• Journal of Institute of Control, Robotics and Systems
• /
• v.15 no.3
• /
• pp.255-257
• /
• 2009

The robust stabilization problem of a multivariable uncertain system with a polytopic model is considered. A PI-type $H_{\infty}$ controller with a low pass filter is used for robust stabilization and noise rejection. The problem is reduced to an LMI optimization problem. A sufficient condition for the existence of the PI controller is derived in terms of LMIs. The PI gain matrices are parameterized by using the solution matrices to the existence conditions. Finally, a numerical design example is given.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.24 no.2
• /
• pp.39-43
• /
• 2010

This paper presents an LMI-based method to design an adaptive sliding mode controller for a class of uncertain systems. In terms of LMIs an existence condition of a sliding surface is derived. And an adaptive switching feedback control law to guarantee the asymptotic stability as well as to estimate the norm bound of disturbances is proposed. Finally, a numerical design example for controlling a overhead crane model is given to show the effectiveness of the proposed method.

• Journal of Institute of Control, Robotics and Systems
• /
• v.20 no.3
• /
• pp.270-276
• /
• 2014

This survey paper reviews robust control problems in both frequency domain and time domain. Robust control is focused on model uncertainties such as modeling error, system parameter variations, and disturbances. Robust control design problems are discussed according to parameter uncertainty, polytopic uncertainty, and norm-bounded uncertainty. Nowadays, robust control theory is combined with various control theory such as model predictive control, adaptive control, intelligent control, and time delay control.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.41 no.3
• /
• pp.300-310
• /
• 1992

This paper deals with the problem of robust pole-assignment control for linear systems with structured uncertainty. It considers two cases whose colsed-loop characteristic equations are presented as a family of interval polynomial and polytopic polynomial family respectively. We propose a method of finding the pole-placement region in which the fixed gain controller guarantees the required damping ratio and stability margin despite parameter perturbation. Some results of Kharitonov like stability and two kinds of transformations are included. As an illustrative example, we show that the proposed method can apply effectivly to the single magnet levitation system including some uncertainties (mass, inductance etc.).

• Journal of Institute of Control, Robotics and Systems
• /
• v.16 no.1
• /
• pp.1-4
• /
• 2010

Based on the sliding mode control theory, a decentralized controller design method is developed for a large scale system with a poly topic model. In terms of LMIs, we derive sufficient conditions for the existence of the decentralized controller guaranteeing a stable sliding motion. We also give an LMI-based control design algorithm. Finally, the proposed method is applied to decentralized stabilization of double-inverted pendulums. Simulation results show that our method gives not only the robust stability but perfect rejection of norm-bounded uncertainties.

• Journal of Institute of Control, Robotics and Systems
• /
• v.6 no.7
• /
• pp.611-616
• /
• 2000

This paper presents a design method for the robust flight controller of a hyghly maneuvering aircraft subject to C.G variation. This method is based on LMI(Linear Matrix ZInequality) pole-placement design methodology for the polytopic models. Simulation results show that the proposed LMI-based pole-placement design methodology robustly yields uniform performance with adequate Flying Qualities (FQ) over the entire CG variation range.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.45 no.3
• /
• pp.32-41
• /
• 2008

In this paper, we describe the synthesis of robust and non-fragile $H^{\infty}$ state feedback controllers for linear systems with affine parameter uncertain tracking servo system of blu-ray disc drive, as well as static state feedback controller with polytopic uncertainty Similarity any other control system, the objective of the track-following system design for optical disc drives is to construct the system with better performance and robustness against modeling uncertainties and various disturbances. Also, the obtained condition can be rewritten as parameterized linear matrix inequalities(PLMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a resulted polytopic region.

• Proceedings of the IEEK Conference
• /
• 2003.07c
• /
• pp.2589-2592
• /
• 2003

In this paper, a robust mixed H$_2$/H$\_$$\infty$/ output feedback control method is applied to the design of loop filter for PLL carrier phase tracking. The proposed method successfully copes with large S-curve slope uncertainty and a significant decision delay in the closed-loop that may exist In modern receivers due to a convolutional decoder or an equalizer. The objective is to design an output feedback controller which minimizes the H$_2$performance while satisfying the H$\_$$\infty$/ performance to guarantee the gain margin and phase margin for linear time invariant(LTI) polytopic uncertain systems. LMIs based approach is given to solve this problem. We can verify the H$\_$$\infty$/ performance satisfaction and minimize the phase detector error through the simulation result.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.47 no.6
• /
• pp.64-72
• /
• 2010

In general, due to the interactions among subsystems, it is difficult to design an decentralized controller for nonlinear interconnected systems. In this study, the model of nonlinear interconnected systems is studied via decentralized fuzzy control method with time delay and polytopic uncertainty. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. And the represented model can be rewritten as Parameterized Linear Matrix Inequalities(PLMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. We show that the resulting fuzzy controller guarantees the asymptotic stability and disturbance attenuation of the closed-loop system in spite of controller gain variations within a resulted polytopic region by example and simulations.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.66 no.2
• /
• pp.387-393
• /
• 2017

This paper focuses on a horizontal waypoint tracking and a speed control of large diameter unmanned underwater vehicles (LDUUVs) with X-stern configuration plane. The concerned design problem is converted into an asymptotic stabilization of the error dynamics with respect to the desired yaw angle and surge speed. It is proved that the error dynamics under the proposed control scheme based on the linear control and the feedback linearization can be considered as a cascade system; the cascade system is asymptotically stable if its nominal systems are so. This stability connection enables to separately deal with the waypoint tracking problem and the speed control one. By using the sector nonlinearity, the nominal system with nonlinearities is modeled as a polytopic linear parameter varying (LPV) system with parametric uncertainties. Then, sufficient linear matrix inequality (LMI) conditions for its asymptotic stabilizability are derived in the sense of Lyapunov stability criterion. An example is given to show the validity of the proposed methodology.