robust nonlinear control law is adopted to compensate for both the resulting errors(or structured uncertainties) and unstructured uncertainties. The uncertainties assumed in this study are bounded by polynomials in the Euclidean norms of system states with known bounding coefficients. The presented control scheme is relatively simple as well as computationally efficient. With a feasible class of desired trajectories, the proposed control law provides sufficient criteria which guarantee that all possible responses of the closed-loop system are uniformly ultimately bounded in the presence of uncertainties. Therefore, the control algorithm proposed is shown to be robust with respect to the involved uncertainties.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.561-565
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• 2005

Sliding mode control (SMC) is an effective method of controlling systems with uncertainties which satisfy the so-called matching condition. However, how to effectively handle mismatched uncertainties of systems is still an ongoing research issue in SMC. Several methods have been proposed to design a stable sliding surface even if mismatched uncertainties exist in a system. Especially, it is presented that robustness and efficiency of SMC for linear systems with mismatched uncertainties can be improved by reducing mismatched uncertainties in the reduced-order system. The reduction method needs a new sliding surface with an additional component based on Lyapunov redesign technique. In this paper, a stable sliding surface which contains additional component to reduce the influence of mismatched uncertainties, is introduced. It is designed by using linear matrix inequalities that guarantees the stability of the system. A numerical example demonstrates the validity of the proposed scheme.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.8
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• pp.689-696
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• 2000

In this paper we propose an eminent controller for wheeled mobile robots. This controller consists of an input-output linearization controller trying to stabilize the system and a neural network controller to compensate for uncertainties. The uncertainties are divided into two parts. First unstructured uncertainties include the elements related with system order such as friction disturbance. Second structure uncertainties are the incorrect system parameters A neural network structure of the proposed overall controller learns structural errors of the wheeled mobile robots with uncertainties and includes the neural network output. This controller learns quickly the model and has good tracking performance Simulation results show that the proposed controller is more efficient than analog controllers.

• Journal of Electrical Engineering and Technology
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• v.7 no.1
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• pp.124-131
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• 2012

This paper deals with robust stability of linear time-invariant (LTI) systems with unstructured uncertainties. A new relation between uncertainties and system poles perturbed by the uncertainties is derived from a graphical analysis. A stability criterion for LTI systems with uncertainties is proposed based on this result. The migration range of the poles in the proposed criterion is represented as the bound of uncertainties, the condition number of a system matrix, and the disc containing the poles of a given nominal system. Unlike the existing methods depending on the solutions of algebraic matrix equations, the proposed criterion provides a simpler way which does not involves algebraic matrix equations, and a more flexible root clustering approach by means of adjusting the center and the radius of the disc as well as the condition number.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.25-25
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• 2000

This paper presents a design method of sliding mode control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we define a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with only mismatched uncertainties using a form of linear matrix inequality (LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding mode controller that stabilizes the overall closed-loop system.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.3
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• pp.193-197
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• 2001

This paper presents a design method of sliding model control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we defined a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use the SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with mismatched uncertainties using a form of linear matrix inequality(LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding model controller that stabilizes the overall closed-loop system.

• Proceedings of the KIEE Conference
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• 2000.07a
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• pp.224-226
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• 2000

In this paper, a robust $H_{\infty}$ controller, based on the Riccati equation approach, is proposed for HVDC power system with parametric uncertainties. Bounds of power system parametric uncertainties are included in Riccati equation to improve the robustness of controller. The proposed $H_{\infty}$ controller for the stabilization of HVDC power system can ensure that the overall system is asymptotically stable for all admissible uncertainties. Simulation results show that the proposed $H_{\infty}$ controller can achieve good performance in presence of uncertainties of power system.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.459-459
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• 2000

The purpose of this paper is the application of the techniques for the new estimation of robustness for the aircraft systems having structured uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. The number of uncertainties will be the degree of freedoms in the calculation of the robust stability regions called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, in this paper, the quadratic form of Lyapunov function is utilized. In this paper, the practical system of vertical take-off and landing (VTOL) aircraft is analyzed with the proposed stability criteria based upon the Lyapunov direct method. The application of numerical procedures can prove the improvements in estimations of robustness with structured uncertainties. The applicable aircraft system is assumed to be linear with time-varying with nonlinear bounded perturbations.

• Journal of Ocean Engineering and Technology
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• v.11 no.4
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• pp.169-179
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• 1997

This paper presents a discrete-time sliding mode control of an autonomous underwater vehicle with parameter uncertainties and long sample interval based on discrete variable structure system. Although conventional sliding mode montrol techniques are robust to system uncertainties, in the case of the system with long sample interval, the sliding control system reveals chattering phenomenon and even makes the system unstable. This paper considers the AUV which acquires position informations from a surface ship through an acoustic telemetry system with a certain discrete interval. The control system is designed on the basis of a Lyapunov function and a sufficient condition of the switching gain to make the system stable is give. Each component of the switching gain can be determined separately one another. The controller is robust to the uncertainties, and reaching condition of the control system is satisfied for any initial condition. This control law is a generalized form of the discrete sliding mode control and reduce the chattering problem considerably. Motion control of the AUV in the vertical plane shows the effectiveness of the proposed technique.