• Journal of the Institute of Convergence Signal Processing
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• v.2 no.3
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• pp.65-72
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• 2001

Generally, it is said that control of the inertia system is to track the reference input quickly while suppressing the vibration due to the system itself. In this case, the difficulty fur designing a controller is caused by modeling uncertainty and parameter variation. The purpose of this paper is to propose a design method to suppress the vibration of three-mass inertia system based on the LMI theory. That is, the generalized plant model by which we can cope with conservativeness of the existing H$_{*}$ theory is proposed and analyzed in terms of LMI. The results of simulation fur the three-mass inertia system show that the proposed design approach is quite effective under the given situations.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2001.06a
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• pp.129-132
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• 2001

she purpose of this paper is to propose an approach to suppress the vibration of three-mass inertia system based on the LMI theory. and confirm its validity through simulations under the condition of parameter variation. First, the existing $H_{\infty}$ servo problem is modified to a structure to which the LMI theory can be applied by virtue of the interval model principle. By adopting this structure, we can divide given specifications fur the vibration suppression problem into $H_2$and $H_{\infty}$ performance criteria. The results of simulation for the three-mass inertia system show that the proposed design approach is quite effective.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.444-448
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• 2003

In this paper, the Lagrange dynamics is studied. A state space representation of Lagrange dynamics and control algorithm based on the state feedback pole placement are presented. The state space model presented is descriptor type linear parameter dependent system. It is shown that the control algorithms based on the linear system theory can be applicable to the state space representation of Lagrange dynamics. To show that the linear system theory can be applicable to the state space representation of Lagrange dynamics, the LMI based regional pole-placement design algorithm is developed and present two examples.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.433-437
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• 2003

Quantitative Feedback Theory (QFT) is one of effective methods of robust controller design. In QFT design we can considers the phase information of the perturbed plant so it is less conservative than $H_{\infty}$ and ${\mu}$-synthesis methods and as be shown, it is more transparent than the sensitivity reduction methods mentioned . In this paper we want to overcome the major drawback of QFT method which is lack of an automatic method for loop-shaping step of the method so we focus on the following problem: Given a nominal plant and QFT bounds, synthesize a controller that achieves closed-loop stability and satisfies the QFT boundaries. The usual approach to this problem involves loop-shaping in the frequency domain by manipulating the poles and zeros of the nominal loop transfer function. This process now aided by recently developed computer aided design tools proceeds by trial and error and its success often depends heavily on the experience of the loop-shaper. Thus for the novice and First time QFT user, there is a genuine need for an automatic loop-shaping tool to generate a first-cut solution. Clearly such an automatic process must involve some sort of optimization, and while recent results on convex optimization have found fruitful applications in other areas of control theory we have tried to use LMI theory for automating the loop-shaping step of QFT design.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.1
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• pp.57-69
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• 2016

There are three kinds of algorithms(2-ARE, mu-synthesis, LMI) for controller design using closed-loop shaping method. This paper provides the summary of background theory of three algorithms and $H_{\infty}$ controller design results for spacecraft attitude control using the three controller design tools of Matlab$^{TM}$ Toolbox for comparison. As a result, it reveals that LMI design method is more reliable as well as easier than others for spacecraft attitude control design. Comparison results are as follow: 2-ARE method and LMI method provide almost same results in robust stability, robust performance and control authority level. But 2-ARE method is more sensitive than LMI method with respect to proper design of weighting functions: 2-ARE method is more difficult than LMI method in weighting function design. The design result of mu-synthesis method shows worse performance and requires bigger control authority than others.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.81-87
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• 1993

In this paper robust stability conditions are obtained for linear dynamical systems under structured nonlinear time-varying perturbations, using absolute stability theory and the concept of dissipative systems. The conditions are expressed in terms of solutions to linear matrix inequality(LMI). Based on this result, a synthesis methodology is developed for robust feedback controllers with worst-case H$_{2}$ perforrmance via convex optimization and LMI formulation.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.256-259
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• 2000

A new digital redesign method which can construct a digital controller for multiple linear systems is developed. The proposed method utilized the recently developed LMI theory to obtain a single digital controller which provide good state matching properties with multiple linear systems. A numerical example is provided to evaluate the feasibility of the proposed approach.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.592-599
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• 1998

In this paper, we design a tracking controller which satisfies transient response specifications and maintains tracking error within a tolerable limit for the uncertain track-following system of an optical disk drive. To this end, a robust $H_{\infty}$ control problem with regional stability constraints and sinusoidal disturbance rejection is considered. The internal model principle is used for rejecting the sinusoidal disturbance caused by eccentric rotation of the disk. We show that a condition satisfying the regional stability constraints can be expressed in terms of a linear matrix inequality (LMI) using the Lyapunov theory and S-procedure. Finally, a tracking controller is obtained by solving an LMI optimization problem involving two linear matrix inequalities. The proposed controller design method is evaluated through an experiment.

• Advances in aircraft and spacecraft science
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• v.8 no.1
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• pp.69-85
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• 2021

A modified fuzzy mechanical control of large-scale multiple time delayed dynamic systems in states is considered in this paper. To do this, at the first level, a two-step strategy is proposed to divide a large system into several interconnected subsystems. As a modified fuzzy control command, the next was received as feedback theory based on the energetic function and the LMI optimal stability criteria which allow researchers to solve this problem and have the whole system in asymptotically stability. Modeling the Fisher equation and the temperature gauge for high-speed aircraft and spacecraft shows that the calculation method is efficient.