• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.10
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• pp.1425-1435
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• 2013

The useful method for determining parameters of weighting functions used to design the $H_{\infty}$ current controller for attenuating the current ripple due to saliencies which SPMSM(Surface Permanent Magnet Synchronous Motor) also incorporates is described. To analyze the effect, the current ripple due to the structural and the saturation saliencies, the SPMSM model with nonlinear inductance function depending on the two independent variables, rotor position and stator current is simulated. After analysis, parameters of the weighting functions for $H_{\infty}$ current controller is selected to satisfy the robust stability, robust performance and specific performance in time and frequency domain by using the PSO(Particle Swarm Optimization) algorithm in the linear SPMSM model. Especially, the robust performance is proved that the selected weighting functions play a role in reducing the current ripple caused by the saliencies of SPMSM at the desired frequency range by the simple experiment.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.248-251
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• 1991

A robust monitor AGC(Automatic Gauge Control) system for a hot strip mill plant of POSCO Is designed by minimizing the H.inf. norm of a so called mixed sensitivity function. In order to solve the mininizatlon problem, a polynomial approach proposed by Kwakernaak[5] is used. The controller performance is tested by a computer simulation under various circumstances.

• Smart Structures and Systems
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• v.15 no.4
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• pp.1041-1062
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• 2015

In this paper a method of finding optimal positions for piezoelectric actuators and sensors on different structures is presented. The genetic algorithm and multi-objective genetic algorithm are selected for optimization and $H_{\infty}$ norm is defined as a cost function for the optimization process. To optimize the placement concerning the selected modes simultaneously, the multi-objective genetic algorithm is used. The optimization is investigated for two different structures: a cantilever beam and a simply supported plate. Vibrating structures are controlled in a closed loop with feedback gains, which are obtained using optimal LQ control strategy. Finally, output of a structure with optimized placement is compared with the output of the structure with an arbitrary, non-optimal placement of piezoelectric patches.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.197-202
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• 1992

In this paper, we consider the synthesis of mixed H$_{2}$/H$_{\infty}$ controllers such that the closed-loop poles are located in a specified region in the complex plane. Using solution to a generalized Riccati equation and a change of variable technique, it is shown that this synthesis problem can be reduced to a convex optimization problem over a bounded subset of matrices. This convex programming can be further reduced to Generalized Eigenvalue Minimization Problem where Interior Point method has been recently developed to efficiently solve this problem..

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.575-580
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• 1992

Mixed H$_{2}$/H$_{\infty}$ robust control synthesis is considered for finite dimensional linear time-invariant systems under the presence of diagonal structured uncertainties. Such uncertainties arise for instance when there is real perturbation in the nominal model of the state space system or when modeling multiple (unstructured) uncertainty at different locations in the feedback loop. This synthesis problem is reduced to convex optimization problem over a bounded subset of matrices as well as diagonal matrix having certain structure. For computational purpose, this convex optimization problem is further reduced into Generalized Eigenvalue Minimization Problem where a powerful algorithm based on interior point method has been recently developed..

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.3
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• pp.266-272
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• 2014

This study proposes a closed-loop shaping control method with $H_{\infty}$ optimization for optical image stabilization (OIS) in mobile phone cameras. The image stabilizer is composed of a horizontal stage constrained by ball bearings and actuated by the magnetic force from voice coil motors. The displacement of the stage is measured by Hall effect sensors. From the OIS frequency response experiment, the transfer function models of the stage and Hall effect sensor were identified. The weight functions were determined considering the tracking performance, noise attenuation, and stability with considerable margins. The $H_{\infty}$ optimal controller was executed using closed-loop shaping and limiting the controller order, which should be less than 6 for real-time implementation. The control algorithm was verified experimentally and proved to operate as designed.

• 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.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.4
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• pp.1-10
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• 2000

This paper deals with an H$_{\infty}$ output feedback control problem for linear systems with commensurate time delay in both state and input variables. The proposed output feedback controller also has commensurate time delay terms in the controller state. The controller can be synthesized based on the solution of the linear matrix inequalities(LMI) which can be easily solved using the convex optimization method. In order to demonstrate the efficacy of the proposed method, numerical examples are presented.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.1
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• pp.6-11
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• 2014

Repetitive control is a specialized control scheme to track and/or attenuate a periodic reference trajectory and/or disturbance. Most researches about repetitive control have been performed in the frequency domain. Recently, several approaches to deal with repetitive control systems in the state space are developed by representing a q filter as a state-space equation. This paper presents a design method of a repetitive control system in the state space to satisfy $H_{\infty}$ performance. The overall system is composed of a plant, a repetitive controller, and a state-feedback controller, which can be converted to a standard form used in $H_{\infty}$ control. A LMI (Linear Matrix Inequality)-based stability condition is derived for fixed state-feedback gains. Under a given q filter, another LMI condition is derived to improve $H_{\infty}$ performance and is employed to find state-feedback gains by solving an optimization problem. Finally, to verify the feasibility of the proposed method, a numerical example is demonstrated.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.56-59
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• 1996

Worst-case state estimation will be proposed in this paper. By using the worst-case disturbance and worst-case state estimation, we can obtain right/left constrained coprime factors. If constrained coprime factors are used in designing a controller, the infinity-norm of closed-loop transfer matrix can be smaller than any constant .gamma.(> .gamma.$_{opt}$) without matrix dilation optimization. The derivation of left/right constrained coprime factors is achieved by doubly coprime factorization for the plant constrained by the infinity norm. And the parameterization of stabilizing controllers gives us easily understanding for H$_{\infty}$ control theory.ry.