• Title/Summary/Keyword: Bilinear Method

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Robust H$_{\infty}$ Control Method for Bilinear Systems

  • Kim, Beom-Soo;Lim, Myo-Taeg
    • International Journal of Control, Automation, and Systems
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    • v.1 no.2
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    • pp.171-177
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    • 2003
  • In this paper, we investigate a robust $H_{\infty}$ state feedback control technique for continuous time bilinear systems with an additive disturbance input. The nonlinear robust $H_{\infty}$control for bilinear systems requires a solution to the state dependent algebraic Riccati equation (SDARE). We present a new robust $H_{\infty}$control technique based on the successive approximation method for solving the SDARE by converting bilinear systems into time-varying linear systems. The proposed control method guarantees robust stability for closed loop bilinear systems. The proposed algorithm is verified by numerical examples.

An adaptive predictive control for the bilinear process (쌍일차 공정의 적응 예측제어)

  • Lo, K.;Yoon, E. S.;Yeo, Y. K.;Song, H. K.
    • 제어로봇시스템학회:학술대회논문집
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    • 1990.10a
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    • pp.344-349
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    • 1990
  • Under the assumption that process input/output data are sufficiently rich to allow reasonable plant identification, a long-range predictive control method for SISO bilinear plant is derived. In order to ensure offset-free behaviour of the control method, a new bilinear CARIMA model with variable dead-time is introduced. Furthermore, to extend the maximum output prediction horizon, the future predicted outputs in the bilinear term are assumed to be equal to the known future set-points. With a classical recursive adaptation algorithm, the proposed control scheme is capable of stable control of bilinear plants with variable parameters, with variable dead-time, and with a model order which changes instantaneously. Several simulation results demonstrate the characteristics of the proposed bilinear model predictive control method.

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A Controller Design of Bilinear Systems via Iterative Method (반복법에 의한 쌍선형 시스템의 제어기 설계)

  • 이돈구;김주식;이상혁
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.17 no.5
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    • pp.88-93
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    • 2003
  • This paper presents a controller design method of bilinear systems via iterative method. The iterative procedure with auxiliary sequences is defined in the process of constructing coupled linear time varying systems from bilinear systems. To design the feedback controller for bilinear systems with quadratic cost function, an optimization procedure is given by the representation closely related to the Riccati approach. In the simulation results, it is shown that the suggested method accomplishes the improved performance and good convergence.

SOME BILINEAR ESTIMATES

  • Chen, Jiecheng;Fan, Dashan
    • Journal of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.609-620
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    • 2009
  • We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

A study on the observer design of bilinear system via walsh function (WALSH 함수에 의한 쌍일차계의 관측자설계에 관한 연구)

  • 안두수;김종부
    • 제어로봇시스템학회:학술대회논문집
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    • 1987.10b
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    • pp.115-119
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    • 1987
  • In this paper the observer design problem in bilinear systems is studied using the Walsh functions as approximating set of functions to find a finite series expansion of the state of bilinear system. A classical Liapnove method, to finding a class of observer feedback matrix, is applied to ensure uniform asymptotic stability of the observation error dynamics. An algorithm is derived for observer state eq. via Walsh function. The basic objective is to develop a computational algorithm for the determination of the coefficients in the expansion. This approach technique gives satisfactory result as well provides precise and effective method for the bilinear observer design problem.

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A Study on compensation of Frequency Distortion of SCF by Using Prewarping Procedure (Prewarping법을 이용한 SCF의 주파수 #곡 보상에 관한 연구)

  • 최민호;김도현
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.22 no.5
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    • pp.69-74
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    • 1985
  • In this paper five-order Butterworth Low pass active RC filter is designed by using FDNR (Frequency Dependent Ncgative Resistor) Method from LC ladder filter having the lowest sensitivity. In process of Transformation to SCF (Switched Capacitor Filter) from active RC filter, Bilinear Z Transfomation method is utilized. By the design of SCF using the bilinear Z transform method the problem of aliasing can be avoided, but the frequency distortion is generated. The transformation from analog filter to digital filter is not equal in the region of the cut off frequency caused by this effect. Avoiding the problem of this effect, we use prewarping method. The result shows that the prewarped SCF makes more remarkable improvement in the frequency distortion than SCF which is transformed by using bilinear Z transform.

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Probabilistic Bilinear Transformation Space-Based Joint Maximum A Posteriori Adaptation

  • Song, Hwa Jeon;Lee, Yunkeun;Kim, Hyung Soon
    • ETRI Journal
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    • v.34 no.5
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    • pp.783-786
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    • 2012
  • This letter proposes a more advanced joint maximum a posteriori (MAP) adaptation using a prior model based on a probabilistic scheme utilizing the bilinear transformation (BIT) concept. The proposed method not only has scalable parameters but is also based on a single prior distribution without the heuristic parameters of the previous joint BIT-MAP method. Experiment results, irrespective of the amount of adaptation data, show that the proposed method leads to a consistent improvement over the previous method.

Extension and Appication of Total Least Squares Method for the Identification of Bilinear Systems

  • Han, Seok-Won;Kim, Jin-Young;Sung, Koeng-Mo
    • The Journal of the Acoustical Society of Korea
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    • v.15 no.1E
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    • pp.59-64
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    • 1996
  • When the input-output record is available, the identification of a bilinear system is considered. It is assumed that the input is noise free and the output is contaminated by an additive noise. It is further assumed that the covariance matrix of the noise is known up to a factor of proportionality. The extended generalized total least squares (e-GTLS) method is proposed as one of the consistent estimators of the bilinear system parameters. Considering that the input is noise-free and that bilinear system equation is linear with respect to the system parameters, we extend the GTLS problem. The extended GTLS problem is reduced to an unconstrained minimization problem, and is solved by the Newton-Raphson method. We compare the GTLS method and the e-GTLS method in the point of the accuracy of the estimated system parameters.

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BILINEAR SYSTEMS CONTROLLER DESIGN WITH APPROXIMATION TECHNIQUES

  • Lee, Sang-Hyuk;Lee, Keonhee
    • Journal of the Chungcheong Mathematical Society
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    • v.18 no.1
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    • pp.101-116
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    • 2005
  • Using the iterative method, we derive an controller realization of the bilinear system, which is resulted from the system reformulation. We utilize Banach Fixed Point Theorem to support proposed controller, and the simulation results are also illustrated to verify usefulness of this technique.

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On the stabilization of singular bilinear systems

  • Liang, Jia-Rong;Choi, Ho-Lim;Lim, Jong-Tae
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.449-451
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    • 2003
  • In this paper, the stability problem for singular bilinear system is investigated. We present state feedback control laws for two classes of singular bilinear plants. Asymptotic stability of the closed-loop systems is derived by employing singular Lyapunov's direct method. The primary advantage of our approach lies in its simplicity. In order to verify effectiveness of the results, two numerical examples are given.

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