• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.10
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• pp.1287-1292
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• 1999

In large-scale systems, we frequently encounter the time-delay and the uncertainty, and these should be considered in the design of controller because these are the source of the degradation of the system performance and instability of system. In this paper, we consider the robust stability of the linear large scale systems with the uncertainties and the time-delays. The considered uncertainties are both structured uncertainty and the unstructured uncertainty. Also, the considered time-delays are time-varying having finite time derivative limits. Based on the Lyapunov theorem and the linear matrix inequality(LMI) technique, we present two sufficient conditions that guarantee the robust stability of the system. The conditions are expressed as the LMI forms which can be easily checked their feasibility by using the well-known LMI control toolbox. Finally, we show by two examples that our results are less conservative than the previous results.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.2
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• pp.125-125
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• 1996

In order to reject the steady-state tracking error, it is common to introduce integral compensators in servosystems for constant reference signals. However, the mathematical model of the plant is exact and no disturbance input exists, the integral compensation is not necessary. From this point of view, a two-degree-of-freedom(2DOF) servosystem has been proposed, in which the integral compensation is effective only when there is a modeling error or a disturbance input. The present paper considers robust stability of this 2DOF servosystem to the unstructured uncertainty of the controlled plant. A robust stability condition is obtained using Riccati inequality, which is independent of the gain of the integral compensator. An example is presented, which demonstrates that the tracking response of the 2DOF servosystem with uncertainty becomes faster when the integral gain made larger under the robust stability condition.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.2
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• pp.57-62
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• 1996

In order to reject the steady-state tracking error, it is common to introduce integral compensators in servosystems for constant reference signals. However, the mathematical model of the plant is exact and no disturbance input exists, the integral compensation is not necessary. From this point of view, a two-degree-of-freedom(2DOF) servosystem has been proposed, in which the integral compensation is effective only when there is a modeling error or a disturbance input. The present paper considers robust stability of this 2DOF servosystem to the unstructured uncertainty of the controlled plant. A robust stability condition is obtained using Riccati inequality, which is independent of the gain of the integral compensator. An example is presented, which demonstrates that the tracking response of the 2DOF servosystem with uncertainty becomes faster when the integral gain made larger under the robust stability condition.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.2
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• pp.93-102
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• 2005

The Nyquist robust stability margin is proposed as a measure of robust stability for systems with Affine TFM(Transfer Function Matrix) parametric uncertainty. The parametric uncertainty is modeled through a Affine TFM MIMO (Multi-Input Multi-Output) description with dead-time, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. Multiloop PI/PID controllers can be tuned by using a modified version of the Ziegler-Nichols (ZN) relations. Consequently, this paper provides sufficient conditions for the robustness of Affine TFM MIMO uncertain systems with dead-time based on Rosenbrock's DNA. Simulation examples show the performance and efficiency of the proposed multiloop design method for Affine uncertain systems with dead-time.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.95.3-95
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• 2001

This paper investigates the simultaneous use of mixed H2/H_inf and mu-synthesis design methodology to design a robust controller for flexible link. We adopt four steps to design control system as follows: Step 1 : Generally, there are differences between the nominal and real model, so we consider the plant as a combination of parametric model uncertainty and unstructured uncertainty represents real structural uncertainties associated with the damping ratios of the flexible modes retained in the nominal model without payload. denotes the uncertainty which is due to the payload added at the tip. Step 2 : We adopt the mixed H2/H_inf theory to design a feedback controller K(s) by using the model uncertainty ...

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.10
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• pp.799-805
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• 2001

In this paper, we propose eigenstructure assigned sliding mode control for mismatched uncertain system. Variable structure control has the sliding mode in which the system is robust against the uncertainty and the sliding motion depends upon the sliding surface. Therefore, the surface design is one of the important problems. Also in mismatched cases, the uncertainty may affect on the sliding motion and may cause unexpected instability of the system. Thus, that should be considered, too. For robust sliding mode against the mismatched uncertainty, we suggest the design method of the sliding surface using the eigenstructure assignment, define an index as the measure of the robustness which shows the size of affordable unstructured uncertainty, and present the computation method. And also we propose the controller which can ensure the sliding mode and prove the robust stability of the proposed controller by using Lyapunov method. Finally we show the appropriateness of the proposed scheme for the mismatched uncertainty via the example.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.8
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• pp.923-931
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• 1999

In this paper, a modeling and a robust time-delay control for the reclaimer are investigated. Supplying the same amount of a raw material throughout the reclamation process from the raw yard to a sinter plant is important to keep the quality of the molten steel uniform in blast furnaces. As the actual parameter values of the reclaimer are not available, the boom rotational dynamics are modeled as a second order differential equation with unknown coefficients. The unknown parameters in the nominal model are estimated using a recursive estimation method. Another important factor in the control design of the reclaimer is the large time-delay in output measurement. Assuming a multiplicative uncertainty, that accounts for both the unstructured uncertainty neglected in the modeling and the structured uncertainty contained in the parameter estimation, a robust Smith predictor is designed. A robust stability criterion for the multiplicative uncertainty is also derived. Following the work of Goodwin et al. [4], a quantifying procedure of the multiplicative uncertainty bound, through experiments , is described. Experimental and simulation results are provided.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.1
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• pp.17-25
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• 2005

This paper provides sufficient conditions for the robustness of Affine linear TFM(Transfer Function Matrix) MIMO (Multi-Input Multi-Output) uncertain systems based on Rosenbrock's DNA (Direct Nyquist Array). The parametric uncertainty is modeled through a Affine TFM MIMO description, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. For this type of parametric robust performance we show robustness of the Affine TFM systems using Nyquist diagram and GB, DNA(Direct Nyquist Array). Multiloop PI/PB controllers can be tuned by using a modified version of the Ziegler-Nickels (ZN) relations. Simulation examples show the performance and efficiency of the proposed multiloop design method.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.351-354
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• 1993

In this paper, reheat-fan engine is described as class of models constructed from nominal and uncertainty model for robust control. In this class of models, uncertainty model consists of structured and unstructured uncertainty, and each model is identified from nonlinear simulation using FFT and ML technique. Then, control requirements and augmented plant are specified. H$_{\infty}$ controller satisfying the control requirements is designed by using constant scaling matrix. Finally, efficacy of the H$_{\infty}$ controller is showed by computer simulation.n.