• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.1975-1987
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• 2005

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay maneuvering an automobile.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.5
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• pp.827-837
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• 1994

This paper presents robustness propertis of the Kalman Fiter and the associated LQG/LTR method for linear time-invariant output-delayed systems. It is shown that, even for minimum phase plants, the LQG/LTR method can not recover the target loop transfer function. Instead, an upper bound on the recovery error is obtained using an upper bound of the solution of the Kalman filter Riccati equations. Finally, some dual properties between output-delayed systems and input-delayed systems are exploited.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.239-245
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• 2002

In this Paper, we present a method for designing fuzzy $H_2/H_{\infty}$ controllers of delayed nonlinear systems with saturating input. Takagi-Sugeno fuzzy model is employed to represent delayed nonlinear systems with saturating input. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. And a sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is given in terms of linear matrix inequalities(LMIs). The designing fuzzy $H_2/H_{\infty}$ controllers minimize an upper bound on a linear quadratic performance measure. Finally, a design example of fuzzy $H_2/H_{\infty}$ controller for uncertain delayed nonlinear systems with saturating input.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.46 no.3
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• pp.244-250
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• 2018

Multilateration acquires the transponder signal of target from receivers installed on the ground and calculates the position of the target using the difference of the signal acquisition time of each receiver. One of the factors that influence the positioning accuracy of Multilateration using the TDOA calculation method is the error due to the precision measurement of signal input time. When measuring the signal input time at the receiver, the input signal is sampled using the reference clock of the receiver and a reference sample having the same sampling rate is applied to the cross correlation technique. Therefore, the accuracy of the signal input time is proportional to the reference clock. In this paper, the algorithm for precisely measuring the signal input time by performing cross correlation between the input signal of the receiver and DRS(Delayed Reference Sample) is proposed. In order to verify this, we implemented the pulse signal of the transponder that is transmitted from the target using Matlab. Through the simulation, cross correlation between the proposed DRS and the input signal was performed. From this result, the performance of the precise measurement of signal input time was analyzed.

• International Journal of Control, Automation, and Systems
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• v.4 no.3
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• pp.293-301
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• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.2
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• pp.52-60
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• 2009

This paper proposes a digital controller for a nonlinear multi-input/multi-output(MIMO) system with time-delayed input. A nonlinear system with multi-input time delay is discretized using Taylor's discretization method, and the discretized system can be converted into a general nonlinear system. Consequently, general nonlinear controller synthesis can be applied to the discretized time-delay system We adopted MAC controller synthesis and verified the performance of the proposed method by conducting computer simulations. The results of the simulation showed that the proposed controller synthesis performs well and the proposed method is useful for controlling a nonlinear time-delay system.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.688-691
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• 1997

This paper presents an $H^{\infty}$ controller design method for linear time-invariant systems with delayed state and control. Using the second method of Lyapunov, the stability for delayed systems is discussed. For delayed systems, we derive a sufficient condition of the bounded real lemma(BRL) which is similar to BRL for nondelayed systems. And the sufficient conditions for the existence of an output feedback $H^{\infty}$ controller of any order are given in terms of three linear matrix inequalities(LMls). Futhermore, we briefly explain how to construct such controllers from the positive definite solutions of their LMIs and give a simple example to illustrate the validity of the proposed design procedure.e.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.151-156
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• 1998

This paper presents an $H_{\infty)$ output feedback controller design method for linear systems with delayed state, delayed control input, and delayed masurement output. Using a Lyapunov functional, the stability for delayed systems is discussed independently of delays. Also, sufficient condition for the existence of $H_{\infty)$ controllers of any order is given in terms of three linear matrix inequalities(LMIs). Based on positive definite solutions of their LMIs, we briefly explain the way to construct $H_{\infty)$ controller, which stabilizes time-delay systems independently of delays and guarantees an $H_{\infty)$norm bound.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1905-1910
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• 2003

It is well known that parameter uncertainties and time-delays cannot be avoided in practice and result in poor performance and even instability. Nevertheless, to the authors' best knowledge, there exist few results on model predictive control (MPC) handling explicitly uncertain time-delayed systems. In this paper, we present an MPC algorithm for uncertain time-varying systems with input constraints and state-delay. An optimization problem is suggested to find a memoryless state-feedback MPC law and the closed-loop stability is established under feasibility and certain conditions.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.07b
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• pp.1234-1238
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• 2004

A Controlled neural networks are proposed in order to measure nonlinear environments in adaptive and in realtime. The structure of it is similar to recurrent neural networks: a delayed output as the input and a delayed error between tile output of plant and neural networks as a bias input. In addition, we compute the desired value of hidden layer by an optimal method instead of transfering desired values by backpropagation and each weights are updated by RLS(Recursive Least Square). Consequently, this neural networks are not sensitive to initial weights and a learning rate, and have a faster convergence rate than conventional neural networks. This new neural networks is Error Estimated Neural Networks. We can estimate nonlinear models in realtime by the proposed networks and control nonlinear models. To show the performance of this one, we have various experiments. And this controller call prove effectively to be control in the environments of various systems.