• Structural Engineering and Mechanics
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• v.26 no.2
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• pp.163-178
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• 2007

In practical engineering, the uncertain concept plays an important role in the control problems of the vibration structures. In this paper, based on matrix perturbation theory and interval finite element method, the closed-loop vibration control system with uncertain parameters is discussed. A new method is presented to develop an algorithm to estimate the upper and lower bounds of the real parts and imaginary parts of the complex eigenvalues of vibration control systems. The results are derived in terms of physical parameters. The present method is implemented for a vibration control system of the frame structure. To show the validity and effectiveness, we compare the numerical results obtained by the present method with those obtained by the classical random perturbation.

• Journal of Industrial Technology
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• v.11
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• pp.107-114
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• 1991

This paper deals with the robustness of closed-loop poles of a linear time-invariant system with uncertain parameters. A new method is presented to calculate the perturbation of a pole-located region due to parameter uncertainties. A method to calculate allowable bounds on parameter uncertainties is also presented to retain closed-loop poles in a specified region. Based on Lyapunov equations and norm operations, they provide useful measures on the robustness of closed-loop poles. An example is given to illustrate proposed methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.6
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• pp.1173-1178
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• 2010

In this note, a systematic design of a new robust nonlinear integral variable structure controller based on state dependent nonlinear form is presented for the control of uncertain more affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear integral variable structure controller is presented. To be linear in the closed loop resultant dynamics and remove the reaching phase problems, the linear integral sliding surface is suggested. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear integral sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1754-1760
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• 2011

In this paper, a systematic design of a robust nonlinear multivariable variable structure controller based on state dependent nonlinear form is presented for the control of MIMO uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After a MIMO uncertain affine nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding diagonalized control input is proposed to satisfy the closed loop global exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.945-949
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• 2010

In this paper, a systematic design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.7
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• pp.1295-1301
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• 2010

In this note, a systematic general design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and mismatched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the nonlinear integral-type sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the nonlinear integral-type sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.331-342
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• 2004

The vibration control problem of structures with random parameters is discussed, which is approximated by a deterministic one. A method for calculating the standard deviations of eigenvalues of the closed-loop systems is presented by using the random perturbation. The method presented in this paper will not require the distribution function of the random parameters of the systems other than their means and variances. Similarly, the distribution function of the random eigenvalues will not be computed other than their means and variances. The standard deviations of eigenvalues of the uncertain closed-loop systems can be used to estimate the stability robustness. The present method is applied to a vibration control system to illustrate the application. The numerical results show that the present method is effective.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.8
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• pp.682-690
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• 2002

This paper presents an output feedback controller design method for uncertain linear systems with sinusoidal disturbance of uncertain frequencies. The controller needs to compensate for the performance deterioration due to the uncertain frequencies of sinusoidal disturbance. To this end, we introduce a virtual system including the dynamics corresponding to the uncertain frequencies and design a controller which minimizes the output difference between the virtual system and the closed-loop system. In other words, the controller is designed so that the closed-loop system approximates the virtual system. The feedback controller is achieved by solving an LMI optimization problem involving a robust $H_{\infty}$ constraint. The advantages of the proposed design method are examined by comparing it with a design method that only minimizes the $H_{\infty}$ norm of the transfer function between the sinusoidal disturbance and the output. The proposed design method is applied to the track-following system of rewritable optical disk drives and is evaluated through an experiment.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1414-1417
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• 2003

In this paper, sliding mode controller for discrete-time nonlinear systems with uncertainties and disturbances are proposed. The concept of time-delay control (TDC) which consists of estimating the uncertain dynamics of the system through past observations of the system response is used. The proposed controller guarantees that the closed-loop system states are globally uniformly ultimately bounded (GUUB). It is also shown that the closed-loop system states are globally uniformly asymptotically stable (GUAS) if uncertainties are constant.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.8
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• pp.1-14
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• 1996

Design of a reliable control systems is investigated for a class of uncertain linear plants. The uncertainty considered here is for the ase of uncertainty in the system matrix. A decentralized control scheme with two observer-based feedback controllers is developed, and it is shown that the resulting closed-loop system is reliable in the sense that the control scheme provides guaranteed stability and $H_{\infty}$-norm bounded performance in the event of sensor and/or actuator failures as well as in the presence of parameter uncertainties. We observed that soft-type failures were additional exogenous inputs to the closed-loop system. As a results, the sensor and/or actuator failures can be tolerated in the design, which is achieved by extending the methodology developed in.