Active vibration control of container cranes against earthquake by the use of delay dependent H8 controller under consideration of actuator saturation

Hakan Yazici, C. Oktay Azeloglu, I. Beklan Kucukdemiral

    Research output: Contribution to journalArticle

    Abstract

    This paper studies the design of a state-feedback delay-dependent H8 controller for vibration attenuation problem of a seismic-excited container crane subject to having time-varying actuator delay, L2 type disturbances and actuator saturation. First, a sufficient delay-dependent stability criterion is developed by choosing a Lyapunov-Krasovskii functional candidate based on matrix inequalities for a stabilizing H8 synthesis. To convexify the Bilinear Matrix Inequality (BMI) based optimization problem involved in the delay dependent conditions; a cone complementary linearization method is adopted to find a sub-optimal solution. The proposed method also utilizes convex description of nonlinear saturation phenomenon by means of convex hull of some linear feedback which leads to a few additional ellipsoidal conditions in terms of Linear Matrix Inequalities (LMIs). By use of the proposed method, a suboptimal controller with maximum allowable delay bound and minimum allowable disturbance attenuation level can be easily obtained by a convex optimization technique. In order to show effectiveness of the proposed approach, a five Degrees-of-Freedom (DOF) container crane structure is modeled using a spring-mass-damper subsystem. The system is then simulated against the real ground motions of Kobe and Northridge earthquakes. Finally, the time history of the crane parts displacements,
    accelerations, control forces and frequency responses of the both uncontrolled and controlled cases are presented. Additionally, the performance of the proposed controller is also compared with a nominal state-feedback H8 controller performance. Simulation results show that, in spite of the actuator saturation, the designed controller is all effective in reducing vibration amplitudes of crane parts and guarantees stability at maximum actuator delay.
    Original languageEnglish
    Pages (from-to)289-316
    Number of pages28
    JournalJournal of low frequency noise, vibration and active control
    Volume33
    Issue number3
    DOIs
    Publication statusPublished - 5 Aug 2014

    Fingerprint

    Earthquakes
    Vibration control
    Cranes
    Vibration
    Containers
    Actuators
    Controllers
    State feedback
    Acceleration control
    Convex optimization
    Stability criteria
    Linear matrix inequalities
    Linearization
    Frequency response
    Cones
    Feedback

    Keywords

    • active vibration control
    • container cranes
    • earthquake-induced vibration
    • H8 control
    • actuator delay
    • actuator saturation
    • Linear matrix inequality

    Cite this

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    title = "Active vibration control of container cranes against earthquake by the use of delay dependent H8 controller under consideration of actuator saturation",
    abstract = "This paper studies the design of a state-feedback delay-dependent H8 controller for vibration attenuation problem of a seismic-excited container crane subject to having time-varying actuator delay, L2 type disturbances and actuator saturation. First, a sufficient delay-dependent stability criterion is developed by choosing a Lyapunov-Krasovskii functional candidate based on matrix inequalities for a stabilizing H8 synthesis. To convexify the Bilinear Matrix Inequality (BMI) based optimization problem involved in the delay dependent conditions; a cone complementary linearization method is adopted to find a sub-optimal solution. The proposed method also utilizes convex description of nonlinear saturation phenomenon by means of convex hull of some linear feedback which leads to a few additional ellipsoidal conditions in terms of Linear Matrix Inequalities (LMIs). By use of the proposed method, a suboptimal controller with maximum allowable delay bound and minimum allowable disturbance attenuation level can be easily obtained by a convex optimization technique. In order to show effectiveness of the proposed approach, a five Degrees-of-Freedom (DOF) container crane structure is modeled using a spring-mass-damper subsystem. The system is then simulated against the real ground motions of Kobe and Northridge earthquakes. Finally, the time history of the crane parts displacements,accelerations, control forces and frequency responses of the both uncontrolled and controlled cases are presented. Additionally, the performance of the proposed controller is also compared with a nominal state-feedback H8 controller performance. Simulation results show that, in spite of the actuator saturation, the designed controller is all effective in reducing vibration amplitudes of crane parts and guarantees stability at maximum actuator delay.",
    keywords = "active vibration control, container cranes, earthquake-induced vibration, H8 control, actuator delay, actuator saturation, Linear matrix inequality",
    author = "Hakan Yazici and Azeloglu, {C. Oktay} and Kucukdemiral, {I. Beklan}",
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    language = "English",
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    TY - JOUR

    T1 - Active vibration control of container cranes against earthquake by the use of delay dependent H8 controller under consideration of actuator saturation

    AU - Yazici, Hakan

    AU - Azeloglu, C. Oktay

    AU - Kucukdemiral, I. Beklan

    PY - 2014/8/5

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    N2 - This paper studies the design of a state-feedback delay-dependent H8 controller for vibration attenuation problem of a seismic-excited container crane subject to having time-varying actuator delay, L2 type disturbances and actuator saturation. First, a sufficient delay-dependent stability criterion is developed by choosing a Lyapunov-Krasovskii functional candidate based on matrix inequalities for a stabilizing H8 synthesis. To convexify the Bilinear Matrix Inequality (BMI) based optimization problem involved in the delay dependent conditions; a cone complementary linearization method is adopted to find a sub-optimal solution. The proposed method also utilizes convex description of nonlinear saturation phenomenon by means of convex hull of some linear feedback which leads to a few additional ellipsoidal conditions in terms of Linear Matrix Inequalities (LMIs). By use of the proposed method, a suboptimal controller with maximum allowable delay bound and minimum allowable disturbance attenuation level can be easily obtained by a convex optimization technique. In order to show effectiveness of the proposed approach, a five Degrees-of-Freedom (DOF) container crane structure is modeled using a spring-mass-damper subsystem. The system is then simulated against the real ground motions of Kobe and Northridge earthquakes. Finally, the time history of the crane parts displacements,accelerations, control forces and frequency responses of the both uncontrolled and controlled cases are presented. Additionally, the performance of the proposed controller is also compared with a nominal state-feedback H8 controller performance. Simulation results show that, in spite of the actuator saturation, the designed controller is all effective in reducing vibration amplitudes of crane parts and guarantees stability at maximum actuator delay.

    AB - This paper studies the design of a state-feedback delay-dependent H8 controller for vibration attenuation problem of a seismic-excited container crane subject to having time-varying actuator delay, L2 type disturbances and actuator saturation. First, a sufficient delay-dependent stability criterion is developed by choosing a Lyapunov-Krasovskii functional candidate based on matrix inequalities for a stabilizing H8 synthesis. To convexify the Bilinear Matrix Inequality (BMI) based optimization problem involved in the delay dependent conditions; a cone complementary linearization method is adopted to find a sub-optimal solution. The proposed method also utilizes convex description of nonlinear saturation phenomenon by means of convex hull of some linear feedback which leads to a few additional ellipsoidal conditions in terms of Linear Matrix Inequalities (LMIs). By use of the proposed method, a suboptimal controller with maximum allowable delay bound and minimum allowable disturbance attenuation level can be easily obtained by a convex optimization technique. In order to show effectiveness of the proposed approach, a five Degrees-of-Freedom (DOF) container crane structure is modeled using a spring-mass-damper subsystem. The system is then simulated against the real ground motions of Kobe and Northridge earthquakes. Finally, the time history of the crane parts displacements,accelerations, control forces and frequency responses of the both uncontrolled and controlled cases are presented. Additionally, the performance of the proposed controller is also compared with a nominal state-feedback H8 controller performance. Simulation results show that, in spite of the actuator saturation, the designed controller is all effective in reducing vibration amplitudes of crane parts and guarantees stability at maximum actuator delay.

    KW - active vibration control

    KW - container cranes

    KW - earthquake-induced vibration

    KW - H8 control

    KW - actuator delay

    KW - actuator saturation

    KW - Linear matrix inequality

    U2 - 10.1260/0263-0923.33.3.289

    DO - 10.1260/0263-0923.33.3.289

    M3 - Article

    VL - 33

    SP - 289

    EP - 316

    JO - Journal of low frequency noise, vibration and active control

    JF - Journal of low frequency noise, vibration and active control

    SN - 0263-0923

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    ER -