• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.316-323
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• 2004

This paper deals with an $H_{\infty}$ output feedback controller design for singularly perturbed T-S fuzzy systems. It is shown that the $H_{\infty}$ norm of the singularly perturbed T-S fuzzy system is less than ${\gamma}$ for a sufficiently small ${\varepsilon}$>0 if the $H_{\infty}$ norms of both the slow and fast subsystem are less than ${\gamma}$. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter ${\varepsilon}$. A numerical example is provided to demonstrate the efficacy of the proposed design method.

• Journal of the Korea Convergence Society
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• v.8 no.5
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• pp.1-11
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• 2017

With a given spring-mass-damper system, $H_{\infty}$ and ${\mu}$-synthesis control methods are used to build system controllers which minimize vibrations at two major natural frequencies in two cases; without uncertainty; with 20% uncertainty. In order to check the stability and performance of two controllers, those are examined using GM and PM values. The signal strength of output responses is compared using the concept of central numerical differentiation and then results are quantified using the RMS method. Lastly, 40 random samples of $H_{\infty}$ and ${\mu}$-synthesis controllers are obtained for three different $W_{per\;f1}$ weighting functions and drawn in the time domain in order to compare the stability. Overall, ${\mu}$-synthesis controller manages the vibrations much better than $H_{\infty}$ controller according to the robust stability and performance values obtained by simulating random samples of 40 plant models.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.6
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• pp.15-24
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• 2000

This paper presents an output feedback robust H$\infty$ control problem for a class of uncertain nonlinear systems, which can be represented by an fuzzy dynamic model. The nonlinear system is represented by Takagi-Sugeno fuzzy model, and the control design is carried out on the basis of the fuzzy model. Using a single quadratic Lyapunov function, the globally exponential stability and disturance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust H$\infty$ controllers are given in terms of linear matrix inequalities(LMIs). Constructive algorithm for design of robust H$\infty$ controller is also developed. The resulting controller is nonlinear and automatically tuned based on fuzzy operation.

• Journal of Power System Engineering
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• v.7 no.1
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• pp.60-67
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• 2003

This paper introduces basic study how to restrain the vibration of a four story shear structure. We have modeled a four story shear structure mathematically and have identified each parameters by experiment. We have gotten a reduced nominal model through modal analyzing method and the $H_{\infty}$ control theory is used in the control system design to get the robust controller. It's shown that the desirable performances is confirmed through the mathematical simulation. And a designed controller applying the $H_{\infty}$ control theory shows the good performance for the impulse disturbance through the simulation results. That is, the robustness of this control system is confirmed for the ability of disturbance rejection and modeling error.

• Journal of Power System Engineering
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• v.7 no.3
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• pp.48-53
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• 2003

This paper deals with the control of a horizontally placed flexible rotor levitated by electromagnets in a multi-input/multi-output (MIMO) active magnetic bearing(AMB) system. AMB is a kind of novel high performance bearing which can suspend the rotor by magnetic force. Its contact-free manner between the rotor and stator results in it being able to operate under much higher speed than conventional rolling bearings with relatively low power losses, as well as being environmental-friendly technology for AMB system having no wear and no lubrication requirements. In this MIMO AMB system, the rotor is a complex mechanical system, it not only has rigid body characteristics such as translational and slope motion but also bends as a flexible body. Reduced order nominal model is computed by consideration of the first 3 mode shapes of rotor dynamics. Then, the $H_{\infty}$ control strategy is applied to get robust controller. Such robustness of the control system as the ability of disturbance rejection and modeling error is guaranteed by using $H_{\infty}$ control strategy. Simulation results show the validation of the designed control system and the modeling method to the rotor.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.1
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• pp.57-69
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• 2016

There are three kinds of algorithms(2-ARE, mu-synthesis, LMI) for controller design using closed-loop shaping method. This paper provides the summary of background theory of three algorithms and $H_{\infty}$ controller design results for spacecraft attitude control using the three controller design tools of Matlab$^{TM}$ Toolbox for comparison. As a result, it reveals that LMI design method is more reliable as well as easier than others for spacecraft attitude control design. Comparison results are as follow: 2-ARE method and LMI method provide almost same results in robust stability, robust performance and control authority level. But 2-ARE method is more sensitive than LMI method with respect to proper design of weighting functions: 2-ARE method is more difficult than LMI method in weighting function design. The design result of mu-synthesis method shows worse performance and requires bigger control authority than others.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.6
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• pp.46-54
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• 1998

This paper presents a method for designing robust fuzzy $H^{\infty}$ controllers which stabilize nonlinear systems with parameter uncertainty adn guarantee an induced $L_{2}$ norm bound constraint on disturbance attenuation for all admissible uncertainties. Takagi and Sugeno's fuzzy models with uncertainty are used as the model for the uncertain nonlinear systems. Fuzzy control systems utilize the concept of so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the stability condition satisfying decay rate and disturbance attenuation condition for Takagi and Sugeno's fuzzy model with parameter uncertainty are discussed. A sufficient condition for the existence of robust fuzzy $H^{\infty}$ controllers is then presented in terms of linear matrix inequalities(LMIs). Finally, design examples of robust fuzzy $H^{\infty}$ controllers for uncertain nonlinear systems are presented.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.42 no.4
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• pp.47-52
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• 2005

In this paper, the genetic algorithm is used to design a fixed order square decoupling $H_{\infty}$ controllers based on the Two-Degree-of-freedom standard model. The proposed decoupling $H_{\infty}$ controller which is minimizes the maximum energy in the output signal is designed to reduce the coupling properties between the input/output variables which make it difficult to control a system efficiently. A minimal set of assumptions for existence of the decoupling controller formula is described in the state-space formulas. It is verified by an example.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.4
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.426-429
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• 1997

This paper proposes a robust H$_{\infty}$ tracking filter to improve the unacceptable target tracking performance for systems with parameter uncertainties. Also, we use here the input estimation approach to account for the possibility of maneuver. Simulation results show that the robust H$_{\infty}$ tracking filter which is proposed here to solve the systems with all system parameter uncertainties, has a good tracking performance for a maneuvering target tracking problem.m.