• Title/Summary/Keyword: Lyapunov Function

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Second order integral sliding mode observer and controller for a nuclear reactor

  • Surjagade, Piyush V.;Shimjith, S.R.;Tiwari, A.P.
    • Nuclear Engineering and Technology
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    • v.52 no.3
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    • pp.552-559
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    • 2020
  • This paper presents an observer-based chattering free robust optimal control scheme to regulate the total power of a nuclear reactor. The non-linear model of nuclear reactor is linearized around a steady state operating point to obtain a linear model for which an optimal second order integral sliding mode controller is designed. A second order integral sliding mode observer is also designed to estimate the unmeasurable states. In order to avoid the chattering effect, the discontinuous input of both observer and controller are designed using the super-twisting algorithm. The proposed controller is realized by combining an optimal linear tracking controller with a second order integral sliding mode controller to ensure minimum control effort and robustness of the closed-loop system in the presence of uncertainties. The condition for the selection of gains of discontinuous control based on the super-twisting algorithm is derived using a strict Lyapunov function. Performance of the proposed observer based control scheme is demonstrated through non-linear simulation studies.

Design of Single-input Direct Adaptive Fuzzy Logic Controller Based on Stable Error Dynamics

  • Park, Byung-Jae
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.1 no.1
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    • pp.44-49
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    • 2001
  • For minimum phase systems, the conventional fuzzy logic controllers (FLCs) use the error and the change-of-error as fuzzy input variables. Then the control rule table is a skew symmetric type, that is, it has UNLP (Upper Negative and Lower Positive) or UPLN property. This property allowed to design a single-input FLC (SFLC) that has many advantages. But its control parameters are not automatically adjusted to the situation of the controlled plant. That is, the adaptability is still deficient. We here design a single-input direct adaptive FLC (SDAFLC). In the AFLC, some parameters of the membership functions characterizing the linguistic terms of the fuzzy rules are adjusted by an adaptive law. The SDAFLC is designed by a stable error dynamics. We prove that its closed-loop system is globally stable in the sense that all signals involved are bounded and its tracking error converges to zero asymptotically. We perform computer simulations using a nonlinear plant and compare the control performance between the SFLC and the SDAFLC.

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Sensorless Speed Control of IPMSM using an Adaptive Sliding mode Observer (적응 슬라이딩 관측기를 이용한 매입형 영구자석 동기전동기의 센서리스 속도제어)

  • Kang, Hyung-Seok;Kim, Won-Seok;Kim, Young-Seok
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.55 no.5
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    • pp.271-279
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    • 2006
  • In this paper, a new speed sensorless control based on an adaptive sliding mode observer is proposed lot the interior permanent magnet synchronous motor(IPMSM) drives. With using voltage equation only, the adaptive sliding mode observer was investigated. Since the parameter of the dynamic equation such as machine inertia or viscosity friction coefficient are not well known and these values can be easily changed during normal operation, there are many restrictions in the actual implementation. The proposed adaptive sliding mode observer applied to overcome the problem caused by using the dynamic equation. Furthermore, the Lyapunov function is used to prove the system stability included speed estimate and speed control. The effectiveness of the proposed algorithm is confirmed by the experiments.

Voltage Stability Analysis Based on Energy Function considering Tap of Transformer (변압기 탭영향을 고려한 에너지함수를 이용한 전압안정도 해석)

  • Kim Beom Shik;Kwon Yong Jun;Lee Ki Je;Moon Young Hyun
    • Proceedings of the KIEE Conference
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    • summer
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    • pp.242-244
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    • 2004
  • 본 논문에서는 전력계통에서 에너지 함수를 이용하여 탭의 영향이 고려된 전압안정도 해석방법을 제시하였다. 전력계통의 전압안정도 해석은 부하단 변압기 탭의 특성과 밀접하게 연관되어 있으며 역학적 등가모델(EMM)을 이용하여 탭의 영향을 고려한 새로운 에너지함수를 유도하였다. 이 에너지 함수는 Lyapunov 함수의 조건을 만족시키며, 유도된 에너지함수로부터 안정평형점과 불안정평형점을 구하여 두 점에서의 에너지의 차이로서 전압붕괴를 예측할 수 있음을 1기 무한대 모선에 대하여 검증해 보았다.

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Networked Nonlinear Control Systems with Time-Delay via T-S Fuzzy Approach (시간 지연을 포함하는 비선형 네트워크 시스템의 퍼지 제어)

  • Song, Min-Kook;Park, Jin-Bae;Joo, Young-Hoon;Kim, Jong-Sun
    • Proceedings of the IEEK Conference
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    • 2009.05a
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    • pp.390-392
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    • 2009
  • This paper is concerned with the stabilization problem of nonlinear networked control systems with time-delay via Takagi-Sugeno(T-S) fuzzy control approach. The T-S fuzzy models are employed to represent nonlinear systems with Markovian jump parameters and time-delay. The purpose of this paper is to design a fuzzy controller such that the closed-loop Markovian jump fuzzy system is stochastically stable. Based on a stocastic Lyapunov function, stabilization sufficient conditions using a mode-independent fuzzy controller are derived for the Markovian jump fuzzy system in terms of Linear Matrix Inequalities(LMIs). Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

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Networked Nonlinear Control Systems with Time-Delay via T-S Fuzzy Approach (시간 지연을 포함하는 비선형 네트워크 시스템의 퍼지 제어)

  • Song, Min-Kook;Park, Jin-Bae;Kim, Jin-Kyu;Joo, Young-Hoon
    • Proceedings of the IEEK Conference
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    • 2009.05a
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    • pp.329-331
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    • 2009
  • This paper is concerned with the stabilization problem of nonlinear networked control systems with time-delay via Takagi-Sugeno(T-S) fuzzy control approach. The T-S fuzzy models are employed to represent nonlinear systems with Markovian jump parameters and time-delay. The purpose of this paper is to design a fuzzy controller such that the closed-loop Markovian jump fuzzy system is stochastically stable. Based on a stocastic Lyapunov function, stabilization sufficient conditions using a mode-independent fuzzy controller are derived for the Markovian jump fuzzy system in terms of Linear Matrix Inequalities(LMIs). Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

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Numerical Study for Mixing Characteristics of an Oscillating Micro-stirrer (미소진동교반기의 혼합특성에 대한 수치적 연구)

  • Kim, Yong-Dae;Maeng, Joo-Sung
    • 유체기계공업학회:학술대회논문집
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    • 2006.08a
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    • pp.309-312
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    • 2006
  • Effective mixing is an important problem in microfluidics for chemical and biomechanical applications. In this study, the influences of the Reynolds number and the oscillating frequency on mixing characteristics of micro-stirrer are studied in a microchannel with single stirrer. The influence of fluid inertial effects in an active mixer is first discussed. It is found that the stirring effects by stirrer oscillation are promptly attenuated at low Reynolds number, which makes greatly difficult the rapid mixing. As the inertial effects are increased, the chaotic advection is generated and then developed. The mixing phase is finally developed some mushroom shaped structure. And the mixing efficiency is also studied as a function of the oscillating frequency. We found that the mixing efficiency does not always increase with higher oscillating frequency of stirrer. Consequently, we found the functional relation between the optimal frequency of a stirrer and the Reynolds number.

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A Backstepping Design with Sliding Mode Control for Uncertain Discrete System

  • Park, Seung-Kyu;Kim, Min-Chan;Kim, Tae-Won;Ahn, Ho-Kyun
    • 제어로봇시스템학회:학술대회논문집
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    • 2002.10a
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    • pp.63.6-63
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    • 2002
  • The technique of backstepping have can avoid cancellations of useful nonlinearities. It is widely used in nonlinear adaptive control. But it is difficult to use this technique for uncertain nonlinear systems. Sliding mode control has robustness and application with feedback linearization. This paper shows that the robustness can be used for back stopping technique to solve the uncertainty problem and to improve the scalar design problem using Control Lyapunov function which is the motivation of back stepping technique with recursive design for high-order systems. In the respect of SMC, the result of this paper does not need to satisfy the matching condition.

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Design of T-S(Takagi-Sugeno) Fuzzy Control Systems Under the Bound on the Output Energy

  • Kim, Kwang-Tae;Joh, Joog-Seon;Kwon, Woo-Hyen
    • Transactions on Control, Automation and Systems Engineering
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    • v.1 no.1
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    • pp.44-49
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    • 1999
  • This paper presents a new T-S(Tae-Sugeno) fuzzy controller design method satisfying the output energy bound. Maximum output energy via a quadratic Lyapunov function to obtain the bound on output energy is derived. LMI(Linear Matrix Inequality) problems which satisfy an output energy bound for both of the continuous-time and discrete-time T-S fuzzy control system are also derived. Solving these LMIs simultaneously, we find a common symmetric positive definite matrix P which guarantees the global asymptotic stability of the system and stable feedback gains K's satisfying the output energy bound. A simple example demonstrates validity of the proposed design method.

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Performance Analysis of Conventional and Modified Proportional Navigation Guidance Laws for a Random Maneuvering Targeta (임의의 방향조정을 하는 목표물에 대한 비례항법 및 수정비례항법의 성능분석)

  • 하인중;허종성;고명삼;이장규;송택렬;안조영
    • 제어로봇시스템학회:학술대회논문집
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    • 1988.10a
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    • pp.597-602
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    • 1988
  • In this paper, we consider conventional and modified proportional navigation guidance(PNG) laws for a random maneuvering target. By means of Lyapunov function approach, we show that an ideal missile guided by the conventional PNG law can always intercept a random maneuvering target if some specified initial conditions are satisfied and the navigation constant is chosen sufficiently high. In addition, we propose a modified PNG law. At the final phase of pursuit, the proposed guidance law has a better acceleration profile than the conventional PNG law.

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