• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.438-443
• /
• 2003

In this paper, we propose a control algorithm for two-wheel mobile robot that can move the rider to his or her command and autonomously keep its balance. The control algorithm is based on a mixed $H_2/H_{\infty}$ control scheme. In this control problem the main issue is to move the rider while keeping its balance in the presence of disturbances and parameter uncertainties. The disturbance force caused by uneven road surfaces and the uncertainty due to different rider's heights are considered. To this end we first consider a state feedback controller as a basic framework. Secondly, we obtain the state feedback gain $K_2$ minimizing the $H_2$ norm and the state feedback gain $K_{\infty}$ minimizing the $H_{\infty}$ norm over the whole range of parameter uncertainty. Finally, we select mixed $H_2$/$H_{\infty}$ state feedback controller K as the geometric mean of $K_2$ and $K_{\infty}$. Simulation results show that the mixed $H_2/H_{\infty}$ state feedback controller combines the effects of the optimal $H_2$ state feedback controller and robust $H_{\infty}$ controller state feedback controller efficiently in the presence of disturbance and parameter uncertainty.

• 제어로봇시스템학회:학술대회논문집
• /
• 1999.10a
• /
• pp.88-91
• /
• 1999

The purpose of this paper is to propose an approach to design a robust servo controller based on the Mixed H$_2$/H$\sub$$\infty$/ theory. In order to do this, we first modify the generalized plant for the usual H$\sub$$\infty$/ servo problem to a structure of the Mixed H$_2$/H$\sub$$\infty$/ minimization problem by virtue of the internal model principle. By doing this, we can divide specifications adopted for robust servo system design into H$_2$and H$\sub$$\infty$/ performance criteria, respectively. Then, the mixed H$_2$/H$\sub$$\infty$/ problem is solved in order to find the best solution, by which we can minimize H$_2$-norm of the transfer function under the condition of H$\sub$$\infty$/-norm value, through Linear Matrix Equality (LMI).

• Proceedings of the KIEE Conference
• /
• 1996.07b
• /
• pp.999-1001
• /
• 1996

In this paper, we represented the relation of minimum entropy/$H_{\infty}$-controller and mixed $H_2/H_{\infty}$-controller. An $H_2$ controller design problem involving a constraint on $H_{\infty}$ disturbance attenuation is considered. By the equivalence of the mixed $H_2/H_{\infty}$ control problem and the minimum entropy/$H_{\infty}$-control problem, we presented the controller state-space realization. Decentralized case was illustrated briefly.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.33B no.5
• /
• pp.10-16
• /
• 1996

In this paper, we consider a generalized mixed H_2/H_{\infty}$ output feedback problem. It is finding an internally stabilizing controller that minimizes a mixed $H_{2}$/ $H_{performance}$ measure. We show that a generalized mixed H_2/H_{\infty}$ system with two exogenous inputs and two controlled signals is transformed into auxiliary system with two exogenous inputs and one controlled signal. The two systems have equivalent performance. Therefore, a complete solution of generalized mixed H_2/H_{\infty}$ output feedback problem is achieved by existing results of mixed H_2/H_{\infty}$ control theory.

• Proceedings of the IEEK Conference
• /
• 2003.11a
• /
• pp.401-404
• /
• 2003

In this paper, $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FIR filters are newly proposed for discrete-time state space signal models. The proposed filters require linearity, unbiased property, FIR structure, and independence of the initial state information in addition to the performance criteria in both $H_2$ and $H_{\infty}$ sense. It is shown that $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FIR filter design problems can be converted into convex programming problems via linear matrix inequalities (LMIs) with a linear equality constraint. Simulation studies illustrat that the proposed FIR filter is more robust against uncertainties and has faster convergence than the conventional IIR filters. the conventional IIR filters.

• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.892-897
• /
• 2003

This paper considers the design of mixed $H_2/\;H_{\infty}$ controllers for linear time-invariant descriptor systems. Firstly, an $H_{\infty}$ and $H_2$ synthesis problem for a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, the existence of a mixed $H_2/\;H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_{\infty}$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables. In addition, we show the procedure by which a obtained descriptor controller can be transformed to a non-descriptor one.

• Journal of Institute of Control, Robotics and Systems
• /
• v.6 no.5
• /
• pp.356-366
• /
• 2000

In this paper, a nonlinear $H_2/H_\infty/LTR$ control for the flexible inverted pendulum of a parallel type with Coulomb friction is presented. The dynamic equation for this system is derived by the Hamilton's principle and assumed-mode method. This hard nonlinear system can be modeled by a the quasi-linear state space model using the REF method. It is shown that the $H_2/H_\infty$ control can be applied to the nonlinear controller design of the system having Coulomb frictions if the proper LTR conditions are satisfied. In order to present the usefulness of the suggested control method, the nonlinear $H_2/H_\infty/LTR$ controller is designed to control the Position of the end point of the flexible inverted pendulum that has Coulomb frictions present in actuator parts. The results are given via computer simulations.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.331-331
• /
• 2000

This paper presents the mixed $H_2/H_{\infty}$ output feedback controIler design method for linear systems with delayed state. The objective is to design the output feedback controller which minimizes the H$_2$-norm of one transfer function while ensuring the H$_{\infty}$-norm of the other is held below a chosen level. When objective is tormulated in terms of a common Lyapunov function, the sufficient conditions of existence of mixed $H_2/H_{\infty}$ controller are given in terms of LMIs. terms of LMIs.

• International Journal of Control, Automation, and Systems
• /
• v.4 no.5
• /
• pp.645-652
• /
• 2006

In this paper a new type of filter, called the $H_2/H_{\infty}$ FIR filter, is proposed for discrete-time state space signal models. The proposed filter requires linearity, unbiased property, FIR structure, and independence of the initial state information in addition to the performance criteria in both $H_2$ and $H_{infty}$ sense. It is shown that $H_2,\;H_{\infty}$, and $H_2/H_{\infty}$ FIR filter design problems can be converted into convex programming problems via linear matrix inequalities (LMIs) with a linear equality constraint. Simulation studies illustrate that the proposed FIR filter is more robust against temporary uncertainties and has faster convergence than the conventional IIR filters.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.35-40
• /
• 1998

A nonlinear attitude model of a satellite with thrusters, magnetic torquers and a reaction wheel cluster is developed. Then the linearized version of this satellite attitude model is derived far the attitude hold mode. For comparison purpose, various control methods are considered for attitude control of a satellite. We consider a proportional derivative controller which is actually used in the remote sensing satellite, KOMPSAT. Then a comparison is made with an H$_2$controller, an H$\sub$$\infty$/ controller, and a mixed H$_2$/ H$\sub$$\infty$/ controller. The analysis and numerical studies show that the proportional derivative controller's performance is limited in the sense that the pitch angle cannot approach zero. The simulations also show that among three control methods (H$_2$control, H$\sub$$\infty$/ control, and mixed H$_2$/ H$\sub$$\infty$/ control) H$_2$control has the fastest response time, H$\sub$$\infty$/ control has the slowest and mixed H$_2$/ H$\sub$$\infty$/ control comes in between the first two control methods. On the other hand, H$\sub$$\infty$/ control used least amount of control effort while H$_2$control required the most.