• Title/Summary/Keyword: integral of squared error (ISE)

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Design of optimal PID controller for the reverse osmosis using teacher-learner-based-optimization

  • Rathore, Natwar S.;Singh, V.P.
    • Membrane and Water Treatment
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    • v.9 no.2
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    • pp.129-136
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    • 2018
  • In this contribution, the control of multivariable reverse osmosis (RO) desalination plant using proportional-integral-derivative (PID) controllers is presented. First, feed-forward compensators are designed using simplified decoupling method and then the PID controllers are tuned for flux (flow-rate) and conductivity (salinity). The tuning of PID controllers is accomplished by minimization of the integral of squared error (ISE). The ISEs are minimized using a recently proposed algorithm named as teacher-learner-based-optimization (TLBO). TLBO algorithm is used due to being simple and being free from algorithm-specific parameters. A comparative analysis is carried out to prove the supremacy of TLBO algorithm over other state-of-art algorithms like particle swarm optimization (PSO), artificial bee colony (ABC) and differential evolution (DE). The simulation results and comparisons show that the purposed method performs better in terms of performance and can successfully be applied for tuning of PID controllers for RO desalination plants.

Decentralized $H_{\infty}$ Control of Multiple Magnetic Levitation System (다중 자기부상 시스템의 분산형 $H_{\infty}$ 제어)

  • Kim Jong-Moon;Lee Sang-Hyuk;Choi Young-Kiu
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.54 no.12
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    • pp.689-697
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    • 2005
  • In this paper, an application of a decentralized $H_{\infty}$ controller(DHC) to multiple controlled-permanent magnet(CMAG) magnetic levitation(Maglev) systems is presented. The designed DHC using two Riccati equations iteratively has simpler structure and needs less computational loads than conventional centralized $H_{\infty}$ controller. A target plant is a hybrid-type CMAG system with permanent magnet and coil, and its mathematical model is firstly derived to design the DHC. To implement the designed algorithm, a real Maglev vehicle system including digital controller, chopper, sensor, etc., is manufactured. To compare the performances of the DHC method with an observer-based state feedback control(OSFC), the input tracking and disturbance rejection characteristics are experimentally tested. As performance indices(PI), integral of squared error(ISE), integral of absolute error(IAE), integral of time multiplied by absolute error(ITAE) and integral of time multiplied by squared error(ITSE) are used. From the experimental results, it can be seen that the input tracking and disturbance rejection performances of the DHC are better than those of the conventional controller.

A GA based on-line tuning of robust minimax I-PD controller with penalty on manipulated variable

  • Kawabe, Tohru;Tagami, Takanori;Katayama, Tohru
    • 제어로봇시스템학회:학술대회논문집
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    • 1995.10a
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    • pp.428-431
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    • 1995
  • In this paper we propose an on-line tuning method by using genetic algorithm for robust minimax I-PD controller based on new criterion. The new criterion is the Integral of Squared Error (ISE) with a penalty of the derivative of manipulated variable. The work focuses on robust tuning of I-PD controller's parameters in the presence of plant parameter uncertainty. The result of several simulation studies are provided to illustrate the performance of this robust tunig method.

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Efficient Design of 2-D FIR Fan Filters Using New Formulas for McClellan Transform Parameters

  • Song, Young-Seog;Lee, Yong-Hoon
    • Journal of Electrical Engineering and information Science
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    • v.1 no.1
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    • pp.160-163
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    • 1996
  • New formulas for McClellan transform parameters for the design of 2-D zero-phase FIR fan filters are optimally derived under the integral squared error(ISE) criterion. By imposing the constraint that F(0, 0)=\ulcorner, where F($.$) is the McClellan transform and $\omega$\ulcorner is the cutoff frequency of the 1-D prototype filter, the ISE is directly minimized without modifying it and, as a consequence, closed-form formulas for the McClellan transform parameters are obtained. It is shown that these formulas lead to a very efficient design for 2-D zero-phase FIR fan filters.

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Efficient Design of 2-D FIR Fan Filters Using Formulas for MaClellan Transform Parameters (새로운 맥클레란변환 계수 공식을 이용한 2차원 Fan 유한응답여파기의 효율적 설계)

  • 송영석;이용훈
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • 1995.06a
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    • pp.155-157
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    • 1995
  • New formulas for McClellan transform parameters for the design of 2-D Zero-phase FIR fan filters are optimally derived under the integral squared error(ISE) criterion. By imposing the constraint that F(0,0)=coswc, where F($.$) is the McClellan transform and w is the cutoff frequency of the 1-D prototype filter, the ISE is directly minimized without modifying it and, as a consequence, closed-form formulas for the McClellan transform parameters are obtained. It is shows that these formulas lead to a very efficient design for 2-D zero-phase FIR fan filters.

Disturbance Rejection and Optimal Tuning of PID Controller Using $H_\infty$ and Immune Algorithms (PID제어기루프의 외란제거 및 최적화 튜닝을 위한 면역 알고리즘 적용)

  • Kim, Dong-Hwa;Cho, Jea-Hoon;Lee, Hwan
    • Proceedings of the KIEE Conference
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    • 2003.11b
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    • pp.319-322
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    • 2003
  • 본 논문에서는 PID제어기를 이용해 외란이 존재하는 이차 시스템을 제어하는 경우 외란 제거와 최적제어가 동시에 될 수 있는 PID 파라메터를 면역 알고리즘을 통해 구하였다. 지금까지 면역알고리즘을 적용한 최적화 문제에서는 외란이 존재하는 시스템에 대한 적용 사례가 매우 적었다. 그러므로 본 논문에서는 면역알고리즘이 외란이 존재하는 시스템에서 어떠한 성능을 가지는 알아보기 위하여 외란이 존재하는 이차 시스템에 적용하여 그 성능을 알아보았다. 외란제거를 위해 $H_\infty$-norm을 응용하여 제어시스템의 외란제거 조건들을 제시하고 이 조건들을 만족하는 PID 제어기를 설계하였다. 설계된 PID제어기의 최적 파라메터를 구하기 위해 면역 알고리즘을 적용하였고 최적 파라메터를 평가하기 위하여 ISE(integral of squared error)성능지수를 이용하여 만족할 만한 결과를 얻었다.

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