• Journal of Mechanical Science and Technology
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• 제20권6호
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• pp.759-769
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• 2006

This paper proposes a new method of discretization for nonlinear systems using a Taylor series expansion and the zero-order hold assumption. The method is applied to sampled-data representations of nonlinear systems with input time delays. The delayed input varies in time and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. The mathematical expressions of the discretization method are presented and the ability of the algorithm is tested using several examples. A computer simulation is used to demonstrate that the proposed algorithm accurately discretizes nonlinear systems with variable time-delayed inputs.

• Journal of Mechanical Science and Technology
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• 제19권11호
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.38.5-38
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• 2001

In this paper, we propose new digital optimal control approach for controlling continuous-time nonlinear chaotic systems, which show very complex behavior and cannot be easily controlled by conventional control methods. Most real systems are represented as continuous-time system, whereas some control methods should be implemented under the condition of computer-based platforms, which are discrete-time systems. To achieve the control objective for chaotic systems successfully, the sampled-data controller, which considers the inter-sample behavior of the continuous-time systems effectively, should be needed. The proposed optimal controller is designed based on the linearized estimation model of chaotic systems. By the computer simulation, we show the control ...

• 대한임베디드공학회논문지
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• 제14권5호
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• pp.269-275
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• 2019

This paper addresses the control problem of cyber-physical systems under controller attack. A novel discontinuous Lyapunov functionals are employed to fully utilize sampled-data pattern which characteristic is commonly appeared in cyber-physical systems. By considering the limited resource of networks, cyber-attacks on the controller are considered randomly occurring and are described as an attack function which is nonlinear but assumed to be satisfying Lipschitz condition. Novel criteria for designing controller with robustness for cyber-attacks are developed in terms of linear matrix inequality (LMI). Finally, a numerical example is given to prove the usefulness of the proposed method.

• Journal of Power Electronics
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• 제19권1호
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• pp.190-200
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• 2019

The flyback converter, which can be regarded as a nonlinear time-varying system, has complex dynamics and nonlinear behaviors. These phenomena can affect the stability of the converter. To simplify the modeling process and retain the information of the output capacitor branch, a special sampled-data model of a peak current-mode (PCM) controlled flyback converter is established in this paper. Based on this, its dynamic behaviors are analyzed, which provides guidance for designing the circuit parameters of the converter. With the critical stability boundary equation derived by a Jacobian matrix, the stable operation range with a varied output capacitor, proportional coefficient of error the amplifier, input voltage, reference voltage and slope of the compensation ramp of a PCM controlled flyback converter are investigated in detail. Research results show that the duty ratio should be less than 0.5 for a PCM controlled flyback converter without ramp compensation to operate in a stable state. The stability regions in the parameter space between the output capacitor and the proportional coefficient of the error amplifier are enlarged by increasing the input voltage or by decreasing the reference voltage. Furthermore, the ramp compensation also can extend to the stable region. Finally, time-domain simulations and experimental results are presented to verify the theoretical analysis results.

• 전자공학회논문지S
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• 제35S권11호
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• pp.96-105
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• 1998

비선형 시스템 출력 조절기의 디지털 구현시에 고려해야 할 샘플링 영향을 조사하였다. 조사결과, 선형 시스템에서와 마찬가지로 '출력 조절됨'은 보존되나, 일반적으로 '출력 조절 가능성'은 보존되지 않음이 밝혀졌다. 또한, 출력 조절 가능성이 보존되는 것을 쉽게 판별할 수 있는 비선형 시스템의 어떤 종류를 파악하였다. 이러한 결과는 일반적으로 연속시간 비선형 시스템에서 설계된 출력 조절기를 이산화하여 얻은 디지털 출력 조절기는 샘플링 시간에 대해 1차 근사에 불구함을 알려준다. 따라서, 이 결과는 일반적으로 보다 개선된 근사 샘플치 비선형 출력 조절기를 구할 필요가 있다는 것을 암시한다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(I)
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• pp.125-128
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• 1987

We investigate the feedback linearizability of nonlinear discrete-time system s of a specific form, $x_k=G_{u_k}oF(x_k)$ where F is a diffeomorphism and [$G_{u_k}$] forms an one parameter group of diffeomorphisms. This structure represents a class of systems which are state equivalent to linear ones and approximates the sampled data model of a continuous-time system. It is also considered a relationship between linearizability and discretization.

• Nuclear Engineering and Technology
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• 제27권2호
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• pp.155-164
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• 1995

증기발생기 수위조절계통의 무작위추출 비선형 제어계통의 경우로 연구되었다. 무작위 변수로는 시간불연속 계통의 추출시간간격 이 고려되었다. Lyapunov 함수를 구하지 않는 확률론적 Lyapunov 방법이 용되었다. 유도된 안정성 요건은 CANDU 형 원자로인 월성 1호기의 자료를 이용하여 시간 존속 모사로 검증하였다.

• 제어로봇시스템학회논문지
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• 제13권5호
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• pp.487-492
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• 2007

This paper presents the development of digital robust fuzzy controller for uncertain nonlinear systems. The proposed approach is based on the intelligent digital redesign(IDR) method with considering the relaxed stability condition of fuzzy control system. The term IDR in the concerned system is to convert an existing analog robust control into an equivalent digital counterpart in the sense of the state-matching. We shows that the IDR problem can be reduced to find the digital fuzzy gains minimizing the norm distance between the closed-loop states of the analog and digital robust control systems. Its constructive conditions are expressed as the linear matrix inequalities(LMIs) and thereby easily tractable by the convex optimization techniques. Based on the nonquadratic Lyapunov function, the robust stabilization conditions are given for the sampled-data fuzzy system, and hence less conservative. A numerical example, chaotic Lorentz system, is demonstrated to visualize the feasibility of the proposed methodology.