• Journal of Electrical Engineering and Technology
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• 제10권3호
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• pp.1255-1263
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• 2015

In the previous work, the authors studied the problem of robust discretization of linear time-invariant systems with polytopic uncertainties, where linear matrix inequality (LMI) conditions were developed to find an approximate discrete-time (DT) model of a continuous-time (CT) system with uncertainties in polytopic domain. The system matrices of obtained DT model preserved the polytopic structures of the original CT system. In this paper, we extend the previous approach to solve the problem of robust discretization of polytopic uncertain systems with aperiodic sampling. In contrast with the previous work, the sampling period is assumed to be unknown, time-varying, but contained within a known interval. The solution procedures are presented in terms of unidimensional optimizations subject to LMI constraints which are numerically tractable via LMI solvers. Finally, an example is given to show the validity of the proposed techniques.

• Journal of Electrical Engineering and Technology
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• 제10권6호
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• pp.2427-2433
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• 2015

This paper presents an observer-based robust controller for constant reference tracking of linear time invariant systems with polytopic model uncertainties. To this end, this paper not only designs a robust integral controller gain but also suggests how to determine the robust observer gain and the observer model used in the observer. Since the observer model selection is not obvious due to the polytopic uncertainties, particular attention needs to be paid to that. This paper computes the robust controller and observer gains first. Then, the observer model is selected in a way that the whole closedloop is stable and LMIs are used in the middle of choosing the gains and observer model. Simulation examples show that the proposed observer-based feedback control successfully achieves robust reference tracking.

• 전기학회논문지
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• 제59권4호
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• pp.797-802
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• 2010

In this paper, a systematic procedure to design a nonlinear controller for nonlinear active magnetic bearing (AMB) systems is presented. To do this, we effectively convert the AMB system into a polytopic quasi-linear parameter varying (LPV) system, which is a representation of nonlinear state-space models and is described by the convex combination of a set of precisely known vertices. Unlike the existing quasi-LPV systems, the nonlinear weighting functions, which construct the polytopic quasi-LPV model of the AMB system by connecting the vertices, include not only state variables but also the input ones. This allows us to treat the input nonlinearity effectively. By means of the derived polytopic quasi-LPV model and linear matrix inequality (LMI) conditions, nonlinear controller that stabilizes the AMB system is obtained. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations.

• 제어로봇시스템학회논문지
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• 제15권7호
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• pp.667-670
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• 2009

This paper presents an LMI-based method to design a sliding mode controller for a multivariable uncertain system with a polytopic model. In terms of LMIs an existence condition of a sliding surface is derived. And a switching feedback control law is given. Finally, a numerical design example is given to show that the proposed method can be better than the existing results.

• 조명전기설비학회논문지
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• 제24권9호
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• pp.44-48
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• 2010

This paper presents an LMI-based method to design an integral sliding mode controller for an uncertain system with a polytopic model. The uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as in the input matrix. Using LMIs we derive an existence condition of a sliding surface. And we give a switching feedback control law.

• 대한전자공학회논문지TE
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• 제42권3호
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• pp.13-18
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• 2005

본 논문은 안정화 조절기와 추종 성능을 확보하기 위하여 폴리도프 모델를 갖는 도립진자 시스템의 다목적 $H_2/H_{\infty}$ 제어기를 설계를 나타낸다. 꼭지점 기법을 갖는 LMI 설계 기법에 의하여 폴리토프 모델에 대한 다목적 제어기를 설계한다. 각 폴리포프 모델에 대하여 설계된 제어기에 의해 제어된 도립진자를 경사각의 초기값에 대한 수직 각을 안정하게 연직 위치로 복원시키는 곳을 관찰한다.

• 한국정보통신학회논문지
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• 제6권1호
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• pp.6-13
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• 2002

본 논문은 선형 행렬 부등식 (LMI) 기법을 이용하여, 도립진자 시스템의 안정화 조절 제어 및 추종 제어 특성을 만족하는 다목적 제어기를 선계하기 위하여, 도립진자의 모델을 복수개의 모델을 원소로 가진 폴리토프 모델(polytopic model)로 표현하고, 극점 배치 Η$_2$/Η$_{\infty}$ 제어기를 설계하는 과정을 예시한 것이다. 도립진자의 진폭이 비교적 큰 경우, 하나의 동작점에서 구한 선형 시불변 모델의 오차를 불확실성으로 고려하여 설계한 제어기가 가지기 쉬운 보수성(conservativeness)을 극복하기 위하여, 도립진자 시스템에 대하여 다수의 경사 각도를 선형화의 동작점으로 취하여 복수개의 선형시불변 모델로써 이루어진 하나의 폴리토프 모델(polytopic model)을 구성하였다. 이 모델에 대하여, 볼록 최적화(convex optimization) 알고리즘을 사용하는 LMI 소프트웨어를 사용하여 다목적 성능을 만족하는 제어기를 설계하였다. 폴리토프 모델에 대하여 설계된 제어기로써 제어된 도립 진자는, 비교적 큰 경사 각도의 초기치에 대한 실험에서, 안정하게 연직 위치로 복원되는 제어 효과를 관찰할 수 있었다.

• Journal of Electrical Engineering and Technology
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• 제4권4호
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• pp.566-569
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• 2009

In this paper, we propose a less conservative a linear matrix inequality (LMI) condition for the constrained robust model predictive control of systems with input constraints and polytopic uncertainty. Systems with input constraints are represented as perturbed systems with sector bounded conditions. For the infinite horizon control, closed-loop stability conditions are obtained by using a parameter dependent Lyapunov function. The effectiveness of the proposed method is shown by an example.

• International Journal of Control, Automation, and Systems
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• 제6권6호
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• pp.836-844
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• 2008

This paper presents an approach to order reduction of linear parameter varying controller for polytopic model. Feasible solutions which satisfy relevant linear matrix inequalities for constructing full-order parameter varying controller evaluated at each polytopic vertices are first found. Next, sufficient conditions are derived for the existence of a right coprime factorization of parameter varying controller. Furthermore, a singular perturbation approximation for time invariant systems is generalized to reduce full-order parameter varying controller via parameter varying right coprime factorization. This generalization is based on solutions of the parameter varying Lyapunov inequalities. The closed loop performance caused by using the reduced order controller is developed. To examine the performance of the reduced-order parameter varying controller, the proposed method is applied to reduce vibration of flexible structures having the transverse-torsional coupled vibration modes.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.1435-1437
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• 2003

In this paper, we proposed static output feedback model predictive control for Wiener models. We adopted polytopic uncertainty description of Wiener Model Predictive Control (WMPC) algorithms for considering output nonlinearities. Robust stability conditions have been presented under which the closed loop stability of static output feedback MPC is guaranteed. The proposed control law is determined from the static output feedback WMPC based on the current estimated state with explicit satisfaction of input constraints.