• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.229-244
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• 2015

H-infinity norm relates to the maximum in the frequency response function and H-infinity control method focuses on the case that the vibration is excited at the fundamental frequency, while 2-norm relates to the output energy of systems with the input of pulses or white noises and 2-norm control method weighs the overall vibration performance of systems. The trade-off between the performance in frequency-domain and that in time-domain may be achieved by integrating two indices in the mixed vibration control method. Based on the linear fractional state space representation in the modal space for a piezoelectric flexible structure with uncertain modal parameters and un-modeled residual high-frequency modes, a mixed dynamic output feedback control design method is proposed to suppress the structural vibration. Using the linear matrix inequality (LMI) technique, the initial populations are generated by the designing of robust control laws with different H-infinity performance indices before the robust 2-norm performance index of the closed-loop system is included in the fitness function of optimization. A flexible beam structure with a piezoelectric sensor and a piezoelectric actuator are used as the subject for numerical studies. Compared with the velocity feedback control method, the numerical simulation results show the effectiveness of the proposed method.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.58 no.3
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• pp.241-250
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• 2022

This paper describes the design of H-infinity controller for robust control of a DC motor system. The suggested controller can ensure robustness against disturbance and model uncertainty by minimizing H-infinity norm of the transfer function from exogenous input to performance output and applying the small gain theorem. In particular, the controller was designed to reduce the effects of disturbance and model uncertainty simultaneously by formalizing these problems as a mixed sensitivity problem. The validity of the proposed controller was demonstrated by computer simulations and real experiments. Moreover, the effectiveness of the proposed controller was confirmed by comparing its performance with PI controller, which was tested under the same experimental condition as the H-infinity controller.

• 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.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.305-311
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• 2023

We exhibit some properties of the weighted Berezin transform T_αf on L^∞(B_n) and on L¹(B_n). As the main result, we prove that if f ∈ L^∞(B_n) with lim_k→∞ T^k_αf exists, then there exist unique M-harmonic function g and $h{\in}{\bar{(I-T_{\alpha})L^{\infty}(B_n)}}$ such that f = g + h. We also show that of the norm of weighted Berezin operator T_α on L¹(B_n, ν) converges to 1 as α tends to infinity, where ν is an ordinary Lebesgue measure.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1754-1757
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• 2004

For the anti-sway control of traveling cranes, there are several solutions, i.e., by fuzzy control, by optimal control theory, etc. Each of them is reported to be effective. And, H infinity control and $H_2$ control can be also used. However, the full order observer which estimates all states in the controlled object is used in these methods. Therefore, the orders of these controllers are apt to be higher than that of the optimal controller, etc. Because the conventional H2 controller which minimizes $H_2$ norm consists of two parts, that is: feedback gains which make the controlled object stable and the full order observer which estimate those states. If the minimal order observer is used instead of the full order one, the order of the controller can be reduced. In this paper, we propose a new method based on the minimalization of $H_2$ norm using the minimal order observer. And, we confirm the effect of a new $H_2$ controller in the experiments of the anti-sway control of a traveling crane.

• Journal of Aerospace System Engineering
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• v.2 no.3
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• pp.1-6
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• 2008

The tilt rotor aircraft has the flight characteristics which takes off vertically like a helicopter and flies forward like an airplane. Especially, the transition process from a helicopter to an airplane mode requires not only the mixing of control inputs but also the stability and controllability augmentation system(SCAS) in order to keep the safe flight because there are compound flight dynamic characteristics of a helicopter and an airplane including non-linearity, uncertainty. This paper describes the design of SCAS in a lateral motion for the tilt rotor aircraft based on the $H_{\infty}$ control method, which was performed from mathematical model with weighting matrix based on the relationship between the $H_{\infty}$ norm and the sensitivity function. Through simulation analysis for the controller designed on the $H_{\infty}$ control theory, it was shown that this method may be applied to the control design of the tilt rotor aircraft.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.44-47
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• 1996

An optimal preview controller based on the discrete-time $H_{.inf}$ control is presented. The preview controller is synthesized by considering the bounded unknwon disturbances as well as previewable commands and disturbances. The controller derivation procedure is analogous to the LQ-based scheme. The designed preview gain matrix has a similar structure as the LQ-based one. As the infinity norm .gamma. of the transfer function matrix tends to .inf., the preview gains obtained by $H_{\infty}$ control method approach to the gains by the LQR. The LQ-based preview gains are verified to be subsets of the $H_{.inf}$ -based preview gains..

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.1
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• pp.35-44
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• 1996

A design method for a teleoperator robot system is presented in this paper. The control system consists of two phases; approach phase and contact one. The end-effector position of the estimated slave robot and the contact force between the end-effector and wall are displayed on the monitors at control site, using which the operator controls the teleoperator system. The approach phase controller is designed using Smith's principle and the contact one designed based upon the structured singular value ${\mu}$ in order to increase the robustness of the system. The uncertainatices such as communication time delay and the variations of system parameters are considered as a muliplicative pertubation. Computer simulations are conducted in order to evaluate the performance of the proposed design method. It is found that desirable control performance, especially in the contact phase, is obtained if the control mode is switched into contact phase when the estimated position of the slave robot end-effector is in front of the wall.

• Journal of the Institute of Convergence Signal Processing
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• v.5 no.1
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• pp.66-72
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• 2004

PID control has been well used for several decades. For PID algorithms, some tuning methods are used for selecting PID parameters and with these selected parameters, PID control system is designed. But in some cases various kinds of performance indices are used instead of well-known tuning rules, and so variable type of performance index must be tested so that the designed control system meets the some specifications. For 2 DOF PID controller design this paper presents a linear combinational type of performance indices constituting of index for robust performance, which is obtained by h infinity norm of a weighted complementary sensitivity function, including other time domain indices such as error, energy and changing rate of control input. By numerical methods, the optimal 2 DOF PID parameters are obtained. Therefore various types of 2 degree of freedom PID controllers such as I-PD controller are used so that this two degree of freedom PID controllers may give more desirable output characteristics. Simulations are done with MATLAB m file and mdl files.