• International Journal of Control, Automation, and Systems
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• 제5권2호
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• pp.117-127
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• 2007

Many real world control systems usually track several control objectives, simultaneously. At the moment, it is desirable to meet all specified goals using the controllers with simple structures like as proportional-integral (PI) and proportional-integral-derivative (PID) which are very useful in industry applications. Since in practice, these controllers are commonly tuned based on classical or trial-and-error approaches, they are incapable of obtaining good dynamical performance to capture all design objectives and specifications. This paper addresses a new method to bridge the gap between the power of optimal multiobjective control and PI/PID industrial controls. First the PI/PID control problem is reduced to a static output feedback control synthesis through the mixed $H_2/H_{\infty}$ control technique, and then the control parameters are easily carried out using an iterative linear matrix inequalities (ILMI) algorithm. Numerical examples on load-frequency control (LFC) and power system stabilizer (PSS) designs are given to illustrate the proposed methodology. The results are compared with genetic algorithm (GA) based multiobjective control and LMI based full order mixed $H_2/H_{\infty}$ control designs.

• Journal of the Institute of Electronics Engineers of Korea SC
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• 제41권4호
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• pp.29-37
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• 2004

This paper provides a reliable H$_{\infty}$ state feedback controller design method for delayed singular systems with actuator failures occurred within the prescribed subset. The sufficient condition for the existence of a reliable H$_{\infty}$ controller and the controller design method are presented by linear matrix inequality(LMI), singular value decomposition, Schur complements, and changes of variables. The proposed controller guarantees not only asymptotic stability but also H$_{\infty}$ norm bound in spite of existence of actuator failures. Since the obtained sufficient condition can be expressed as an LMI fen all variables can be calculated simultaneously. Moreover, the controller design method can be extended to the problem of robust reliable H$_{\infty}$ controller design method for singular systems with parameter uncertainties, time-varying delay, and actuator failures. A numerical example is given to illustrate the validity of the result.

• The Transactions of The Korean Institute of Electrical Engineers
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• 제65권9호
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• pp.1524-1530
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• 2016

This paper deals with a robust $H_{\infty}$ sampled-data controller design problem for nonlinear systems in Takagi-Sugeno fuzzy form with singular perturbation. The employed controller takes a state-feedback form. The design condition is represented in terms of linear matrix inequalities. A numerical examples is included to show the effectiveness of the theoretical development.

• International Journal of Control, Automation, and Systems
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• 제3권3호
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• pp.387-396
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• 2005

The Rotational/Translational Actuator (RTAC) benchmark problem considers a fourth-order dynamical system involving the nonlinear interaction of a translational oscillator and an eccentric rotational proof mass. This problem has been posed to investigate the utility of a rotational actuator for stabilizing translational motion. In order to experimentally implement any of the model-based controllers proposed in the literature, the values of model parameters are required which are generally difficult to determine rigorously. In this paper, an approach to the least-squares estimation of the parameters of a system is formulated and practically applied to the RTAC system. On the other hand, this paper shows how to model a nonlinear system as a linear uncertain system via nonparametric system identification, in order to provide the information required for linear robust $H_\infty$ control design. This method is also applied to the RTAC system, which demonstrates severe nonlinearities, due to the coupling from the rotational motion to the translational motion. Experimental results confirm that this approach can effectively condense the whole nonlinearities, uncertainties, and disturbances within the system into a favorable perturbation block.

• Nuclear Engineering and Technology
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• 제30권4호
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• pp.353-363
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• 1998

The H$_{\infty}$ algorithms of the mixed weight sensitivity is used for the robust design of the reactor power control system. The mixed weight sensitivity method requires the selection of the proper weighting functions for the loop shaping in frequency domain. The complexity of the system equation and the non-convexity of the problem make it very difficult to determine the weighting functions. The genetic algorithm which is improved and hybridized with the simulated annealing is applied to determine the weighting functions. This approach permits an automatic calculation and the resultant system shows good robustness and performance.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.339-344
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• 1993

An H$_{\infty}$ control system design for a magnetic levitation system is presented. In the control system design, we consider the influence of both disturbances and uncertainties in the model. The main disturbances stem from the position sensors.The uncertainties are divided into electromagnetic and mechanical ones: the former are due to the gain change in the current amplifier, the influence of leakage flux and modelling error in the magnetic circuit and the latter are due to the changes of the mass and the moments of inertia of the vehicle. Therefore, the designed controller is indispensable to guarantee the robustness of this system for both stability and performance. The controller design is based on the standard H$_{\infty}$ optimal control problem. As the novel features in this paper :(1) there are two poles on j.omega.-axis in the control model;(2) an integrator is included in the controller so that equivalently there are three poles on j.omega.-axis in the model. Finally, several experiments and simulations are carried out to verify the high performance and robustness of the designed control system.m.

• Journal of Electrical Engineering and Technology
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• 제3권4호
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• pp.499-508
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• 2008

Frequency regulation in off-normal conditions has been an important problem in electric power system design/operation and is becoming much more significant today due to the increasing size, changing structure and complexity of interconnected power systems. Increasing economic pressures for power system efficiency and reliability have led to a requirement for maintaining power system frequency closer to nominal value. This paper presents a decentralized frequency control framework using a modified low-order frequency response model containing a proportional-integral(PI) controller. The proposed framework is suitable for near-normal and emergency operating conditions. An $H_{\infty}$ control technique is applied to achieve optimal PI parameters, and an analytic approach is used to analyse the system frequency response for wide area operating conditions. Time-domain simulations with a multi-area power system example show that the simulated results agree with those predicted analytically.

• Proceedings of the Korean Nuclear Society Conference
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• 한국원자력학회 1997년도 추계학술발표회논문집(1)
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• pp.293-298
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• 1997

The H$_{\infty}$robust controller fur the reactor power control system is designed by use of the mixed weight sensitivity. The system is configured into the typical two-port model with which the weight functions are augmented. Since the solution depends on the weighting functions and the problem is of non-convex, the genetic algorithm is used to determine the weighting functions. The cost function applied in the genetic algorithm permits the direct control of the power tracking performances. In addition, the actual operating constraints such as rod velocity and acceleration can be treated as design parameters. Compared with the conventional approach, the controller designed by the genetic algorithm results in the better performances with the realistic constraints. Also, it is found that the genetic algorithm could be used as an effective tool in the robust design. robust design.

• Structural Engineering and Mechanics
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• 제52권1호
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• pp.19-33
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• 2014

Structural robustness refers to the ability of a structure to avoid disproportionate consequences to the original cause. Currently attentions focus on the concepts of structural robustness, and discussions on methods of robustness based structural design are rare. Firstly, taking basis in robust $H_{\infty}$ control theory, structural robustness is assessed by $H_{\infty}$ norm of the system transfer function. Then using the SIMP material model, robustness based design of grid structures is formulated as a continuum topology optimization problem, where the relative density of each element and structural robustness are considered as the design variable and the optimization objective respectively. Generalized elitist genetic algorithm is used to solve the optimization problem. As examples, robustness configurations of plane stress model and the rectangular hyperbolic shell model were obtained by robustness based structural design. Finally, two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that the $H_{\infty}$ structural robustness index can indicate whether the structural response is proportional to the original cause. Robustness based structural design improves structural robustness effectively, and it can provide a conceptual design in the initial stage of structural design.

• Transactions of the Korean Society of Mechanical Engineers A
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• 제36권10호
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• pp.1171-1179
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• 2012

In this study, we consider a dynamic positioning system (DPS) design problem that can be extended to many application fields. Toward this end, tracking and positioning control problems are discussed. In particular, we design a tracking control system that incorporates an observer based on the 2-DOF servo system design approach in order to obtain the desired state information. In the case of observer design, a weighted $H_{\infty}$ error bound approach for a state estimator is considered. Based on an algebraic Riccati equation (inequality) approach, a necessary and sufficient condition for the existence of a full-order estimator that satisfies the weighted $H_{\infty}$ error bound is introduced. The condition for the existence of the estimator is denoted by a linear matrix inequality (LMI) that yields an optimized solution and the observer gain.