• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.31.5-31
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• 2001

In conventional perturbation estimators such as disturbance observers(DOB) [1, 2] or time-delayed controllers(TDC) [3{5}, the low pass filter(so-called Q-filter) plays an important role in the stability and performance. However, a general design guideline or analysis for the Q-filter has not been researched yet. In this paper, a guideline for the design of discrete Q-filter is suggested in terms of the analysis of the relationship between the filter parameters and stability performance robustness in discrete-time domain. The analysis clarifies the discrete-time effect of the perturbation estimator and provides a transparent relationship between performance and robustness depending ...

• Nuclear Engineering and Technology
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• v.51 no.1
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• pp.163-169
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• 2019

The robust controller synthesis and analysis of the water level process in the U-tube system generator (UTSG) is addressed in this paper. The parameter uncertainties of the steam generator (SG) are modeled as multiplicative perturbations which are normalized by designing suitable weighting functions. The relative errors of the nominal SG model with respect to the other operating power level models are employed to specify the weighting functions for normalizing the plant uncertainties. Then, a robust controller is designed based on ${\mu}$-synthesis and D-K iteration, and its stability robustness is verified over the whole range of power operations. A gain-scheduled controller with $H_{\infty}$-synthesis is also designed to compare its robustness with the proposed controller. The stability analysis is accomplished and compared with the previous QFT design. The ${\mu}$-analysis of the system shows that the proposed controller has a favorable stability robustness for the whole range of operating power conditions. The proposed controller response is simulated against the power level deviation in start-up and shutdown stages and compared with the other concerning controllers.

• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.185-204
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• 2005

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to response errors. Hence, the uncertain concept plays an important role in vibration control of the engineering structures. The paper discusses the robustness of the stability of vibration control systems with uncertain parameters. The vibration control problem of an uncertain system is approximated by a deterministic one. The uncertain parameters are described by interval variables. The uncertain state matrix is constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of eigenvalues of the close-loop system with uncertain parameters is presented. The lower bounds of eigenvalues can be used to estimate the robustness of the stability the controlled system with uncertain parameters. Two numerical examples are given to illustrate the applications of the present approach.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.459-459
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• 2000

The purpose of this paper is the application of the techniques for the new estimation of robustness for the aircraft systems having structured uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. The number of uncertainties will be the degree of freedoms in the calculation of the robust stability regions called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, in this paper, the quadratic form of Lyapunov function is utilized. In this paper, the practical system of vertical take-off and landing (VTOL) aircraft is analyzed with the proposed stability criteria based upon the Lyapunov direct method. The application of numerical procedures can prove the improvements in estimations of robustness with structured uncertainties. The applicable aircraft system is assumed to be linear with time-varying with nonlinear bounded perturbations.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.1
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• pp.171-179
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• 2001

The purpose of this paper is the derivation and development of the new definitions and methods for the new estimation of robustness for the systems having structured uncertainties. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. The systems considered are assumed to be nominally linear, with time-variant, nonlinear bounded perturbations. This new techniques demonstrate the improvement of robustness bounds from the numerical results.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.630-635
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• 1993

In this paper, the Monte-Carlo method was applied to the controller robustness evaluation problems with respect to the uncertainty of critical plant parameters. The plant studied is a aerial vehicle. The-variable parameters are nondimensional stability derivatives, inertias. The nominal nondimensional stability derivatives ,were obtained from wind tunnel test. Also the nominal inertia parameters were calculated from the mass distribution along the vehicle axes. But the parameters obtained from the test or calculations are at best probable and always contain some uncertainties which one can not figure out. So some kinds of robustness evaluation method should be applied. The parametric robustness of the designed classical controller evaluated by the method turned out to be satisfactory.

• Journal of Power Electronics
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• v.16 no.4
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• pp.1565-1577
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• 2016

For grid-connected LCL-filtered inverters, dual-loop current control with an inner-loop active damping (AD) based on capacitor current feedback is generally used for the sake of current quality. However, existing studies on capacitor current feedback AD with a control delay do not reveal the mathematical relation among the dual-loop stability, capacitor current feedback factor, delay time and LCL parameters. The robustness was not investigated through mathematical derivations. Thus, this paper aims to provide a systematic study of dual-loop current control in a digitally-controlled inverter. At first, the stable region of the inner-loop AD is derived. Then, the dual-loop stability and robustness are analyzed by mathematical derivations when the inner-loop AD is stable and unstable. Robust design principles for the inner-loop AD feedback factor and the outer-loop current controller are derived. Most importantly, ensuring the stability of the inner-loop AD is critical for achieving high robustness against a large grid impedance. Then, several improved approaches are proposed and synthesized. The limitations and benefits of all of the approaches are identified to help engineers apply capacitor current feedback AD in practice.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.700-705
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• 2005

The purpose of this project is the derivation and development of techniques for the new estimation of robustness for the systems having uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. Bounded means the uncertainties are with same positive/negative range. The number of uncertainties will be the degree of freedoms in the calculation of the stability region. This is so called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, the selection of Lyapunov candidate function is of various forms. In this paper, the quadratic form is selected. this generated techniques has been demonstrated by recent research interest in the area of robust control design and confirms that estimation of robustness bounds will be improved upon those obtained by results of the original Lyapunov method. In this paper, the symbolic algebraic procedures are utilized and the calculating errors are reduced in the numerical procedures. The application of numerical procedures can prove the improvements in estimations of robustness for one-and more structured perturbations. The applicable systems is assumed to be linear with time-varying with nonlinear bounded perturbations. This new techniques will be extended to other nonlinear systems with various forms of uncertainties, especially in the nonlinear case of the unstructured perturbations and also with various control method.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.4
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• pp.298-306
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• 1989

Robustness of adaptive pole-placement control against unmodeled dynamics is proved. This proof is done by showing that the sufficient condition for robustness, conic condition and stability of a specific operator, is satisfied for a larger set of unmodeled dynamics. The simulation results show the proposed method is quite powerful. And the difference between the concept of the pseudoplant control and the known internal model control is shown by the closed loop analysis.