• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.936-938
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• 1996

The $H_{\infty}$ robust controller is designed for on-line adaptive control application by using polynomial approach. The $H_{\infty}$ robust controllers for adaptive system were designed first by Grimble. But they have a problem that two minimum costs can exist and did not minimize the conventional $H_{\infty}$ cost function which is the $H_{\infty}$ sum of weighted sensitivity and complementary sensitivity terms. In this paper, the two minimum costs problem can be avoided and the conventional $H_{\infty}$ cost function is minimized by employing the Youla parameterization and polynomial approach at the same time. In addition pole placement is possible without any relation with weighting function.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.3
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• pp.172-179
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• 2003

Linear matrix Inequality based $H_\infty$ robust controller is designed to control the motion of a 4-axis unbalanced rigid asymmetric rotor supported and controlled by two active magnetic bearings in this paper. To this end, the equations of motion of the system are derived via Hamilton's variational principle and transformed to a state-space form for the standard $H_\infty$ control problem. LMI-based controller, which does not require additional assumptions beyond the usual stabilizability and detectability assumptions, is designed based upon the pole place weighting function and loopshaping technique. The obtained results are compared with those reported in the available literature and the efficiency of the proposed LMI-based $H_\infty$ control is revealed.

• Smart Structures and Systems
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• v.9 no.4
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• pp.373-392
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• 2012

Tracking control of systems with variable stiffness hysteresis using a gain-scheduled (GS) controller is developed in this paper. Variable stiffness hysteretic system is represented as quasi linear parameter dependent system with known bounds on parameters. Assuming that the parameters can be measured or estimated in real-time, a GS controller that ensures the performance and the stability of the closed-loop system over the entire range of parameter variation is designed. The proposed method is implemented on a spring-mass system which consists of a semi-active independently variable stiffness (SAIVS) device that exhibits hysteresis and precisely controllable stiffness change in real-time. The SAIVS system with variable stiffness hysteresis is represented as quasi linear parameter varying (LPV) system with two parameters: linear time-varying stiffness (parameter with slow variation rate) and stiffness of the friction-hysteresis (parameter with high variation rate). The proposed LPV-GS controller can accommodate both slow and fast varying parameter, which was not possible with the controllers proposed in the prior studies. Effectiveness of the proposed controller is demonstrated by comparing the results with a fixed robust $\mathcal{H}_{\infty}$ controller that assumes the parameter variation as an uncertainty. Superior performance of the LPV-GS over the robust $\mathcal{H}_{\infty}$ controller is demonstrated for varying stiffness hysteresis of SAIVS device and for different ranges of tracking displacements. The LPV-GS controller is capable of adapting to any parameter changes whereas the $\mathcal{H}_{\infty}$ controller is effective only when the system parameters are in the vicinity of the nominal plant parameters for which the controller is designed. The robust $\mathcal{H}_{\infty}$ controller becomes unstable under large parameter variations but the LPV-GS will ensure stability and guarantee the desired closed-loop performance.

• Proceedings of the KIPE Conference
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• 1997.07a
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• pp.332-335
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• 1997

In the industrial motor drive system, a shift torsional vibration si often generated when a motor and a load are connected with a flexible shaft. This paper treats the vibration suppression control of such a system. In this paper, the state feedback controller of the two-mass resonant system using the H$\infty$ filter is proposed. The H$\infty$ filter is robust in noise and disturbance. Simulation results show the validity proposed controller.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.486-490
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• 1993

This paper presents an improved algorithm which enables to find a suboptimal $H^{\infty}$ controller. In the $H^{\infty}$ control problem with output multiplicative uncertainty, the Glover-Doyle algorithm has sorne constraints for the standard plant. The proposed algorithm removes them by reformulating the standard plant. We show the validity of this algorithm by investigating the variation of norm-bound.d.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.215-218
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• 1998

In this paper, we design the $H_{\infty}$ controllers satisfying robust stability and performance for underwater vehicle. The underwater vehicle has computations delay time and input delay. In addition, there exist parameter uncertainties by the roll motion coefficient error, buoyance error, and gravity error. We design the $H_{\infty}$ controllers using model-matching method and check the performance of the proposed controller by nonlinear simulation which includes time delay model, sensor error model, and actuator model.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.10a
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• pp.93-99
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• 1998

Mathematical model can be obtained by physical law or engineering theory. However it is always incomplete expression of the real system. In active controls to suppress vibration due to earthquake or wind load, modeling errors can often cause the problems of instability and performance degradation. In this paper, robust optimal controller design method using H$\infty$ control theory is developed for the systems which have uncertain natural frequency and design constraints. Numerical results show that the proposed H$\infty$ controller can avoid the performance degradation due to several errors and has better performance than conventional LQR method.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.11
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• pp.494-502
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• 2002

In this paper, a suspension control of a magnetic levitation(MagLev) system with flexible rail is designed and presented. The numerical modelling for the electromagnetic system to be controlled as a target plant is carried out. And dome kinds of the hardware system including CPU board, AD board, DA board, sensors, and switching power amplifier are described. Using the derived model, the stabilizing controllers, such as PID and $H_{\infty}$ controller, for the MagLev system are designed using the MATLAB toolbox. The designed controllers are validated by some experimental results as well as numerical simulations. So it is shown that $H_{\infty}$ controller can give the better performance for the plant with flexible modes than PID controller.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.729-731
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• 2004

This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.227-230
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• 1998

In this paper, we propose the design method of fuzzy robust H$\infty$ controller for the uncertain nonlinear discete-time systems with time delay. First, we represent a nonlinear plant with a modified T-S(Takagi-Sugeno) fuzzy model. Then design method utilizing the concept of PDC (parallel distributed compensation) is employed. For the modified T-S fuzzy model with uncertainty and delay, the sufficient condition of the quadratic stabilization with an H$\infty$ norm bound is presented in terms of Lyapunov stability theory and fuzzy robust H$\infty$ controller design method is given by LMI(linear matrix inequality) approach. Also an illustrative example is given to demonstrate the result of the proposed method.