• Title/Summary/Keyword: $H_{\infty}$ Optimal Control

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Robust market-based control method for nonlinear structure

  • Song, Jian-Zhu;Li, Hong-Nan;Li, Gang
    • Earthquakes and Structures
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    • v.10 no.6
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    • pp.1253-1272
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    • 2016
  • For a nonlinear control system, there are many uncertainties, such as the structural model, controlled parameters and external loads. Although the significant progress has been achieved on the robust control of nonlinear systems through some researches on this issue, there are still some limitations, for instance, the complicated solving process, weak conservatism of system, involuted structures and high order of controllers. In this study, the computational structural mechanics and optimal control theory are adopted to address above problems. The induced norm is the eigenvalue problem in structural mechanics, i.e., the elastic stable Euler critical force or eigenfrequency of structural system. The segment mixed energy is introduced with a precise integration and an extended Wittrick-Williams (W-W) induced norm calculation method. This is then incorporated in the market-based control (MBC) theory and combined with the force analogy method (FAM) to solve the MBC robust strategy (R-MBC) of nonlinear systems. Finally, a single-degree-of-freedom (SDOF) system and a 9-stories steel frame structure are analyzed. The results are compared with those calculated by the $H{\infty}$-robust (R-$H{\infty}$) algorithm, and show the induced norm leads to the infinite control output as soon as it reaches the critical value. The R-MBC strategy has a better control effect than the R-$H{\infty}$ algorithm and has the advantage of strong strain capacity and short online computation time. Thus, it can be applied to large complex structures.

Robust Tuning of PID Controller With Disturbance Rejection Using Bacterial Foraging Based Optimization

  • Kim, Dong-Hwa;Cho, Jae-Hoon
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.1092-1097
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    • 2005
  • In this paper, design approach of PID controller with rejection function against external disturbance in motor control system is proposed using bacterial foraging based optimal algorithm. Up to the present time, PID Controller has been used to operate for AC motor drive because of its implementational advantages in practice and simple structure. However, it is not easy to achieve an optimal PID gain with no experience, since the gain of the PID controller has to be manually tuned by trial and error in the industrial system with disturbance. To design disturbance rejection tuning, disturbance rejection conditions based on $H_{\infty}$ are illustrated and the performance of response based on the bacterial foraging is computed for the designed PID controller as ITSE (Integral of time weighted squared error). Hence, parameters of PID controller are selected by bacterial foraging based optimal algorithm to obtain the required response

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Optimal Design of a Continuous Time Deadbeat Controller (연속시간 유한정정제어기의 최적설계)

  • Kim Seung Youal;Lee Keum Won
    • Journal of the Institute of Convergence Signal Processing
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    • v.1 no.2
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    • pp.169-176
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    • 2000
  • Deadbeat property is well established in digital control system design in time domain. But in continuous time system, deadbeat is impossible because of it's ripples between sampling points inspite of designs using the related digital control system design theory. But several researchers suggested delay elements. A delay element is made from the concept of finite Laplace Transform. From some specifications such as internal model stability, physical realizations as well as finite time settling, unknown coefficents and poles in error transfer functions with delay elements can be calulted so as to satisfy these specifications. For the application to the real system, robustness property can be added. In this paper, error transfer function is specified with 1 delay element and robustness condition is considered additionally. As the criterion of the robustness, a weighted sensitive function's $H_{infty}$ norm is used. For the minimum value of the criterion, error transfer function's poles are calculated optimally. In this sense, optimal design of the continuous time deadbeat controller is obtained.

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Modeling and adaptive optimal control of a twin roll strip caster (쌍롤형 박판주조기의 모델링과 적응최적제어)

  • 김성훈;홍금식;이교일
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.325-328
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    • 1997
  • In this paper the modeling and control of a twin roll strip caster is investigated. Mathematical models for the strip casting process are obtained by analyzing five critical areas such that the molten steel level in the pool, solidification process, roll separating force and torque, roll dynamics including hydraulic actuators, and roll drive system. A two-level control strategy is proposed. At lower level, three local subsystems are independently feedback-controlled by suitable local controllers which perform well to the behaviors of each subsystem. They are a variable structure control of the molten steel level in the pool, an adaptive predictive control of the roll gap which is directly related to the strip thickness, and an $H^{\infty}$ control of the roll drive system. At higher level, all reference signals to the lower level subsystems are generated by an optimal controller in the perspective of regulating the strip thickness and roll separating force. Simulations are provided..

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Nonlinear Adaptive Control based on Lyapunov Analysis: Overview and Survey (리아프노브 분석법 기반 비선형 적응제어 개요 및 연구동향 조사)

  • Park, Jin Bae;Lee, Jae Young
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.3
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    • pp.261-269
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    • 2014
  • This paper provides an overview of the basics and recent studies of Lyapunov-based nonlinear adaptive control, the aim of which is to improve or maintain the performance and stability of the closed-loop system by cancelling out the presumable uncertainties in the nonlinear system dynamics. The design principles are essentially based on Lyapunov's direct method. In this survey, we provide a comprehensive overview of Lyapunov-based nonlinear adaptive control techniques with simplified effective design examples, which are to be elaborated as related recent results are gradually shown. The scope of the survey contains research on singularity problems in adaptive control, the techniques to deal with linearly and nonlinearly parameterized uncertainties, robust neuro-adaptive control, and adaptive control methodologies combined with various nonlinear control techniques such as sliding-mode control, back-stepping, dynamic surface control, and optimal/$H_{\infty}$ control.

ROBUST CONTROLLER DESIGN FOR IMPROVING VEHICLE ROLL CONTROL

  • Du, H.;Zhang, N
    • International Journal of Automotive Technology
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    • v.8 no.4
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    • pp.445-453
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    • 2007
  • This paper presents a robust controller design approach for improving vehicle dynamic roll motion performance and guaranteeing the closed-loop system stability in spite of vehicle parameter variations resulting from aging elements, loading patterns, and driving conditions, etc. The designed controller is linear parameter-varying (LPV) in terms of the time-varying parameters; its control objective is to minimise the $H_{\infty}$ performance from the steering input to the roll angle while satisfying the closed-loop pole placement constraint such that the optimal dynamic roll motion performance is achieved and robust stability is guaranteed. The sufficient conditions for designing such a controller are given as a finite number of linear matrix inequalities (LMIs). Numerical simulation using the three-degree-of-freedom (3-DOF) yaw-roll vehicle model is presented. It shows that the designed controller can effectively improve the vehicle dynamic roll angle response during J-turn or fishhook maneuver when the vehicle's forward velocity and the roll stiffness are varied significantly.

Robust motion control of a flexible micro-actuator using $H_{\infty}$ control method

  • Okugawa, Masayuki;Sasaki, Minoru;Fujisawa, Fumio
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10a
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    • pp.397-400
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    • 1996
  • In this paper, robust motion control of a flexible micro-actuator is presented. The actuator is made of a bimorph piezoelectric high-polymer material (PVDF). No mathematical model system can exactly model a physical system such a flexible micro-actuator. For this reason we must be aware of how modeling errors might adversely affect the performance of a control system for such a model. The H method addresses a wide range of the control problems, combining the frequency and time domain approaches. The design is an optimal one in the sense of minimization of the maximum of the closed-loop transfer function. It includes colored measurement and process noise. It also addresses the issues of robustness due to model uncertainties, and is applicable to the, flexible micro-actuator control problem. Therefore, we adopt the H control problem to the robust motion control of the flexible micro-actuator. Theoretical and experimental results demonstrate the satisfactory performance and the effectiveness of the designed controller. the effectiveness of the designed controller.

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Development of the Robust Speed Controller for Marine Medium Speed Diesel Engines (선박용 중속 디젤 기관의 로바스트 속도제어기 개발)

  • Jung, B.G.;Yang, J.H.;Kim, C.H.
    • Journal of Advanced Marine Engineering and Technology
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    • v.20 no.4
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    • pp.349-349
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    • 1996
  • The ship's propulsion efficiency depends upon a combibation of engine and propeller. The propeller has better efficiency as the engine has lower rotational speed. This situation led the engine manufacures to design the engine that has lower speed, longer stroke and a small number of cylinders. With this new trends the conventional mechanical-hydrualic governors for engine speed control have been replaced by digital speed controllers which adopted the PID control or the optimal control algorithm. But these control algorithms have not enough robustness to suppress the variations of the delay-time and the parameter perturbation especially in low speed engine. In this study we consider the perturbations of the engine parameters as the modeling uncetainties and design a robust speed controller for marine medium speed diesel engine by means of $ extit{H}_{infty}$control theory having the central solution. By comparing the results of the robust speed controller with those of mechanical governor and PID controller, the validity of the robust speed controller under parameter variations is confirmed. The speed control of the experimental diesel engine of carried out using actuator which is composed of PWM signal generator and D.C servo motor.

A Design on Reference Model Following Fuzzy Control System Using Hysteresis element (비선형 요소를 이용한 기준 모델 추종형 퍼지 제어 시스템의 설계)

  • Hwang, C.S.;Nam, K.W.;Jeong, H.S.;Kim, D.W.
    • Proceedings of the KIEE Conference
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    • 1996.07b
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    • pp.974-976
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    • 1996
  • In this paper, a reference model following control system using a fuzzy logic controller(FLC) is proposed By using an integrator and a nonlinear hysteresis element, a reference model whose response has no overshoot and fast rise time is designed. A FLC is designed to follow as close as possible to the response of the reference model. The proposed design method is shown that the robustness and the optimal tracking property can be achieved under modeling error, disturbance and parameter perturbations. The effectiveness of the proposed design method is verified through the simulation that compare using the FLC with using a $H_{\infty}$ controller.

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Design of the robust bilateral controller for teleoperators with modeling uncertainties (모델링 불확실성이 존재하는 원격조작기에서 강인 안정을 보장하는 양방향 제어기 설계)

  • 이형기;정명진
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.976-979
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    • 1996
  • Teleoperation is the extension of a person's sensing and manipulation capability to a remote location. Teleoperators generally can be modeled as linear transfer function indecently including modeling uncertainty. Modeling uncertainties can make the system unstable and its performance poor. Thus I'm studying about a design framework for a bilateral controller of teleoperator systems with modeling uncertainties. In this paper, a method based on the H$_{\infty}$-optimal control and .mu.-synthesis frameworks are introduced to design a controller for the teleoperator that achieves stability and performance in the presence of the modeling uncertainties..ties.inties.

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