• Title/Summary/Keyword: State weighting matrix

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Robust PI controller design using LQ-servo (LQ-servo를 이용한 강인한 PI제어기 설계)

  • 이동영;윤성오;서병설
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.577-580
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    • 1996
  • LQ-servo is a stability-robustness guaranteed multivariable controller design method based on the LQR structure to improve command following performance with output feedback. In this paper, a new type of PI controller based on LQ-servo is introduced. Then, Command following performance is improved using the limiting behavior of the control gain and weighting factors on the low frequency part of design parameter Q that is the state weighting matrix in the cost function.

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Optimal Control and Robust Control of Rotating Shaft Using Magnetic Bearings (자기베어링을 이용한 회전축의 최적제어 및 강건제어)

  • Kang, Ho-Shik;Jeong, Namheul;Yoon, Il-Soung;Song, Ohseop
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.14 no.12
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    • pp.1330-1337
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    • 2004
  • In this study, the equations of motion of a rigid rotor supported by magnetic bearings are derived via Hamilton's principle, and transformed to a state-space form for control purpose. The optimal motion control of rotor magnetic bearing system based on the LQR(linear quadratic regulator) theory is addressed. New schemes related to the selection of the state weighting matrix Q and the control weighting matrix R involved in the quadratic functional to be minimized are proposed. And the robust control of the system with an LMI(linear matrix inequality) based H$_{\infty}$ theory is dealt with in this paper. Loop shapings of TFM (transfer function matrix) are used to increase the performance of control capability of the system. The control abilities of LQR and H$_{\infty}$ controller are compared by simulation and experimental tests and show that the capability of H$_{\infty}$ controller is superior to that of LQR.

On the improvement of the guaranteed stability margins for the discrete time LQ regulator

  • Kwon, Wook-Hyun;Kim, Sang-Woo;Choi, Han-Hong
    • 제어로봇시스템학회:학술대회논문집
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    • 1989.10a
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    • pp.913-917
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    • 1989
  • In this paper, the selection method of weighting matrices in the discrete-time LQ problem are suggested in order to improve the guaranteed stability margins, i.e. the gain and phase margins. The asymptotic properties of the solution of the algebraic Riccati equations are investigated by using the closed form solution of the difference Riccati equations. It is shown that the solution of the algebraic Riccati equations monotonically increases as the state weighting matrix Q or the control weighting matrix R increase. The increasing rate of the solution is shown to be much less than that of R for large R. It is also proven that the guaranteed stability margins increases as the ratio between Q and R decreases.

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Application of optimal control to a distillation column (증류탑에의 최적제어 응용연구)

  • 장홍래;박현수;서인석
    • 제어로봇시스템학회:학술대회논문집
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    • 1986.10a
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    • pp.209-211
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    • 1986
  • The continuous time linear quadratic problem (LQP) has been applied to the control of a 8-tray distillation column using the code VASP. The weighting matrices for the state variables and control variables were adjusted iteratively. The simulation results of the optimal control with 2 inputs and 2 outputs showed that the LQP method is very satisfactory for a rapid response and feedback control, and any desired response could be obtained by adjusting the weighting matrices Q under = and R under =. The feedback gain matrix K under = was also determined.

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Pole Placement Method of a Double Poles Using LQ Control and Pole's Moving-Range (LQ 제어와 근의 이동범위를 이용한 중근의 극배치 방법)

  • Park, Minho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.1
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    • pp.20-27
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    • 2020
  • In general, a nonlinear system is linearized in the form of a multiplication of the 1st and 2nd order system. This paper reports a design method of a weighting matrix and control law of LQ control to move the double poles that have a Jordan block to a pair of complex conjugate poles. This method has the advantages of pole placement and the guarantee of stability, but this method cannot position the poles correctly, and the matrix is chosen using a trial and error method. Therefore, a relation function (𝜌, 𝜃) between the poles and the matrix was derived under the condition that the poles are the roots of the characteristic equation of the Hamiltonian system. In addition, the Pole's Moving-range was obtained under the condition that the state weighting matrix becomes a positive semi-definite matrix. This paper presents examples of how the matrix and control law is calculated.

Extensions of the solution region for a discrete algebraic riccati equation and its application to$H_{\infty}$ controller design (이산 대수 Rccati방정식의 해의 존재 영역 확장 및 $H_{\infty}$베어기 설계 응용)

  • 권욱현;박부견;김상우
    • 제어로봇시스템학회:학술대회논문집
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    • 1989.10a
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    • pp.461-466
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    • 1989
  • This paper describes some properties of a discrete algebraic Riccati equation and its application to $H^{\infty}$ control design. The conditions, under which an input weighting matrix can be found for a negative output weighting matrix in order that a solution P for a discrete algebraic equation may exist, are suggested in case of a stable A. This result is applied to a $H^{\infty}$ controller design for the special case of nonsingular B. It is based on a state feedback control law whose objective is to reduce the effect of input disterbances below a prespecified level. This law requires the solution of a modified algebraic Riccati equation, which provides an method for the $H^{\infty}$ optimization control problem approximately.ly.

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Stabilizing Receding Horizon $H_\infty$ Control for Linear Discrete Time-varying Systems

  • Kim, Ki-Baek;Yoon, Tae-Woong;Kwon, Wook-Hyung
    • 전기의세계
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    • v.49 no.9
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    • pp.17-24
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    • 2000
  • This paper presents sufficient conditions7 for monotonicity of the saddle point value for receding-horizon H$\infty$ control(RHHC). The resulting monotonicity is used to prove the stability of the closed-loop. Under these sufficient conditions the well-known terminal equality condition is handled as a special case and the condition on the state weighting matrix is weakened so as to include even the zero matrix. The whole procedure is much simpler than the previous results and thus is expected to be easily extended for constrained delayed and/or nonlinear systems with the RHHC.

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Latent Semantic Analysis Approach for Document Summarization Based on Word Embeddings

  • Al-Sabahi, Kamal;Zuping, Zhang;Kang, Yang
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.13 no.1
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    • pp.254-276
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    • 2019
  • Since the amount of information on the internet is growing rapidly, it is not easy for a user to find relevant information for his/her query. To tackle this issue, the researchers are paying much attention to Document Summarization. The key point in any successful document summarizer is a good document representation. The traditional approaches based on word overlapping mostly fail to produce that kind of representation. Word embedding has shown good performance allowing words to match on a semantic level. Naively concatenating word embeddings makes common words dominant which in turn diminish the representation quality. In this paper, we employ word embeddings to improve the weighting schemes for calculating the Latent Semantic Analysis input matrix. Two embedding-based weighting schemes are proposed and then combined to calculate the values of this matrix. They are modified versions of the augment weight and the entropy frequency that combine the strength of traditional weighting schemes and word embedding. The proposed approach is evaluated on three English datasets, DUC 2002, DUC 2004 and Multilingual 2015 Single-document Summarization. Experimental results on the three datasets show that the proposed model achieved competitive performance compared to the state-of-the-art leading to a conclusion that it provides a better document representation and a better document summary as a result.

Adaptive Optimal Control of a Rotary Inverted Pendulum Using Lagrange Interpolation and a Pole's Moving-Range (라그랑지 보간과 근의 이동범위를 이용한 회전형 도립진자의 적응 최적 제어)

  • Park, Minho;Han, Sang-Wan
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.15 no.2
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    • pp.1066-1073
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    • 2014
  • This paper presents a new design method of optimal control of system which are changed the system parameters. The method used for this purpose are the Lagrange interpolation method and Pole's Moving range method. We selects a system within the scope of the changing the system parameters. Using pole's moving range we calculated the state weighting matrix of optimal control. The optimal controller is designed by Lagrange interpolation method of the state weighting matrix. We are compared with a traditional optimal controller and proposed method by simulation. The simulation showed that the proposed method is better control performance than traditional method of optimal controller.

Optimal Control of Nuclear Reactors by Digital Computer (전자계산기에 의한 원자로최적제어)

  • 천희영;박귀태
    • 전기의세계
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    • v.26 no.6
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    • pp.66-71
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    • 1977
  • In this paper a method is presented for the optimal control of a nuclear reactor at equilibrium state by use of a digital computer. Using the optimal control theory, we formulate the control problem of the reactor as a discrete-time linear regulator problem. A quadratic performance index is defined. The effects of choosing different performance index weighting matrices to the feedback gain matrix and reactor transient responses are studied for the deterministic optimal control with all state variables accessible to measurement.

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