• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.561-565
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• 2005

Sliding mode control (SMC) is an effective method of controlling systems with uncertainties which satisfy the so-called matching condition. However, how to effectively handle mismatched uncertainties of systems is still an ongoing research issue in SMC. Several methods have been proposed to design a stable sliding surface even if mismatched uncertainties exist in a system. Especially, it is presented that robustness and efficiency of SMC for linear systems with mismatched uncertainties can be improved by reducing mismatched uncertainties in the reduced-order system. The reduction method needs a new sliding surface with an additional component based on Lyapunov redesign technique. In this paper, a stable sliding surface which contains additional component to reduce the influence of mismatched uncertainties, is introduced. It is designed by using linear matrix inequalities that guarantees the stability of the system. A numerical example demonstrates the validity of the proposed scheme.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.345-345
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• 2000

This paper introduces a new design approach for robust sliding-mode control of a class of mismatched uncertainties. For this, we propose a design method of sliding-mode surface using eigenstructure assignment to be insensitive to perturbation in sliding-mode systems, and also find a formula which is shown bounds of mismatched uncertainties for stability of the system. Simulation results are given to illustrate the approach proposed in this paper.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.119-122
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• 1996

The recently proposed control method using a Lyapunov-like function can give global asymptotic stability to a system with mismatched uncertainties if the uncertainties are bounded by a known function and the uncontrolled system is locally and asymptotically stable. In this paper, we modify the method so that it can be applied to a system not satisfying the latter condition without deteriorating qualitative performance. The assured stability in this case is uniform ultimate boundedness which is as useful as global asymptotic stability in the sense that it is global and the bound can be taken arbitrarily small. By the proposed control law we can deal with both matched and mismatched uncertain systems. The above facts conclude that Lyapunov-like control method is superior to any other Lyapunov direct methods in its applicability to uncertain systems.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.25-25
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• 2000

This paper presents a design method of sliding mode control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we define a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with only mismatched uncertainties using a form of linear matrix inequality (LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding mode controller that stabilizes the overall closed-loop system.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.3
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• pp.193-197
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• 2001

This paper presents a design method of sliding model control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we defined a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use the SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with mismatched uncertainties using a form of linear matrix inequality(LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding model controller that stabilizes the overall closed-loop system.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.62.2-62
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• 2002

1. Introduction 2. System description and preliminary results 3. SMC robust to mismatched uncertainties 4. Simulation results 5. Conclusions

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.7
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• pp.1295-1301
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• 2010

In this note, a systematic general design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and mismatched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the nonlinear integral-type sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the nonlinear integral-type sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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• pp.861-867
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• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.8
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• pp.1188-1194
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• 1997

In this paper, we design output feedback nonlinear dynamic control law by using state feedback nonlinear dynamic compensator and PI observer and show that the controller can stabilize globally and asymptotically a class of nonlinear systems with mismatched uncertainties. We also show that it is possible for a nonlinear system to use the output of PI observer in place of state variables in case that the nonlinear dynamic control law is used, similarly as in the linear system. The effectiveness of the proposed control law is demonstrated by a numerical simulation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.8
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• pp.1184-1184
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• 1997

In this paper, we design output feedback nonlinear dynamic control law by using state feedback nonlinear dynamic compensator and PI observer and show that the controller can stabilized globally and asymptotically a class of nonlinear systems with mismatched uncertainties. We also show that it is possible for a nonlinear system to use the output of PI observer in place of state variables in case that the nonlinear dynamic control law is used, similarly as in the linear system. The effectiveness of the proposed control law is demonstrated by a numerical simulation.