• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1060-1065
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• 2005

An Independent Administrative Corporation Japan Agency for Marine-Earth Science and Technology (JAMSTEC) is developing light-and-small Autonomous Underwater Vehicles (AUV)$^{1)}$, named 'MR-X1' (Marine Robot Experimental 1), which can cruise, investigate and observe by itself without human's help. In this paper, we consider the motion control problem of 'MR-X1' and derive a controller. Since the dynamic property of 'MR-X1' is changed by the influence of the speed, the mathematical model of 'MR-X1' becomes the nonlinear model. In order to design a controller for 'MR-X1', we generally apply nonlinear control theories or linear control theories with some constant speed situation. If we design a controller by applying Linear Quadratic (LQ) optimal control theory, the obtained controller only compensates t e optimality at the designed speed situation, and does not compensate the stability at another speed situations. This paper proposes a controller design method using Linear Matrix Inequalities (LMIs)$^{2),3),4)}$, which can adapt the speed variation of 'MR-X1'. And examples of numerical analysis using our designed controller are shown.

• Journal of Electrical Engineering and Technology
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• v.7 no.4
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• pp.513-523
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• 2012

For precisely regulating the speed of a permanent magnet synchronous motor system with unknown load torque disturbance and disturbance inputs, an LMI-based sliding mode control scheme is proposed in this paper. After a brief review of the PMSM mathematical model, the sliding mode control law is designed in terms of linear matrix inequalities (LMIs). By adding an extended observer which estimates the unknown load torque, the proposed speed tracking controller can guarantee a good control performance. The stability of the proposed control system is proven through the reachability condition and an approximate method to implement the chattering reduction is also presented. The proposed control algorithm is implemented by using a digital signal processor (DSP) TMS320F28335. The simulation and experimental results verify that the proposed methodology achieves a more robust performance and a faster dynamic response than the conventional linear PI control method in the presence of PMSM parameter uncertainties and unknown external noises.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.452-458
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• 2003

This paper presents a robust vibration control methodology of smart structural systems. The governing equations and associated boundary conditions are derived by Hamilton's principle. A robust controller is designed using a linear matrix inequality (LMI) approach to the multiobjective synthesis. The design objectives are to achieve a mix of H$\sub$$\infty$/ performance and H$_2$ performance satisfying constraints on the closed-loop pole locations in the face of model uncertainties. Numerical examples are presented to demonstrate the effectiveness of LMI approach in damping out the multiple modes of vibration of the piezo/beam system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.12
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• pp.2037-2045
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• 2016

This paper presents a fuzzy-model-based design approach to the buoyancy and moment controls of a class of nonlinear underwater glider. Through the linearization and the sector nonlinearity methodologies, the underwater glider dynamics is represented by a Takagi-Sugeno (T-S) fuzzy model. Sufficient conditions are derived to guarantee the asymptotic stability of the closed-loop system in the format of linear matrix inequality (LMI). Simulation results demonstrate the effectiveness of the proposed buoyancy and moment controllers for the underwater glider.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.8
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• pp.616-622
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• 2003

This paper deals with the problem of estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded controllers. Using linear matrix inequalities(LMIs) we estimate the ASR and show the exponential stability of the closed-loop control system in the estimated ASR. We give a simple LMI-based algorithm to get estimates of the ASR. We also give a synthesis algorithm to design a switching surface which will make the estimated ASR big. Finally, we give numerical examples in order to show that our method can give better results than the previous ones for a certain class of uncertain variable structure systems with bounded controllers.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.7
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• pp.612-618
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• 2004

This paper presents a robust vibration control methodology for smart structural systems. The governing equation and associated boundary conditions of the smart structural system are derived by using Hamilton's principle. The assumed mode method is used to discretize the governing equation into a set of ordinary differential equation. A robust controller is designed using a linear matrix inequality (LMI) approach for the multiobjective synthesis. The design objectives are to achieve a mix of H$_{\infty}$ performance and H$_2$ performance satisfying constraints on the closed-loop pole locations in the presence of model uncertainties. Numerical examples are presented to demonstrate the effectiveness of LMI approach in damping out the multiple vibration modes of the piezo/beam system.

• Proceedings of the KIEE Conference
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• 1997.07f
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• pp.2196-2199
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• 1997

In the industrial motor drive system, a shaft torsional vibration is 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, a control system design method using Linear Matrix Inequality (LMI), which is a tool for control design that replaces or complements Lyapunov-Riccati equations, is provided and a $H_{\infty}$ speed controller for a induction motor by LMI is proposed. In the $H_{\infty}$ speed controller, weights are used to satisfy tracking and disturbance rejection. Experimental results show the validity of the proposed $H_{\infty}$ speed controller by LMI, and this controller is compared with the state feedback controller.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2242-2244
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• 2004

This paper deals with the design of a reduced-order stabilizing controller for the linear system. The coupled lineal matrix inequality (LMI) problem subject to a rank condition is solved by a sequential semidefinite programming (SDP) approach. The nonconvex rank constraint is incorporated into a strictly linear penalty function, and the computation of the gradient and Hessian function for the Newton method is not required. The penalty factor and related term are updated iteratively. Therefore the overall procedure leads to a successive LMI relaxation method. Extensive numerical experiments illustrate the proposed algorithm.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.163-177
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• 2012

This paper presents a LMI(linear matrix inequality)-based fuzzy approach of modeling and active vibration control of geometrically nonlinear flexible plates with piezoelectric materials as actuators and sensors. The large-amplitude vibration characteristics and dynamic partial differential equation of a piezoelectric flexible rectangular thin plate structure are obtained by using generalized Fourier series and numerical integral. Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear structural system, which combines the fuzzy inference rule with the local linear state space model. A robust fuzzy dynamic output feedback control law based on the T-S fuzzy model is designed by the parallel distributed compensation (PDC) technique, and stability analysis and disturbance rejection problems are guaranteed by LMI method. The simulation result shows that the fuzzy dynamic output feedback controller based on a two-rule T-S fuzzy model performs well, and the vibration of plate structure with geometrical nonlinearity is suppressed, which is less complex in computation and can be practically implemented.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.4
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• pp.183-190
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• 2000

It is well-known that the poles of a system are closely related with the dynamics of the systems, and the pole assignment problem, which locates the poles in the desired regions, in one of the major problem in control theory. Also, it is always possible to assign poles to specific points for exactly known linear systems. But, it is impossible for the uncertain linear systems because of the uncertainties that originate from modeling error, system variations, sensing error and disturbances, so we must consider some regions instead of points. In this paper, we consider both the analysis and the design of robust pole assignment problem of linear system with time-varying uncertainty. The considered uncertainties are the unstructured uncertainty and the structured uncertainty, and the considered region is the circular region. Based on Lyapunov stability theorem and linear matrix inequality(LMI), we first present the analysis result for robust pole assignment, and then we present the design result for robust pole assignment. Finally, we give some numerical examples to show the applicability and usefulness of our presented results.