• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.151.5-151
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• 2001

Sliding mode control is investigated for a discrete-time system with uncertainties. The narrowest neighborhood of the sliding surface is shown in which the state can remain. The range is determined by the upper bound of the absolute value of the uncertainty and the equation of the sliding surface. A sliding mode control algorithm is proposed to keep the state there without requiring an enormous input. Under the presence of the system parameter variations, the origin is not always stable although the sliding surface represents the stable dynamics and the state is kept in this neighborhood. The condition for the origin to be stable is investigated. Furthermore, the problems occurring when a continuous-time sliding mode control being ...

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3560-3572
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• 1996

This paper presents a new discrete-time fuzzy-sliding mode controller for robust vibration control of a smart structure featuring a piezofilm actuator. A governong equation of motion for the smart beam structure is derived and discrete-time codel with mismatched uncertainties such as parameter variations is constructed ina state space. A discrete-time sliding mode control system consisting of an equivalent controller and a discontinuous controller is formulated. In the design of the equivalent part, so called an equivalent controller separation method is adopted to achieve vzster convergence to a sliding surface without extension of a sliding region, in which the system robustness maynot be guaranteed. On the other hand, the discontinuous part is constructed on the basis of both the sliding and the convergence conditions using a time-varying feedback gain. The sliding moide controller is then incorporated with a fuzzy technique to appropriately determine principal control parameters such as a discountinuous feedback gain. Experimental implementation on the forced and random vibraiton controls is undertaken in order to demonstrate superior control performance of the proposed controller.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.2
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• pp.174-180
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• 1998

Robust stability of discrete-time regulators which utilize state predictors to compensate computation delays is considered. Novel expressions for the return difference matrices and the complementary sensitivity matrices at the input and the output of the regulator are found to obtain simple bounds for unstructured perturbations. Robust stability for pertubations of the system matrix and /or the gain matrix is also considered. under certain restriction on the nominal system simple bounds for the pertubations are obtained directly from the characteristic equation. It is shown that as far as the effect of the computation delays concerns these bounds have explicit relation to those for the unstructured pertubations.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.2
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• pp.123-130
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• 1999

In discrete-time controlled system, sampling time is one of the critical parameters for control performance. It is useful to employ different sampling rates into the system considering the feasibility of measuring system or actuating system. The systems with the different sampling rates in their input and output channels are named multirate system. Even though the original continuous-time system is time-invariant, it is realized as time-varying state equation depending on multirate sampling mechanism. By means of the augmentation of the inputs and the outputs over one period, the time-varying system equation can be constructed into the time-invariant equation. The two multirate formulations have some trade-offs in the simplicity to construct the controller, the control performance. It is good issue to determine the suitable formulation in consideration of performance of them. In this paper, the two categories of multirate formulations will be compared in terms of the linear quadratic (LQ) cost function. The results are used to select the multirate formulation and the sampling rates suitable to the desired control performance.

• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.191-207
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• 2005

Time delay exists inevitably in active control, which may not only degrade the system performance but also render instability to the dynamic system. In this paper, a novel active controller is developed to solve the time delay problem in flexible structures. By using the independent modal space control method, the differential equation of the controlled mode with time delay is obtained from the time-delay system dynamics. Then it is discretized and changed into a first-order difference equation without any explicit time delay by augmenting the state variables. The modal controller is derived based on the augmented system using the discrete variable structure control method. The switching surface is determined by minimizing a discrete quadratic performance index. The modal coordinate is extracted from sensor measurements and the actuator control force is converted from the modal one. Since the time delay is explicitly included throughout the entire controller design without any approximation, the system performance and stability are guaranteed. Numerical simulations show that the proposed controller is feasible and effective in active vibration control of dynamic systems with time delay. If the time delay is not explicitly included in the controller design, instability may occur.

• Journal of Advanced Navigation Technology
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• v.21 no.6
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• pp.608-613
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• 2017

In this paper, we consider the stability bound for uncertainty of delayed state variables in the linear discrete interval time-varying systems with time-varying delay time. The considered system has an interval time-varying system matrix for non-delayed states and is perturbed by the unstructured time-varying uncertainty in delayed states with time-varying delay time within fixed interval. Compared to the previous results which are derived for time-invariant cases and can not be extended to time-varying cases, the new stability bound in this paper is applicable to time-varying systems in which every factors are considered as time-varying variables. The proposed result has no limitation in applicable systems and is very powerful in the aspects of feasibility compared to the previous. Furthermore. the new bound needs no complex numerical algorithms such as LMI(Linear Matrix Inequality) equation or upper solution bound of Lyapunov equation. By numerical examples, it is shown that the proposed bound is able to include the many existing results in the previous literatures and has better performances in the aspects of expandability and effectiveness.

• International Journal of Control, Automation, and Systems
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• v.6 no.3
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• pp.378-385
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• 2008

This paper aims to present a polynomial approach to the steady-state optimal filtering for delayed systems. The design of the steady-state filter involves solving one polynomial equation and one spectral factorization. The key problem in this paper is the derivation of spectral factorization for systems with delayed measurement, which is more difficult than the standard systems without delays. To get the spectral factorization, we apply the reorganized innovation approach. The calculation of spectral factorization comes down to two Riccati equations with the same dimension as the original systems.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.3
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• pp.201-207
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• 2006

A robust Kalman filtering method for uncertain stochastic systems is suggested by adopting a perturbation estimation process which is to reconstruct total uncertainty with respect to the nominal state transition equation. The predictor and corrector of discrete Kalman filter are reformulated with the perturbation estimator. Successively, the state and perturbation estimation error dynamics and the corresponding error covariance propagation equations are derived as well. Finally we have the recursive algorithm of Combined Kalman Filter-Perturbation Estimator (CKF). The proposed combined Kalman filter-perturbation estimator has the property of integrating innovations and the adaptation capability to system uncertainties. A numerical example is shown to demonstrate the effectiveness of the proposed scheme.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.6
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• pp.368-375
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• 1988

This paper is concerned with the design of the optimal gains of the controller in the speed control system for the induction motor controlled by the microprocessor. The system is modelled with the discrete-time state equation, considering the time delay, for the facility of the optimization techniques. Introducing the conjugate gradient descent method, as the optimization technique, are derived the optimal gains, the gains which give the best transient characteristics. At the optimal gains obtained, the theoretcal transient responses are verified by experimental ones on a 5HP induction motor drive system.