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Robust Discretization of LTI Systems with Polytopic Uncertainties and Aperiodic Sampling
이동환,박진배,주영훈 대한전기학회 2015 Journal of Electrical Engineering & Technology Vol.10 No.3
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.
Robust Discretization of LTI Systems with Polytopic Uncertainties and Aperiodic Sampling
Lee, Dong Hwan,Park, Jin Bae,Joo, Young Hoon The Korean Institute of Electrical Engineers 2015 Journal of Electrical Engineering & Technology Vol.10 No.3
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.
Robust Discretization of LTI Systems with Polytopic Uncertainties and Aperiodic Sampling
Dong Hwan Lee,Jin Bae Park,Young Hoon Joo 대한전기학회 2015 Journal of Electrical Engineering & Technology Vol.10 No.3
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.
이동환,주영훈 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.2
For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.
FIR-type State-feedback Control Law for Discrete-time LTI Systems with Polytopic Uncertainties
박진배,이동환,주영훈,김성관 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.4
Recently, the so-called FIR-type (FIR, finite impulse response) state-feedback memory controller andperiodic memory controller have been developed, and it was revealed that this control design approach can reducethe conservatism of stability and stabilization conditions for periodic or uncertain systems. In these work, the systemduality and a descriptor representation of the original system are used. In this paper, we focus only on the FIRtypestate-feedback memory controller design problem, which is a special case of the general memory controllerstructure previously developed. Although the structure of the controller considered in this paper is a particularcase of the existing one, this special consideration gives some benefits, which are the main purpose of this paper. Finally, examples demonstrate the effectiveness of the FIR-type state-feedback memory controller in terms of lessconservatism.
주영훈,김형진,이동환 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.3
In this paper, we propose an iterative linear matrix inequality (LMI) approach to design static outputfeedback (SOF) controllers for continuous-time linear time-invariant (LTI) systems. The method suggested inthis paper can be viewed as a version of some previous iterative LMI methods. Although the proposed methodcannot always provide improved results in comparison with the previous one, it can be used as a less conservativealternative in some cases. In addition, it can be combined with the previous algorithm to improve the results. Finally,an example is gSiven to demonstrate the validity of the proposed methods.
샘플된 데이터 기반 연속시간 선형 시불변 시스템의 시스템 식별
남지연 제어로봇시스템학회 2021 제어로봇시스템학회 국내학술대회 논문집 Vol.2021 No.6
In this paper, we propose a data-driven method for system identification of continuous-time LTI (linear time invariant) system via sampled data. With the persistently excited input, we show that system matrix and input matrix can be computed by sampled states for sufficiently small sampling period. This data-driven method can be performed with data from the system only.
Designing the Sampling Period of a Discretized LTI Descriptor (Regular) System with Inputs
Athanasios D. Karageorgos,Athanasios A. Pantelous,Grigoris I. Kalogeropoulos 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.4
In this brief paper, a new sharper upper bound for the error ||x(kT) – xk || that derives from the procedure of discretization of the solution of a Linear descriptor (regular) differential input system with consistent initial conditions, and Time-Invariant coefficients (LTI) is calculated and fully discussed. Practically speaking, considering numerous applications in engineering (especially in robotics and digital control) and computer science, we are very interested in determining such kind of upper bounds, since they are significant in the design process of the sampling period T.
Jaejun Lee,Moon Ji Hyun,Jee Sung Chul,이호재 대한전기학회 2021 Journal of Electrical Engineering & Technology Vol.16 No.2
We discuss the robust sampled-data dynamic output-feedback controller design problem for linear time-invariant (LTI) systems subject to parametric uncertainties and L∞ disturbances. The descriptor redundancy-based methods are proposed, and their main features are: (i) sampled-data syntheses are performed in a continuous-time domain; (ii) discrete-time modeling of sampled-data systems, which is adversely aff ected by uncertainties in LTI plant dynamics, is not required; (iii) linear matrix inequality conditions are presented for asymptotic stability and L∞ – l∞ disturbance attenuation.
선형 시불변 시스템의 가제어성을 고려한 데이터 기반 칼만 분해
강동운,이주원,김범수,한민규,김진성,방재성,백주훈 대한전기학회 2024 전기학회논문지 Vol.73 No.4
The model-based control technique requires an accurate system model identification process because the performance of the controller varies depending on the accuracy of the system model information. However, there is a limit to finding accurate model information of the system due to noise of measurement data or system disturbance. Recently, active research on data-based controllers has proposed a data-driven problem structure that can design a controller using only data without identifying a system model. In this paper, we propose a method for obtaining a coordinate transformation matrix that enables Kalman decomposition of a linear system within this data-driven problem structure. Using the pre-experimental data, we obtain the uncontrollable generalized left eigenvector and use it as a basis vector to span the uncontrollable subspace. Finally, the proposed algorithm was verified through an example with uncontrollable repeated eigenvalues.