• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.134-140
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• 1999

The robust generalized H2 filtering problem for a class of discrete time uncertain linear systems satisfying the sum quadratic constraints(SQCs) is considered. The objective of this paper is to develop robust stability condition using SQCs and design a robust generalized Ha filter to take place of the existing robust Kalman filter. The robust generalized H2 filter is designed based on newly derived robust stability condition. The robust generalized Ha filter bounds the energy to peak gain from the energy bounded exogenous disturbances to the estimation errors under the given positive scalar ${\gamma}$. Unlike the robust Lalman filter, it does not require any spectral assumptions about the exogenous disturbances . Therefore the robust generalized H2 filter can be considered as a deterministic formulation of the robust Kalman filter. Moreover, the variance of the estimation error obtained by the proposed filter is lower than that by the existing robust Kalman filter. The robustness of the robust generalized H2 filter against the uncertainty and the exogenous signal is illustrated by a simple numerical example.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2731-2743
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• 1996

When modeling error is large of plant is time-varying, it is hard to obtain good robust performance and robust stability by conventional contorl methods. Here, we need to design a robust controller bearing modeling error. In this paper, based on recently developed Time Delay Control(TDC) and Disturbance Observer the output feedback Robust Disturbance Observer(RDO), which is easily combined with general linear control, is proposed. Proposed RDO is derived from extending the main idea of Disturbance Observer to multi-input multi-output linear system. RDO solves robust stability problem of Disturbance Observer and has the robust performance same as nominal performance. RDO controlled dual stage positioning system shows excellent robust performance.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1855-1866
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• 2003

This paper discusses an entire procedure for a robust controller design and its implementation of an AMB (active magnetic bearing) spindle, which is part II of the papers presenting details of system modeling and robust control of an AMB spindle. Since there are various uncertainties in an AMB system and reliability is the most important factor for applications, robust control naturally gains attentions in this field. However, tight evaluations of various uncertainties based on experimental data and appropriate performance weightings for an AMB spindle are still ongoing research topics. In addition, there are few publications on experimental justification of a designed robust controller. In this paper, uncertainties for the AMB spindle are classified and described based on the measurement and identification results of part I, and an appropriate performance weighting scheme for the AMB spindle is developed. Then, a robust control is designed through the mixed ${\mu}$ synthesis based on the validated accurate nominal model of part I, and the robust controller is reduced considering its closed loop performance. The reduced robust controller is implemented and confirmed with measurements of closed-loop responses. The AMB spindle is operated up to 57,600 rpm and performance of the designed controller is compared with a benchmark PID controller through experiments. Experiments show that the robust controller offers higher stiffness and more efficient control of rigid modes than the benchmark PID controller.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.10
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• pp.755-767
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• 2003

This paper proposes a robust fault-tolerant control framework for robot manipulators to maintain the required performance and achieve task completion in the presence of both partial joint failures and complete joint failures and uncertainties. In the case of a complete joint failure or free-swinging joint failure causing the complete loss of torque on a joint, a fully-actuated robot manipulator can be viewed as an underactuated robot manipulator. To detect and identify a complete actuator failure, an on-line fault detection operation is also presented. The proposed fault-tolerant control system contains a robust adaptive controller overcoming partial joint failures based on robust adaptive control methodology, an on-line fault detector detecting and identifying complete joint failures, and a robust adaptive controller overcoming partial and complete joint failures, and so eventually it can face and overcome joint failures and uncertainties. Numerical simulations are conducted to validate the proposed robust fault-tolerant control scheme.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.419-423
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• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.413-423
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• 2005

Consider the problem of estimating the underlying regression function from a set of noisy data which is contaminated by a long tailed error distribution. There exist several robust smoothing techniques and these are turned out to be very useful to reduce the influence of outlying observations. However, no matter what kind of robust smoother we use, we should choose the smoothing parameter and relatively less attention has been made for the robust bandwidth selection method. In this paper, we adopt the idea of robust location parameter estimation technique and propose the robust cross validation score functions.

• East Asian mathematical journal
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• v.31 no.3
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• pp.371-377
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• 2015

We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functions and support functions as its objective function, continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.11
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• pp.1071-1075
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• 2009

This article describes a robust control method by using peak control of a sensitivity function in the state-feedback control systems. This method apparently reduces the peak, and as a result makes closed loop systems more stable. The designed closed loop systems also make the response to an external step disturbance more fast with a lower undershoot. At the conclusion, it is verified that the proposed method enhances robust stability and robust performance to parametric uncertainties through $\mu$-plot.

• KIEE International Transactions on Power Engineering
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• v.4A no.3
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• pp.109-114
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• 2004

In this paper, the H$\infty$ control method is applied in the control of SPFC and generators in order to obtain the robust stability performance of the power system. Moreover, a SPFC H$\infty$ controller based on loop shaping is designed to achieve first-rate tracking properties in addition to the robust stability. This robust control method is applied to a Ward and Hale 6-bus power system and the effects are analyzed. The MATLAB program is used for simulation of the robust controller.

• Journal of Mechanical Science and Technology
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• v.20 no.8
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• pp.1169-1182
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• 2006

Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.