考虑控制延时影响的相邻建筑结构的离散变结构振动控制方法
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摘要
研究了基于离散变结构控制算法的考虑控制延时影响的相邻建筑结构体系地震反应半主动控制的基本设计和计算方法。首先,建立了相邻结构体系的力学模型及连续运动状态方程,并将其离散化成标准离散状态方程形式。其次,简要地讨论了离散变结构控制器的设计方法,包括切换平面的选择及离散趋近率的构成。最后,应用本文方法对主楼12层,裙房5层的实例结构进行了数值仿真分析,结果表明,该控制方法不仅能有效抑制相邻结构地震反应的鞭梢效应,而且在控制延时存在的情况下,仍能保证系统的减震性能和稳定性。
This paper presents a basically-analytical method for semi-active control of seismic responses of adjacent buildings with time-delay in control based on discrete-time variable structure control algorism. Firstly, not only mechanic model but also continuous state equation of motion are set up, which are also discretized and transformed into standard discrete form. Secondly, the design method of discrete variable structure control is discussed, including selection of discrete switching surface and formation of discrete approach-law reaching condition. Lastly, an earthquake-excited tall building with a 12-story tower structure and a 5-story skirt structure is used to validate the analytical method presented. The results of simulated computation imply that, this control method can significantly reduce the seismic 'whiplash effect' of adjacent-buildings, and even under the presence of time-delay in control, it can ensure system performance and stability.
This paper presents a basically-analytical method for semi-active control of seismic responses of adjacent buildings with time-delay in control based on discrete-time variable structure control algorism. Firstly, not only mechanic model but also continuous state equation of motion are set up, which are also discretized and transformed into standard discrete form. Secondly, the design method of discrete variable structure control is discussed, including selection of discrete switching surface and formation of discrete approach-law reaching condition. Lastly, an earthquake-excited tall building with a 12-story tower structure and a 5-story skirt structure is used to validate the analytical method presented. The results of simulated computation imply that, this control method can significantly reduce the seismic 'whiplash effect' of adjacent-buildings, and even under the presence of time-delay in control, it can ensure system performance and stability.
引文
[1]瞿伟廉,等. ER/MR智能阻尼器耦连的带裙房高层建筑结构地震反应的半主动控制[J].地震工程与工程振动,2000,20(4):88-95.(QU Wei-lian, et al.Semi-active control for seismic responses of tallbuilding with skirt structure[J]. Earthquake Engi-neering and Engineering Vibration,2000,20(4):88-95.(in Chinese))
[2]闫石,等.相临建筑结构的模糊振动控制[J].地震工程与工程振动,2000,20(2):40-43.(YAN Shi,et al. Fuzzy vibration control of adjacent structures[J]. Earthquake Engineering and Engineering Vi-bration,2000,20(2):40-43.(in Chinese))
[3] XU Y L, HE Q, KO J M. Dynamic response ofdamper-connected adjacent buildings under earthqu-ake excitation [J]. Engineering Structures,1999,21:135-148.
[4]高为炳.变结构控制的理论及设计方法[M].北京:科学出版社,1996.(GAO Wei-bing. Variable Struc-ture Control Theory and its Design Method[M]. Bei-jing: Science Press,1996.(in Chinese))
[5]蔡国平,等.建筑结构滑模控制的趋近律方法[J].西安交通大学学报,2000,34(5):95-100.(CAIGuo-ping, et al. Sliding-mode control for buildingstructures[J]. Journal of Xi' an Jiaotong Universi-ty,2000,34(5):95-100.(in Chinese))
[6] CAI Guo-ping, HUANG Jin-zhi. Discrete-time vari-able structure control method for seismic-excitedbuilding structures with time delay in control[J].Earthquake Engng Struct Dyn,2002,31:1347-1359.
[7]赵斌,吕西林.结构振动的离散变结构控制方法[J].振动工程学报,2001,14(1):85-89.(ZHAOBin, LU¨Xi-lin. Discrete variable structure controlmethod for vibration control of building structures[J]. Journal of Vibration Engineering,2001,14(1):85-89.(in Chinese))
[8] YANG J N, AKBARPOUR A, ASKAR G. Effectof time delay on control of seismic-excited buildings[J]. Journal of Engineering Mechanics ASCE,1990,116(10):2801-2814.
[9] YANG J N, WU J C, AGRAWAL A K. Slidingmode control for seismically excited linear structures[J]. Journal of Engineering Mechanics ASCE,1995,121(12):1386-1390.
[10] YANG J N, WU J C, LI Z. Control of seismic-excited buildings using active variable stiffness sys-tems[J]. Engineering Structures,1996,18(8):589-596.
[11] AGRAWAL A K, YANG J N. Compensation oftime-delay for control of civil engineering structures[J]. Earthquake Engng Struct Dyn,2000,29:37-62.
[12]孙增圻.计算机控制理论及应用[M].北京:清华大学出版社,1989.(SUN Zeng-qi. Computer ControlTheory and its Application[M]. Beijing: TsinghuaUniversity Press,1989.(in Chinese))
[13]高为炳.离散时间系统的变结构控制[J].自动化学报,1995,21(2):155-161.(GAO Wei-bing. Variablestructure control of discrete-time systems[J]. ActaAutomatica Sinica,1995,21(2):155-161.(in Chi-nese))
[14]翟长连,吴智铭.不确定离散时间系统的变结构控制设计[J].自动化学报,2000,26(2):185-191.(ZHAI Chang-lian, WU Zhi-ming. Variable stru-cture control design for uncertain discrete time sys-tems [J]. Acta Automatica Sinica,2000,26(2):185-191.(in Chinese))
[15]田宏奇.滑模控制理论及其应用[M].武汉:武汉出版社,1995.(TIAN Hong-qi. Sliding Mode ControlTheory and its Application [M]. Wuhan: WuhanPress,1995.(in Chinese))
[16] MAHOUD M S, AL-MUTHAIRI N F. Design ofrobust controller for time-delay systems[J]. IEEETransaction Automatic Control,1994,39:995-999.
[17] CHEN J, XU D, SHAFAI B. On sufficientconditions for stability independent of delay [J].IEEE Transaction Automatic Control,1995,40:1675-1678.
[18]郑锋,程勉,高为炳.时滞系统的变结构控制及其实现问题[J].控制理论与应用,1994,11(3):294-302.(ZHENG Feng, CHENG Mian, GAO Wei-bing. Variable structure control of time-delay sys-tems and its implementation[J]. Control Theory andApplications,1994,11(3):294-302.(in Chinese))
[19]胡海岩,王在华.非线性时滞动力系统的研究进展[J].力学进展,1999,29(4):502-512.(HU Hai-yan, WANG Zai-hua. Review on nonlinear dynamicsystems involving time delays[J]. Advances in Me-chanics,1999,29(4):502-512.(in Chinese))
[2]闫石,等.相临建筑结构的模糊振动控制[J].地震工程与工程振动,2000,20(2):40-43.(YAN Shi,et al. Fuzzy vibration control of adjacent structures[J]. Earthquake Engineering and Engineering Vi-bration,2000,20(2):40-43.(in Chinese))
[3] XU Y L, HE Q, KO J M. Dynamic response ofdamper-connected adjacent buildings under earthqu-ake excitation [J]. Engineering Structures,1999,21:135-148.
[4]高为炳.变结构控制的理论及设计方法[M].北京:科学出版社,1996.(GAO Wei-bing. Variable Struc-ture Control Theory and its Design Method[M]. Bei-jing: Science Press,1996.(in Chinese))
[5]蔡国平,等.建筑结构滑模控制的趋近律方法[J].西安交通大学学报,2000,34(5):95-100.(CAIGuo-ping, et al. Sliding-mode control for buildingstructures[J]. Journal of Xi' an Jiaotong Universi-ty,2000,34(5):95-100.(in Chinese))
[6] CAI Guo-ping, HUANG Jin-zhi. Discrete-time vari-able structure control method for seismic-excitedbuilding structures with time delay in control[J].Earthquake Engng Struct Dyn,2002,31:1347-1359.
[7]赵斌,吕西林.结构振动的离散变结构控制方法[J].振动工程学报,2001,14(1):85-89.(ZHAOBin, LU¨Xi-lin. Discrete variable structure controlmethod for vibration control of building structures[J]. Journal of Vibration Engineering,2001,14(1):85-89.(in Chinese))
[8] YANG J N, AKBARPOUR A, ASKAR G. Effectof time delay on control of seismic-excited buildings[J]. Journal of Engineering Mechanics ASCE,1990,116(10):2801-2814.
[9] YANG J N, WU J C, AGRAWAL A K. Slidingmode control for seismically excited linear structures[J]. Journal of Engineering Mechanics ASCE,1995,121(12):1386-1390.
[10] YANG J N, WU J C, LI Z. Control of seismic-excited buildings using active variable stiffness sys-tems[J]. Engineering Structures,1996,18(8):589-596.
[11] AGRAWAL A K, YANG J N. Compensation oftime-delay for control of civil engineering structures[J]. Earthquake Engng Struct Dyn,2000,29:37-62.
[12]孙增圻.计算机控制理论及应用[M].北京:清华大学出版社,1989.(SUN Zeng-qi. Computer ControlTheory and its Application[M]. Beijing: TsinghuaUniversity Press,1989.(in Chinese))
[13]高为炳.离散时间系统的变结构控制[J].自动化学报,1995,21(2):155-161.(GAO Wei-bing. Variablestructure control of discrete-time systems[J]. ActaAutomatica Sinica,1995,21(2):155-161.(in Chi-nese))
[14]翟长连,吴智铭.不确定离散时间系统的变结构控制设计[J].自动化学报,2000,26(2):185-191.(ZHAI Chang-lian, WU Zhi-ming. Variable stru-cture control design for uncertain discrete time sys-tems [J]. Acta Automatica Sinica,2000,26(2):185-191.(in Chinese))
[15]田宏奇.滑模控制理论及其应用[M].武汉:武汉出版社,1995.(TIAN Hong-qi. Sliding Mode ControlTheory and its Application [M]. Wuhan: WuhanPress,1995.(in Chinese))
[16] MAHOUD M S, AL-MUTHAIRI N F. Design ofrobust controller for time-delay systems[J]. IEEETransaction Automatic Control,1994,39:995-999.
[17] CHEN J, XU D, SHAFAI B. On sufficientconditions for stability independent of delay [J].IEEE Transaction Automatic Control,1995,40:1675-1678.
[18]郑锋,程勉,高为炳.时滞系统的变结构控制及其实现问题[J].控制理论与应用,1994,11(3):294-302.(ZHENG Feng, CHENG Mian, GAO Wei-bing. Variable structure control of time-delay sys-tems and its implementation[J]. Control Theory andApplications,1994,11(3):294-302.(in Chinese))
[19]胡海岩,王在华.非线性时滞动力系统的研究进展[J].力学进展,1999,29(4):502-512.(HU Hai-yan, WANG Zai-hua. Review on nonlinear dynamicsystems involving time delays[J]. Advances in Me-chanics,1999,29(4):502-512.(in Chinese))
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