非线性建筑结构振动的非光滑逆控制方法设计
|
摘要
针对地震波对非线性建筑结构振动性能影响,运用非光滑逆控制方法进行抑制,克服了传统的非线性结构近似线性化控制方法忽略非线性影响的缺点。根据Lyapunov稳定性理论和有限时间稳定性理论,论证了所设计控制方法能够实现非线性建筑结构振动的有限时间稳定。在控制方法实现中,应用扩张状态观测器进行未知干扰项的估计。以一幢受地震冲击的八层建筑为被控对象,并对仿真效果进行对比分析。结果表明,该非光滑逆控制方法具有良好的抗震性能。
Considering the vibration effects of seismic waves on building with nonlinear structures, a nonsmooth and inversed control algorithm is used to suppress the vibration. It overcomes the faults of ignoring nonlinear influence in traditional approximate linearization control method and suppresses the influence of seismic waves effectively. According to Lyapunov stable theory and finite-time stability theory, the proposed control method to realize the stability of the nonlinear structural vibration is demonstrated. In the realization of the control method, the extended state observer is used to estimate the unknown disturbances. The numerical simulation is conducted for an eight-story building influenced by the seismic waves, and the comparative analysis of simulated effect is carried out. The results show that the nonsmooth and inversed control algorithm has a good seismic performance.
Considering the vibration effects of seismic waves on building with nonlinear structures, a nonsmooth and inversed control algorithm is used to suppress the vibration. It overcomes the faults of ignoring nonlinear influence in traditional approximate linearization control method and suppresses the influence of seismic waves effectively. According to Lyapunov stable theory and finite-time stability theory, the proposed control method to realize the stability of the nonlinear structural vibration is demonstrated. In the realization of the control method, the extended state observer is used to estimate the unknown disturbances. The numerical simulation is conducted for an eight-story building influenced by the seismic waves, and the comparative analysis of simulated effect is carried out. The results show that the nonsmooth and inversed control algorithm has a good seismic performance.
引文
[1]周福霖.工程结构减震控制[M].北京:地震出版社,1997.Zhou Fulin.Seismic Control in Engineering Structures[M].Beijing:Seismological Press,1997.
[2]欧进萍.结构振动控制-主动、半主动和智能控制[M].北京:科学出版社,2003.Ou Jinping.Structural Vibration Control-active,Semiactive and Intelligent Control[M].Beijing:Science Press,2003.
[3]李雪峰,汪斌.斜拉桥地震响应线性二次型迭代学习控制(LQILC)研究[J].地震工程与工程振动,2015,35(1):174-182.Li Xuefeng,Wang Bin.Research on Linear Quadratic Iterative Learning Control(LQILC)for Seismic Responses of Cable-stayed Bridge[J].Earthquake engineering and engineering dynamics,2015,35(1):174-182.
[4]高为炳.变结构控制理论[M].北京:中国科学技术出版社,1990.Gao Weibing.Foundation of Variable Structure Control Theory[M].Beijing:China Science and Technology Press,1990.
[5]李春文,苗原,冯元琨,等.非线性系统控制的逆系统方法(I)-单变量控制理论[J].控制与决策,1997,12(5):529-535.Li Chunwen,Miao Yuan,Feng Yuankun,et al.Inverse System Method for Nonlinear Systems Control(I)-Single Variable Control Theory[J].Control and Decision,1997,12(5):529-535.
[6]李春文,苗原,冯元琨,等.非线性系统控制的逆系统方法(II):多变量控制理论[J].控制与决策,1997,12(6):625-630,642.Li Chunwen,Miao Yuan,Feng Yuankun,et al.Inverse System Method for Nonlinear Systems Control(II):Multivariable Control Theory[J].Control and Decision,1997,12(6):625-630,642.
[7]Rosier L.Homogeneous Lyapunov Function for Homogeneous Continuous Vector Field[J].Systems and Control Letters(S0167-6911),1992,19(6):467-473.
[8]Kawski M.Stabilizability and Nilpotent Approximations[C]//Proceedings of the 27th IEEE Conference on Decision and Control,Austin USA,1988,2:1244-1248.
[9]Hermes H.Homogeneous Coordinates and Continuous Asymptotically Stabilizing Feedback Controls[M].Differential Equations:Stability and Control,1991.
[10]马克茂.航天器连续非光滑姿态控制律设计[J].宇航学报,2012,33(6):713-719.Ma Kemao.Design of Non-smooth Attitude Control Laws for Spacecraft[J].Journal of Astronautics,2012,33(6):713-719.
[11]刘慧贤,丁世宏,李世华,等.永磁同步电机位置伺服系统的有限时间控制[J].电机与控制学报,2009,13(3):424-430.Liu Huixian,Ding Shihong,Li Shihua,et al.Finite-time Control of PMSM Position Servo System[J].Electric Machines and Control,2009,13(3):424-430.
[12]王建晖,王清,马克茂.一种永磁同步电机非光滑控制器设计[J].计算机仿真,2016,33(3):227-230+263.Wang Jianhui,Wang Qing,Ma Kemao.Non-smooth Controller Design for Permanent Magnet Synchronous Motors[J].Computer Simulation,2016,33(3):227-230,263.
[13]Yang J N,Li Z,Vongchavalitkul S.Generalization of Optimal Control Theory:Linear and Nonlinear Control[J].Journal of Engineering Mechanics(S0733-9399),1994,120(2):266-283.
[14]An K,Cai G.Discretization of Preisach Hysteresis Model[J].Journal of Central South University(S2095-2899),2015(22):4724-4730.
[15]Su C Y,Wang Q Q,Chen X K,et al.Adaptive Variable Structure Control of a Class of Nonlinear Systems with Unknown Prandtl-Ishlinskii Hysteresis[J].IEEETransactions on Automatic Control(S0018-9286),2005,12(50):2069-2073.
[16]赵新龙,李智,苏春翌.基于Bouc-Wen模型的迟滞非线性系统自适应控制[J].系统科学与数学,2014,34(12):1496-1507.Zhao Xinlong,LI Zhi,Su Chunyi.Adaptive Control for Nonlinear System with Hysteresis Based on Bouc-wen Model[J].Journal of System Science and Mathematical Sciences,2014,34(12):1496-1507.
[17]Bhat S P,Bernstein D S.Finite-time Stability of Homogeneous Systems[C]//Proceedings of the American Control Conference.Albuquerque,New Mexico,USA,1997:2513-2514.
[18]马克茂,贺风华,姚郁.目标机动加速度的估计与导引律实现[J].宇航学报,2009,30(6):2213-2219.Ma Kemao,He Fenghua,Yao Yu.Estimation of Target Maneuver Acceleration and Guidance Law Implementation in Homing Terminal Guidance[J].Journal of Astronautics,2009,30(6):2213-2219.
[2]欧进萍.结构振动控制-主动、半主动和智能控制[M].北京:科学出版社,2003.Ou Jinping.Structural Vibration Control-active,Semiactive and Intelligent Control[M].Beijing:Science Press,2003.
[3]李雪峰,汪斌.斜拉桥地震响应线性二次型迭代学习控制(LQILC)研究[J].地震工程与工程振动,2015,35(1):174-182.Li Xuefeng,Wang Bin.Research on Linear Quadratic Iterative Learning Control(LQILC)for Seismic Responses of Cable-stayed Bridge[J].Earthquake engineering and engineering dynamics,2015,35(1):174-182.
[4]高为炳.变结构控制理论[M].北京:中国科学技术出版社,1990.Gao Weibing.Foundation of Variable Structure Control Theory[M].Beijing:China Science and Technology Press,1990.
[5]李春文,苗原,冯元琨,等.非线性系统控制的逆系统方法(I)-单变量控制理论[J].控制与决策,1997,12(5):529-535.Li Chunwen,Miao Yuan,Feng Yuankun,et al.Inverse System Method for Nonlinear Systems Control(I)-Single Variable Control Theory[J].Control and Decision,1997,12(5):529-535.
[6]李春文,苗原,冯元琨,等.非线性系统控制的逆系统方法(II):多变量控制理论[J].控制与决策,1997,12(6):625-630,642.Li Chunwen,Miao Yuan,Feng Yuankun,et al.Inverse System Method for Nonlinear Systems Control(II):Multivariable Control Theory[J].Control and Decision,1997,12(6):625-630,642.
[7]Rosier L.Homogeneous Lyapunov Function for Homogeneous Continuous Vector Field[J].Systems and Control Letters(S0167-6911),1992,19(6):467-473.
[8]Kawski M.Stabilizability and Nilpotent Approximations[C]//Proceedings of the 27th IEEE Conference on Decision and Control,Austin USA,1988,2:1244-1248.
[9]Hermes H.Homogeneous Coordinates and Continuous Asymptotically Stabilizing Feedback Controls[M].Differential Equations:Stability and Control,1991.
[10]马克茂.航天器连续非光滑姿态控制律设计[J].宇航学报,2012,33(6):713-719.Ma Kemao.Design of Non-smooth Attitude Control Laws for Spacecraft[J].Journal of Astronautics,2012,33(6):713-719.
[11]刘慧贤,丁世宏,李世华,等.永磁同步电机位置伺服系统的有限时间控制[J].电机与控制学报,2009,13(3):424-430.Liu Huixian,Ding Shihong,Li Shihua,et al.Finite-time Control of PMSM Position Servo System[J].Electric Machines and Control,2009,13(3):424-430.
[12]王建晖,王清,马克茂.一种永磁同步电机非光滑控制器设计[J].计算机仿真,2016,33(3):227-230+263.Wang Jianhui,Wang Qing,Ma Kemao.Non-smooth Controller Design for Permanent Magnet Synchronous Motors[J].Computer Simulation,2016,33(3):227-230,263.
[13]Yang J N,Li Z,Vongchavalitkul S.Generalization of Optimal Control Theory:Linear and Nonlinear Control[J].Journal of Engineering Mechanics(S0733-9399),1994,120(2):266-283.
[14]An K,Cai G.Discretization of Preisach Hysteresis Model[J].Journal of Central South University(S2095-2899),2015(22):4724-4730.
[15]Su C Y,Wang Q Q,Chen X K,et al.Adaptive Variable Structure Control of a Class of Nonlinear Systems with Unknown Prandtl-Ishlinskii Hysteresis[J].IEEETransactions on Automatic Control(S0018-9286),2005,12(50):2069-2073.
[16]赵新龙,李智,苏春翌.基于Bouc-Wen模型的迟滞非线性系统自适应控制[J].系统科学与数学,2014,34(12):1496-1507.Zhao Xinlong,LI Zhi,Su Chunyi.Adaptive Control for Nonlinear System with Hysteresis Based on Bouc-wen Model[J].Journal of System Science and Mathematical Sciences,2014,34(12):1496-1507.
[17]Bhat S P,Bernstein D S.Finite-time Stability of Homogeneous Systems[C]//Proceedings of the American Control Conference.Albuquerque,New Mexico,USA,1997:2513-2514.
[18]马克茂,贺风华,姚郁.目标机动加速度的估计与导引律实现[J].宇航学报,2009,30(6):2213-2219.Ma Kemao,He Fenghua,Yao Yu.Estimation of Target Maneuver Acceleration and Guidance Law Implementation in Homing Terminal Guidance[J].Journal of Astronautics,2009,30(6):2213-2219.