Conference PaperPDF Available

An Investigation of the Effects of Structural Nonlinearity on the Performance of Active and Passive Control Systems

Authors:
1
دﺮﮑﻠﻤﻋ ﯽﮕﺘﺴﺑاو ﯽﺑﺎﯾزرا ﻢﺘﺴﯿﺳلﺎﻌﻓﺮﯿﻏ و لﺎﻌﻓ لﺮﺘﻨﮐ يﺎﻫ ﻪﺑ رﺎﺘﻓر
ﺎﻫ هزﺎﺳ ﯽﻄﺧﺮﯿﻏ
نﺎﺧ ﯽﻠﻋﺪﯿﻔﺳ
آ*
، يﺪﻤﺣا يﺪﻬﻣهداز
آ
آ
ناﺮﯾا ،ناﺮﻬﺗ ،،يدازآ نﺎﺑﺎﯿﺧ ﻒﯾﺮﺷ ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧاد، ناﺮﻤﻋ هﺪﮑﺸﻧاد، 11155-11365
*
khansefid@mehr.sharif.ir
هﺪﯿﮑﭼ
ﺑ ردﯿ شوريﺎﻫ هزﺎﺳ لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣﺎﻫﻮﻗ ناﻮﻨﻋ ﻪﺑ لﺎﻌﻓ لﺮﺘﻨﮐ شور ﺎﻣﻮﻤﻋ ،ﺮﺘ اﺮﺑ رﺎﮑﻫاري د رﺎﺘﻓر دﻮﺒﻬﺑﻣﺎﻨﯿ هزﺎ ﻪﺘﺧﺎﻨﺷ ﺎﻫ
.ﺖﺳا هﺪﺷﺎﻣا ﻪﮐ ﺖﺷاد ﻪﺟﻮﺗ ﺪﯾﺎﺑ عﻮﺿﻮﻣ ﻦﯾاهزﺎﺳ رد ﺎﺗﺪﻤﻋيﺎﻫ ﻄﺧ ﺳر تﺎﺒﺛا ﻪﺑﯿهﺪز ،اﺮ دﻮﺟو ﺎﺑﯿﻢﺘﺴﺎﻫي ﻼﻣﺎﮐ رﺎﺘﻓر ،لﺮﺘﻨﮐ
ﻄﺧ ﺎﻈﺘﻧا زا رود حﺮﻃ ﻪﻟﺰﻟز لﺎﻤﻋا نﺎﻣز رد هزﺎﺳﻧ رﯿﺖﺴ. ﻢﺘﯾرﻮﮕﻟا زا يدﺎﯾز داﺪﻌﺗ ﻞﯿﻟد ﻦﯿﻤﻫ ﻪﺑ رﺎﺘﻓر يﺎﻨﺒﻣ ﺮﺑ لﺎﻌﻓ لﺮﺘﻨﮐ يﺎﻫ
ﻪﺘﻓﺎﯾ ﻪﻌﺳﻮﺗ هزﺎﺳ ﯽﻄﺧ.ﺪﻧا ا ﺎﺑ ﻪﻟﺰﻟز لﺎﻤﻋا ﺎﺑ ﻪﮐ ﺖﺳا ﺢﺿاو دﻮﺟوﯽﯾﺎﻫ ﻮﻗيﺮﺗ ﺣاﺮﻃ ﻪﻟﺰﻟز زا، ﻄﺧ رﺎﺘﻓر ضﺮﻓ ﺮﺒﺘﻌﻣ هزﺎﺳ
ﻏ رﺎﺘﻓر و دﻮﺑ ﺪﻫاﻮﺨﻧﯿﻄﺧﺮ ﺚﻋﺎﺑ هزﺎﺳ ﺳ دﻮﺷﯿﻢﺘﺴيﺎﻫ زا لﺮﺘﻨﮐﻈﻨﺗ ﺖﻟﯿ .ﺪﻧﻮﺷ جرﺎﺧ ﯽﻣ ﺖﯿﻌﺿو ﻦﯾا دﻮﺟو ﺮﺛا رد ﺪﻧاﻮﺗ
ور ﻦﯾا زا .ﺪﯾآ دﻮﺟو ﻪﺑ ﺰﯿﻧ هزﺎﺳ تﺎﺼﺨﺸﻣ ﻦﯿﻤﺨﺗ رد ﺎﻄﺧ ﻢﺘﺴﯿﺳ دﺮﮑﻠﻤﻋ ﺮﺑ هزﺎﺳ ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر ﺮﯿﺛﺎﺗ ﺶﻫوﮋﭘ ﻦﯾا رد لﺮﺘﻨﮐ يﺎﻫ
ﯽﺑﺎﯾزرا ﺖﺳا هﺪﺷهزﺎﺳ ياﺮﺑ هﺪﻣآ ﺖﺳد ﻪﺑ ﺞﯾﺎﺘﻧ .هﺪﻨﻫد نﺎﺸﻧ ﻒﻠﺘﺨﻣ يﺎﻫدرﻮﮐر و ﺎﻫ ﯽﮕﺘﺴﺑاو ﺮﺘﺸﯿﺑ ﻢﺘﺴﯿﺳ ﻪﺑ لﺎﻌﻓ لﺮﺘﻨﮐ يﺎﻫ
.ﺖﺳا هزﺎﺳ تﺎﺼﺨﺸﻣ ﺮﯿﯿﻐﺗ ﺘﻧ ردﯿﻪﺠ ﻐﺗ ﺎﺑﯿﯿ ا دورو ﺮﺛا رد تﺎﺼﺨﺸﻣﻪﺑ ﻏ رﺎﺘﻓر هدوﺪﺤﻣﯿﻄﺧﺮ، ﺳ دﺮﮑﻠﻤﻋﯿﻢﺘﺴيﺎﻫ لﺎﻌﻓ لﺮﺘﻨﮐ
ﻄﺧ رﺎﺘﻓر ضﺮﻓ ﺎﺑ ﻪﮐ ﺣاﺮﻃ هزﺎﺳ هﺪﺷﺪﻧا شﻮﺨﺘﺳد ﯿﯿﻐﺗتاﺮ ﺪﺷﺮﺗﺪي ﺳ ﻪﺑ ﺖﺒﺴﻧﯿﻢﺘﺴيﺎﻫ ﯿلﺎﻌﻓﺮ زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ زا هدﺎﻔﺘﺳا ﺎﺑ
ﯽﻣ.دﻮ ﺐﯿﺗﺮﺗ ﻦﯾا ﻪﺑناﻮﺗ ﯽﻣ ﺖﯿﺳﺎﺴﺣﺮﺘﻤﮐ ﻦﯾا ﺘﺴﯿﺳﺎﻫي لﺎﻌﻓﺮﯿﻏ لﺮﺘﻨﮐ ار هزﺎﺳ تﺎﺼﺨﺸﻣ ﻪﺑ ﺖﺒﺴﻧ) ﻖﯾﺮﻃ زا ﺎﻬﻧآ ﺮﯿﯿﻐﺗ و
ﺎﻬﻧآ ﻦﯿﻤﺨﺗ رد ﺎﻄﺧ ﺎﯾ ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر( .ﺖﺴﻧاد لﺎﻌﻓ يﺎﻬﻤﺘﺴﯿﺳ ﺖﺒﺴﻧ لﺎﻌﻓ ﺮﯿﻏ يﺎﻬﻤﺘﺴﯿﺳ ﯽﻠﻤﻋ ﺢﯿﺟﺮﺗ ياﺮﺑ يﺮﮕﯾد قﻮﺸﻣ ﻞﻣﺎﻋ
يﺪﯿﻠﮐ تﺎﻤﻠﮐلﺎﻌﻓ لﺮﺘﻨﮐ :؛ اﺮﯿﻣزﻮﮑﺴﯾو ﺮﮔ؛ ﺲﯾزﺮﺘﺴﯿﻫ ﺮﮔاﺮﯿﻣ؛ هزﺎ .ﯽﻄﺧﺮﯿﻏ
1.
ﻪﻣﺪﻘﻣ
ﻢﺘﺴﯿﺳ ﻻﻮﻤﻌﻣ ﯽﻄﺧ رﺎﺘﻓر ضﺮﻓ ﺎﺑ لﺮﺘﻨﮐ يﺎﻫلﻮﻃ رد هزﺎﺳ تﺪﻣ ﻪﻟﺰﻟز عﻮﻗوﯽﻣ ﯽﺣاﺮﻃﻮﺷ ]1 -4[ﻞﺑﺎﻘﻣ رد و ، ﯽﺗﺎﻌﻟﺎﻄﻣ
ﻪﮐ هزﺎﺳ يور ﺮﻪﺘﻓﺮﮔ مﺎﺠﻧا ﯽﻄﺧﺮﯿﻏ يﺎﻫاﺪﻧﺮﺗدوﺪﺤﻣ رﺎﯿﺴﺑ ﺪﻧ ]5-8[ﻢﺘﺴﯿﺳ دﺮﮑﻠﻤﻋ ﻪﮐ ﺖﺳا ﻦﯾا رد ﻪﯿﺿﺮﻓ ﻦﯾا ﻪﺸﯾر . لﺮﺘﻨﮐ يﺎﻫ
ﯽﻄﺧﺮﯿﻏ ﻪﯿﺣﺎﻧ ﻪﺑ هزﺎﺳ دورو هزﺎﺟا ﻪﮐ ﺖﺳا بﻮﻠﻄﻣ يرﺪﻗ ﻪﺑ ﯽﻤﻧ ارﺪﻫددور ﯽﻤﻧ رﺎﻤﺷ ﻪﺑ ﯽﻘﯿﻗد ضﺮﻓ عﻮﺿﻮﻣ ﻦﯾا ﻪﮐ ﺪﻨﭼﺮﻫ ، اﺮﯾز .
شور سﺎﺳا ﺮﺑدﻮﺟﻮﻣ يﺎﻫ ردهزﺎﺳ ﯽﺣاﺮﻃﺎﻫ ﻪﮐﻪﻣﺎﻧ ﻦﯿﯾآ ردﻒﻠﺘﺨﻣ يﺎﻫ ﺖﺳا هﺪﻣآ ﻪﻟﺰﻟز ﯽﺣاﺮﻃ يوﺮﯿﻧ ،ﯽﻣ لﺎﻤﻋا هزﺎﺳ ﺮﺑ ﻪﮐدﻮﺷ
ﯽﻣ ﻪﺘﻓﺮﮔﺮﻈﻧ رد نآ ﯽﻌﻗاو راﺪﻘﻣ زا ﺮﺘﻤﮐ ﺐﺗاﺮﻣ ﻪﺑهزﺎﺳ ﻪﺑ و دﻮﺷ هداد هزﺎﺟا ﻦﯾا ﯽﻣ دﻮﺷﺎﺗ ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر ﻪﯿﺣﺎﻧ دراوددﺮﮔ ،ﻦﯾاﺮﺑﺎﻨﺑ .
ﻦﯿﻣﻮﺳﻦﯿﺑ ﺲﻧاﺮﻔﻨﮐ تﺎﺷﺎﻌﺗرا و ﮏﯿﺘﺳﻮﮐآ ﯽﻠﻠﻤﻟا- 4 و5 هﺎﻤﯾد1392- ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧادﺳﻮﻃ ﻦﯾﺪﻟاﺮﯿﺼﻧ ﻪﺟاﻮﺧ- ناﺮﻬﺗ- ناﺮﯾا
2
ﻢﺘﺴﯿﺳ دﺮﮑﻠﻤﻋ ﺮﺘﻬﺑ ﯽﺑﺎﯾزرا رﻮﻈﻨﻣ ﻪﺑ ﻪﮐ ﺪﺳر ﯽﻣ ﺮﻈﻧ ﻪﺑﺖﺳا مزﻻ ﺮﮕﯾﺪﮑﯾ ﺮﺑ ﺎﻬﻧآ ﯽﺒﺴﻧ ﺖﯾﺰﻣ و لﺮﺘﻨﮐ يﺎﻫ هزﺎﺳ رﺎﺘﻓرﻪﺑ ﺰﻬﺠﻣ يﺎﻫ
ﻦﯾا ﯿﺳﻢﺘﺴ هزﺎﺳ ﻪﮐ ﯽﺘﻟﺎﺣ رد ﺎﻫ هدوﺪﺤﻣ دراوﯿﻏ رﺎﺘﻓرﻮﺧ ﯽﻄﺧﯽﻣ ددﻮﺷ درﻮﻣﻪﻌﻟﺎﻄﻣ ﮔ راﺮﻗ .دﺮﯿ
ﺶﻫوﮋﭘ ﻦﯾا رد ﻪﮐ ﯽﻋﻮﺿﻮﻣ ﺖﻓﺮﮔ ﺪﻫاﻮﺧ راﺮﻗ ﯽﺳرﺮﺑ درﻮﻣ ﻪﺴﯾﺎﻘﻣﯿﺳ ﺖﯿﺳﺎﺴﺣ ناﺰﯿﻣﻢﺘﺴ ﻪﺑ لﺎﻌﻓ ﺮﯿﻏ و لﺎﻌﻓ لﺮﺘﻨﮐ يﺎ
ﺮﯿﻏ هزﺎﺳ نﺪﺷ ﯽﻄﺧﺖﺳا. ﻪﮑﻨﯾا ﻪﺑ ﻪﺟﻮﺗ ﺎﺑﻢﺘﺴﯿﻦﯿﺑ زا ،لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣ يﺎﻫﻢﺘﺴﯿﺳﻪﺑ ﺖﺒﺴﻧ لﺎﻌﻓ يﺎﻫ ﺮﯾﺎﺳ ﻢﺘﺴﯿﺳ ﯽﮕﺘﺴﺑاو ﺎﻫ
هزﺎﺳ تﺎﺼﺨﺸﻣ ﻪﺑ يﺮﺘﺸﯿﺑﺮﺟ ﻞﯿﺒﻗ زاﺪﻧراد نآ ﯽﺘﺨﺳ و ﯽﯾاﺮﯿﻣ ،مﯽﻣ رﺎﻈﺘﻧا ، دورﻪﭽﻧﺎﻨﭼ ﻦﯾا ﯽﯾارﺎﮐ دﻮﺷ ﯽﻄﺧﺮﯿﻏ ﻪﯿﺣﺎﻧ دراو هزﺎﺳ
ﻢﺘﺴﯿﺳدﺮﯿﯿﻐﺗ شﻮﺨﺘﺳيﺮﺘﺸﯿﺑ تا دﺮﯿﮔ راﺮﻗ. ﻦﯾا تاﺮﯿﯿﻐﺗ ﯿﺳ ﯽﯾارﺎﮐ نﺪﺷ ﮏﯾدﺰﻧ يﺎﻨﻌﻣ ﻪﺑﻢﺘﺴﻢﺘﺴﯿﺳ ﻪﺑ لﺎﻌﻓﺮﯿﻏ يﺎﻫ لﺎﻌﻓ يﺎﻫ
ﺖﺳاهدﺮﺘﺴﮔ هدﺎﻔﺘﺳا ياﺮﺑ يﺮﺘﺸﯿﺑ ﻞﯾﻻد ﺪﻧاﻮﺗ ﯽﻣ ﻪﮐ ،آ زا ﺮﺗ.ﺪﻫد ﺖﺳد ﻪﺑ ﺎﻬﻧ
ردنﺎﯾﺎﭘ ﯿﺳ ﯽﯾارﺎﮐ ناﺰﯿﻣﻢﺘﺴﯽﮔﮋﯾو و ﻒﻠﺘﺨﻣ يﺎﻫيﺎﻫ نآﺎﻫ ﺰﯿﻧ .ﺖﻓﺮﮔ ﺪﻫاﻮﺧ راﺮﻗ ﯽﺳرﺮﺑ درﻮﻣ ﯽﺒﻧﺎﺟ ترﻮﺻ ﻪﺑ ﻞﯿﻧ ﺖﻬﺟ
ﻪﺑ ﻦﯾا هزﺎﺳ لﺪﻣ ﻪﺳ فاﺪﻫاﻪﻋﻮﻤﺠﻣ ﺖﺤﺗ و ﺪﺷ بﺎﺨﺘﻧا ﻒﻠﺘﺨﻣ ياﻪﻟﺰﻟز زا يا ﺮﻄﺧ ﺢﻄﺳ ﺎﺑ ﺎﻫ
1
DBE هزﺎﺳ ﻦﯾا ﺲﭙﺳ .ﺖﻓﺮﮔ راﺮﻗ ﺎﺑ ﺎﻫ
ﻓر ﻪﮑﻨﯾا ضﺮﻓﯽﻣ نﺎﺸﻧ دﻮﺧ زا ﯽﻄﺧ يرﺎﺘ ﻢﺘﯾرﻮﮕﻟا ﺎﺑ لﺎﻌﻓ لﺮﺘﻨﮐ) ﻒﻠﺘﺨﻣ لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ ﻪﺳ ﻪﻠﯿﺳو ﻪﺑ ﺪﻨﻫد
2
LQR زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ ،
هﺪﺷ ﯽﺣاﺮﻃ ﻪﻨﯿﻬﺑ ترﻮﺻ ﻪﺑ و ﻪﻧﺎﮔاﺪﺟ ماﺪﮐ ﺮﻫ ﻪﮐ (ﺲﯾزﺮﺘﺴﯿﻫ ﺮﮔاﺮﯿﻣ و ﺪﻧاموﺎﻘﻣهزﺎﺳ ﻦﯾا ﻪﮑﻨﯾا ضﺮﻓ ﺎﺑ ﻪﻣادا رد .ﺪﺷ يزﺎﺳ يﺎﻫ
ﻄﺧﺮﯿﻏ ِيرﺎﺘﻓر ﺖﯿﻫﺎﻣ ياراد هﺪﺷ ﺰﯿﻬﺠﺗﻪﻟﺰﻟز ضﺮﻌﻣ رد ادﺪﺠﻣ ،ﺪﻨﺷﺎﺑ ﯽ راﺮﻗ ﺮﻈﻧ درﻮﻣ يﺎﻫ ﺪﻨﺘﻓﺮﮔ ﺎﺗﻢﺘﺴﯿﺳ دﺮﮑﻠﻤﻋ ﺮﯿﯿﻐﺗ يﺎﻫ
دﻮﺷ ﯽﺑﺎﯾزرا ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر ﺮﺛا رد لﺮﺘﻨﮐ.
2.
تﺎﻌﻟﺎﻄﻣ ﻪﭽﺨﯾرﺎﺗ
راﺰﺑا يﺮﯿﮔرﺎﮑﺑ لﺮﺘﻨﮐ ردهزﺎﺳﺎﻫﯽﻧاﺮﻤﻋ ي ﯽﻋﻮﺿﻮﻣ ﺎﺘﺒﺴﻧ ﺪﯾﺪﺟ رد ﻪﮐ ﺖﺳا ﺮﯿﺧا ﻪﻫد ﺪﻨﭼ ﻪﺘﻓﺮﮔ راﺮﻗ ﻪﺟﻮﺗ درﻮﻣ ﺖﺳا . رد
تﺪﻣ ﻦﯿﻤﻫ ﺰﯿﻧ هﺎﺗﻮ ﺖﻓﺮﺸﯿﭘا ﻦﯾا ﻪﺟﻮﺗ ﻞﺑﺎﻗ ﻪﺘﮑﻧ ﺎﻣا ،ﺖﺳا هﺪﺷ ﻞﺻﺎﺣ ﻪﻨﯿﻣز ﻦﯾا رد ﯽﻬﺟﻮﺗ ﻞﺑﺎﻗ رﺎﯿﺴﺑ يﺎﻫ تﺎﻌﻟﺎﻄﻣ هﺪﻤﻋ ﻪﮐ ﺖﺳ
ﻪﺘﻓﺮﮔ ترﻮﺻ هزﺎﺳ ﻪﺑ طﻮﺑﺮﻣﺘﻓر صاﻮﺧ ﺎﺑ ﯽﯾﺎﻫﺖﺳا هدﻮﺑ ﯽﻄﺧ يرﺎ ]1-4[ ﺶﺨﺑ ﻦﯾا رد . ﯽﺗﺎﻌﻟﺎﻄﻣ زا ﯽﺧﺮﺑﺮﻤﺗ ﻪﮐﺮﺑ ﺎﻬﻧآ ﺰﮐ يور
هزﺎﺳﻪﺴﯾﺎﻘﻣ ﺎﯾ و هدﻮﺑ ﯽﻄﺧﺮﯿﻏ يﺎﻫ ياﺎﻣﻢﺘﺴﯿﺳ ﻦﯿﺑآ رد هزﺎﺳ لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣ يﺎﻫ ترﻮﺻ ﺎﻬﻪﺘﻓﺮﮔ ﺖﺳا .ﺪﺷ ﺪﻫاﻮﺧ روﺮﻣ ،
لﺎﺳ رد1992 نﺎﯿﺗ و ﮓﻨﭼ]5[ لﺎﻌﻓ لﺮﺘﻨﮐ ﻢﺘﯾرﻮﮕﻟا ﻪﻌﺳﻮﺗ و ﻂﺴﺑ ﻪﺑLQR ﺮﯿﻏ ﻪﺑ ﯽﻄﺧ هزﺎﺳ زا .ﺪﻨﺘﺧادﺮﭘ ﯽﻄﺧ رد
ﺶﻧارﺎﮑﻤﻫ و اﺪﻤﯿﺷ لﺎﺳ ﻦﯿﻤﻫ]8[ ﻢﺘﺴﯿﺳ ﻪﺴﯾﺎﻘﻣهزﺎﺳ رد لﺎﻌﻓ و لﺎﻌﻓ ﻪﻤﯿﻧ ،لﺎﻌﻓﺮﯿﻏ لﺮﺘﻨﮐ يﺎﻫ ﯽﻄﺧﺮﯿﻏ يﺎﻫﺪﻧدﺮﮐ ﯽﺳرﺮﺑ ار .
ﺶﻧارﺎﮑﻤﻫ و ﮓﻨﯾ]7[ ﻢﺘﺴﯿﺳ ﻪﻌﻟﺎﻄﻣ ﻪﺑ لﺎﺳ ﻦﯿﻤﻫ رد ﺰﯿﻧهزﺎﺳ رد نآ بﻮﻠﻄﻣ دﺮﮑﻠﻤﻋ و ﺪﻨﺘﺧادﺮﭘ ﯽﺒﯿﮐﺮﺗ لﺮﺘﻨﮐ يﺎﻫ ﯽﻄﺧﺮﯿﻏ يﺎﻫ
.ﺪﻧداد نﺎﺸﻧ ار يﺪﻤﺣا هداز]1[ لﺎﺳ رد2006 ﻪﺑصﻮﺼﺧ رد ﺚﺤﺑ و ﯽﻓﺮﻌﻣ ﻢﺘﺴﯿﺳ لدﺎﻌﻣ لﺎﻌﻓﺮﯿﻏ يﺎﻫ ﺎﺑﯿﺳﻢﺘﺴ يﺎﻫﻪﻤﯿﻧ لﺎﻌﻓ
داد نﺎﺸﻧ ،ﻪﺘﺧادﺮﭘ هزﺎﺳ رد ﻪﮐﯽﻄﺧ يﺎﻫ، لدﺎﻌﻣ ﻢﺘﺴﯿﺳ، ﮑﯾدﺰﻧ رﺎﯿﺴﺑ يدﺮﮑﻠﻤﻋﻪﻤﯿﻧ ﻢﺘﺴﯿﺳ ﻪﺑ ﯽ لﺎﺳ رد .دراد لﺎﻌﻓ2009 ورﻼﯿﻤﯿﺳ
ﻧارﺎﮑﻤﻫ و]6[ رﺎﮐ ﻦﯾا ار ﺮﮕﯾد عﻮﻧ ﻪﺑي هزﺎﺳ يور ﺮﺑ مﺎﺠﻧا ﯽﻄﺧﺮﯿﻏ يﺎﻫاددﺪﻧ ﺣاﺮﻃ ياﺮﺑ ﯽﺷور نآ رد وﻢﺘﺴﯿﺳ لﺎﻌﻓﺮﯿﻏ يﺎﻫ
هزﺎﺳ رد لﺎﻌﻓ ﻢﺘﺴﯿﺳ ﺎﺑ لدﺎﻌﻣ دﺎﻬﻨﺸﯿﭘ ﯽﻄﺧﺮﯿﻏ و ﯽﻄﺧ يﺎﻫﺪﻧدﺮﮐ .
ﺖﯿﻌﻣﺎﺟ زا قﻮﻓ تﺎﻌﻟﺎﻄﻣ زا ﮏﯾ ﭻﯿﻫ ﺖﺳا ﺺﺨﺸﻣ ﻪﮑﻧﺎﻨﭽﻧآمزﻻ ﻠﻤﻋ ﺮﺑ هزﺎﺳ ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر ﺮﯿﺛﺎﺗ ﯽﺳرﺮﺑ ردﻢﺘﺴﯿﺳ دﺮﮑ يﺎﻫ
لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣ يﺎﻬﺘﻟﺎﺣ رد ﺎﻬﻧآ ﻪﺴﯾﺎﻘﻣ و رادرﻮﺧﺮﺑﺪﻨﺘﺴﯿﻧور ﻦﯾا زا . نوﺪﻣ ﯽﺗرﻮﺻ ﻪﺑ عﻮﺿﻮﻣ ﻦﯾا ﺎﺗ ﺖﺳا هﺪﺷ ﯽﻌﺳ ﻪﻌﻟﺎﻄﻣ ﻦﯾا رد
ﻢﺘﺴﯿﺳ يﺮﯾﺬﭘ ﺮﯿﺛﺎﺗ ﻪﻨﯿﻣز رد ﯽﻠﮐ هﺪﯾا ﮏﯾ ﺎﺗ دﺮﯿﮔ راﺮﻗ ﯽﺳرﺮﺑ درﻮﻣ.ﺪﯾآ ﺖﺳد ﻪﺑ هزﺎﺳ تﺎﺼﺨﺸﻣ ﺮﯿﯿﻐﺗ زا لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣ يﺎﻫ
3.
لﺪﻣيزﺎﺳ
ردﻢﺘﺴﯿﺳ دﺮﮑﻠﻤﻋ ﯽﺳرﺮﺑ رﻮﻈﻨﻣ ﻪﺑ ﺶﻫوﮋﭘ ﻦﯾانﺎﻤﺘﺧﺎﺳ رد لﺮﺘﻨﮐ يﺎﻫعﺎﻔﺗرا ﺎﺑ ﯽﯾﺎﻫ نﺎﻤﺘﺧﺎﺳ ﻪﺳ ،توﺎﻔﺘﻣ يﺎﻫ5 ،10 و
15 يدﻻﻮﻓ ﻪﻘﺒﻃ هزﺎﺳ ﻢﺘﺴﯿﺳ ﺎﺑ)(ﻂﺳﻮﺘﻣ ﯽﺸﻤﺧ بﺎﻗ يا نﺎﻤﺘﺧﺎﺳ ﻦﯾا .ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ ﺮﻈﻧ ﺪﻣ ﺮﺑ ﺎﻫ سﺎﺳا ﻂﺑاﻮﺿﻪﻣﺎﻧ ﻦﯿﯾآ 2800
]9[ ثﺎﺤﺒﻣ ،6 و10 نﺎﻤﺘﺧﺎﺳ ﯽﻠﻣ تارﺮﻘﻣ]10 ,11[ هﺪﺷ ﯽﺣاﺮﻃ .ﺪﻧا
ﻦﯾانﺎﻤﺘﺧﺎﺳ ترﻮﺻ ﻪﺑ ﯽﮕﻤﻫ ﺎﻫ3 هﺪﺷ ﯽﺣاﺮﻃ يﺪﻌﺑبﺎﻗ زا ماﺪﮐ ﺮﻫ .ﺪﻧا ﻪﻧﺎﻫد ﻪﺳ ياراد نﺎﻤﺘﺧﺎﺳ يﺎﻫ5 يﺮﺘﻣ .ﺪﻨﺘﺴﻫ
تﺎﻘﺒﻃ عﺎﻔﺗرا ﺰﯿﻧ ﺮﺑاﺮﺑ5/3 ﺮﺘﻣﺖﺳابﺎﻗ زا ﯽﮑﯾ يﺪﻌﺑ تﺎﻌﻟﺎﻄﻣ مﺎﺠﻧا رﻮﻈﻨﻣ ﻪﺑ يﺪﻌﺑ ﻪﺳ نﺎﻤﺘﺧﺎﺳ حﺮﻃ زا ﺲﭘ . نﺎﻤﺘﺧﺎﺳ يﺎﻫ
1 Designed Based Earthquake
2 Linear Quadratic Regulator
ﻦﯿﻣﻮﺳﻦﯿﺑ ﺲﻧاﺮﻔﻨﮐ تﺎﺷﺎﻌﺗرا و ﮏﯿﺘﺳﻮﮐآ ﯽﻠﻠﻤﻟا- 4 و5 هﺎﻤﯾد1392- ﯽﺳﻮﻃ ﻦﯾﺪﻟاﺮﯿﺼﻧ ﻪﺟاﻮﺧ ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧاد- ناﺮﻬﺗ- ناﺮﯾا
3
ﻌﻟﺎﻄﻣ ﻪﻣادا و بﺎﺨﺘﻧا تﺎ ﺮﺑ يور نآ مﺎﺠﻧاﺪﺷلﺪﻣ ﻦﯾا رد .بﺎﻗ تﻻﺎﺼﺗا ﻪﮐ ﺖﺳا هﺪﺷ ضﺮﻓ يزﺎﺳ ﻞﻤﻋ ﺐﻠﺻ ترﻮﺻ ﻪﺑ ﯽﮕﻤﻫ ﺎﻫ
ﯽﻣ نﺎﺸﻧ دﻮﺧ زا ﯽﺷﺮﺑ يرﺎﺘﻓر هزﺎﺳ و ﺪﻨﻨﮐﯽﻣ .ﺪﻫد
لوﺪﺟ1بﺎﻗ ﯽﻠﺻا تﺎﺼﺨﺸﻣ .ﯽﻧﺎﻤﺘﺧﺎﺳ يﺎﻫ ﻪﺑﺎﺟ و ﯽﺘﺨﺳ ،مﺮﺟ ﻞﻣﺎﺷتﺎﻘﺒﻃ ﻢﯿﻠﺴﺗ ﯽﯾﺎﺟ
تﺎﻘﺒﻃ
ﺘﺧﺎﺳ
نﺎﻤ
5
ﻪﻘﺒﻃ
نﺎﻤﺘﺧﺎﺳ
10
ﻪﻘﺒﻃ
نﺎﻤﺘﺧﺎﺳ
ﻪﻘﺒﻃ
مﺮﺟ
(ton)
ﯽﺘﺨﺳ
(KN/mm)
ﻪﺑﺎﺟ ﯽﯾﺎﺟ
ﻢﯿﻠﺴﺗ
(mm)
مﺮﺟ
(ton)
ﯽﺘﺨﺳ
(KN/mm)
ﻪﺑﺎﺟﯽﯾﺎﺟ
ﻢﯿﻠﺴﺗ
(mm)
مﺮﺟ
(ton)
ﯽﺘﺨﺳ
(KN/mm)
ﻪﺑﺎﺟ ﯽﯾﺎﺟ
ﻢﯿﻠﺴﺗ
(mm)
1 53.2 26.02 13 55.1 80.40 9 66.1 292.79 3
2 51.9 17.42 19 52.7 50.82 14 57.6 139.86 7
3 51.2 12.37 27 52.5 48.51 15 57.1 116.22 8
4 50.9 6.95 49 52.5 45.91 15 57.3 110.86 8
5 50.8 6.58 51 51.4 30.77 14 57.3 110.19 8
6 ___ ___ ___ 51.4 26.92 16 57.2 106.39 9
7 ___ ___ ___ 50.8 21.70 20 56.4 91.62 10
8 ___ ___ ___ 50.5 15.61 28 55.9 86.86 11
9 ___ ___ ___ 50.3 11.23 39 55.6 78.89 12
10 ___ ___ ___ 50.3 10.65 41 55.1 68.97 13
11 ___ ___ ___ ___ ___ ___ 54.3 46.79 20
12 ___ ___ ___ ___ ___ ___ 54.2 39.08 18
13 ___ ___ ___ ___ ___ ___ 53.3 24.41 29
14 ___ ___ ___ ___ ___ ___ 53.3 23.15 30
15 ___ ___ ___ ___ ___ ___ 53.3 22.24 32
ﻦﯿﯾآ رد جرﺪﻨﻣ شور زا تﺎﻘﺒﻃ ﯽﺘﺨﺳ ﻪﺒﺳﺎﺤﻣ رد ﻪﻣﺎﻧ2800 ]9[ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺰﯿﻧ تﺎﻘﺒﻃ ﻢﯿﻠﺴﺗ ﺖﯿﻓﺮﻇ .ﺖﺳا هﺪﺷ هدﺎﻔﺘﺳا
يﻮﻗ نﻮﺘﺳ دﺮﮑﻠﻤﻋ مﺰﯿﻧﺎﮑﻣ- ﻪﺒﺳﺎﺤﻣ ﻒﯿﻌﺿ ﺮﯿﺗﺪﯾدﺮﮔ .ﺖﺳا ه رد ﺖﯾﺎﻬﻧياﺮﺑ ﻪﺒﺳﺎﺤﻣﻢﺘﺴﯿﺳ ﯽﺗاذ ﯽﯾاﺮﯿﻣ ﯽﻠﯾار شور
1
]12[ درﻮﻣ
ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ هدﺎﻔﺘﺳا، ضﺮﻓ رﻮﻈﻨﻣ ﻦﯾا ﻪﺑﯽﯾاﺮﯿﻣ ﺖﺒﺴﻧ ﻪﮐ ﺖﺳا هﺪ
2
ﺮﺑاﺮﺑ هزﺎﺳ مﻮﺳ و لوا يﺎﻫدﻮﻣ05/0 .ﺪﺷﺎﺑ
3,1 لﺪﻣ رﺎﺘﻓرﯽﻄﺧﺮﯿﻏ كﻮﺑ -نو
3
ﺪﺷ ﺮﮐذ ﻪﮐ رﻮﻄﻧﺎﻤﻫ ﻢﺘﺴﯿﺳ ﯽﯾارﺎﮐ رد نﺪﺷ ﯽﻄﺧﺮﯿﻏ زا ﯽﺷﺎﻧ تاﺮﺛا ﯽﺳرﺮﺑ ﺶﻫوﮋﭘ ﻦﯾا ﯽﻠﺻا فﺪﻫ ﻦﯾا زا ،ﺖﺳا لﺮﺘﻨﮐ يﺎﻫ
ﯽﺘﺴﯾﺎﺑ وروﺮﯿﻧ ﻪﻄﺑار ياﺮﺑ ﯽﻄﺧﺮﯿﻏ لﺪﻣ - هزﺎﺳ ﻪﮑﻨﯾا ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ .دﻮﺷ ﻪﺋارا هزﺎﺳ نﺎﮑﻣﺮﯿﯿﻐﺗ ﺖﻠﮑﺳا عﻮﻧ زا ﯽﺳرﺮﺑ درﻮيﺎﻫ
يدﻻﻮﻓﺪﻨﺘﺴﻫ ﻢﺘﺴﯿﺳ عﻮﻧ ﻦﯾا وﻪﺧﺮﭼ ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر ياراد ﺎﻫيااﺪﻧكﻮﺑ ﯽﻄﺧﺮﯿﻏ لﺪﻣ زا ،- نو ]13[ ﯽﻣ هدﺎﻔﺘﺳا لﺪﻣ ﻦﯾا رد .دﻮﺷ
ياﺮﺑ ﺮﺛا ﻦﺘﻓﺮﮔ ﺮﻈﻧ ردتا .دﻮﺷ ﻞﺣ ﻪﻈﺤﻟ ﺮﻫ رد ﻢﺘﺴﯿﺳ ﺖﻋﺮﺳ ﻪﺑ ﻪﺘﺴﺑاو ﯽﻠﯿﺴﻧاﺮﻔﯾد ﻪﻟدﺎﻌﻣ ﯽﺘﺴﯾﺎﺑ ﯽﻄﺧﺮﯿﻏ
)
1
(
( ) ( ) ( ) ( ) ( )
h d g
mx t cx t F t F t mx t
 
 
)
2
(
( ) ( ) ( ), ( ) ( ), ( ) (1 ) ( )
h he hp he hp
F t F t F t F t kx t F t kz t
 
 
ر رد ﻪﮐاﻄﺑ
)1(
m
،
c
،
h
F
،
d
F
،
x
،
x
و
g
x
ﯿﺗﺮﺗ ﻪﺑ لدﺎﻌﻣادزﺎﺑ يوﺮﯿﻧ ،ﯽﯾاﺮﯿﻣ ،مﺮﺟرﻪﺑﺎﺟ ،لﺮﺘﻨﮐ هﺎﮕﺘﺳد يوﺮﯿﻧ ،هﺪﻧ ﯽﯾﺎﺟ
ﻦﯿﻣز بﺎﺘﺷ و ﻢﺘﺴﯿﺳ ﺖﻋﺮﺳ ،ﻢﺘﺴﯿﺳﺪﻨﺘﺴﻫ ﻪﻄﺑار رد .
)2(
يﺎﻫﺮﺘﻣارﺎﭘ ﺰﯿﻧ
he
F
،
hp
F
،
α
وz ترﺎﺒﻋ ﺐﯿﺗﺮﺗ ﻪﺑ ﯽﻄﺧ ﺶﺨﺑ :زا ﺪﻧاوﺮﯿﻧ
1 Rayleigh
2 Damping Ratio
3 Bouc- Wen
ﻦﯿﻣﻮﺳﻦﯿﺑ ﺲﻧاﺮﻔﻨﮐ تﺎﺷﺎﻌﺗرا و ﮏﯿﺘﺳﻮﮐآ ﯽﻠﻠﻤﻟا- 4 و5 هﺎﻤﯾد1392- ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧادﺳﻮﻃ ﻦﯾﺪﻟاﺮﯿﺼﻧ ﻪﺟاﻮﺧ- ناﺮﻬﺗ- ناﺮﯾا
4
يﺮﯿﻤﺧ ﯽﺘﺨﺳ ﺖﺒﺴﻧ ،هﺪﻧرادزﺎﺑ يوﺮﯿﻧ ﯽﻄﺧﺮﯿﻏ ﺶﺨﺑ ،هﺪﻧرادزﺎﺑ
1
ﯽﻋﺎﺠﺗرا ﯽﺘﺨﺳ ﻪﺑ
2
كﻮﺑ ﺮﯿﻐﺘﻣ و هزﺎﺳ- .نو
ﻞﮑﺷ1ﻮﻤﻧ .وﺮﯿﻧ راد- كﻮﺑ ﯽﻄﺧﺮﯿﻏ لﺪﻣ ﭗﯿﺗ نﺎﮑﻣﺮﯿﯿﻐﺗ - نو]13[
كﻮﺑ ﺮﯿﻐﺘﻣ-ﯿﺴﻧاﺮﻔﯾد ﻪﻟدﺎﻌﻣ ﻞﺣ زا نو ﯽﻣ ﺖﺳﺪﺑ ﺖﺳا ﻪﺘﺴﺑاو ﻢﺘﺴﯿﺳ ﺖﻋﺮﺳ ﻪﺑ ﻪﮐ ﺮﯾز :ﺪﯾآ
)3(
1
1
( ) ( ( ) | ( ) | . | ( ) | ( ) ( ) | ( ) | )
n n
y
z t Ax t x t z t z t x t z t
U
 
 
 
رد ﻪﮐ ﻪﻄﺑار
)3(
y
U
ﻪﺑﺎﺟﯽﻣ ﻪﻘﺒﻃ ﻢﯿﻠﺴﺗ ﯽﯾﺎﺟﯿﻨﭽﻤﻫ .ﺪﺷﺎﺑ
A
،
،
كﻮﺑ ﻪﻟدﺎﻌﻣ ﺐﯾاﺮﺿ- نو ﻞﮑﺷ هﺪﻨﻨﮐ ﻦﯿﯿﻌﺗ ﻪﮐ ﺪﻨﺘﺴﻫ
رادﻮﻤﻧ ﺘﺴﻫﺪﻨناﻮﺗ . n
ﺰﯿﻧ
ﻤﻧ يﺰﯿﺗ ناﺰﯿﻣ هﺪﻨﻨﮐ ﻦﯿﯿﻌﺗ يﺮﯿﻤﺧ ﻪﺑ ﯽﻋﺎﺠﺗرا زا رﺎﺘﻓر ﺖﯿﻫﺎﻣ ﺮﯿﯿﻐﺗ ﻪﯿﺣﺎﻧ رد رادﺖﺳا
.
ﺶﻫوﮋﭘ ﻦﯾا رد
ﺐﯾﺮﺿ ﻪﺒﺳﺎﺤﻣ ﺖﻬﺟα ﯽﺸﻧار ﺰﯿﻟﺎﻧآ
3
ﺮﺑ هزﺎﺳ يورهزﺎﺳ ياﺮﺑ نآ سﺎﺳا ﺮﺑ و ﺖﺳا ﻪﺘﻓﺮﮔ مﺎﺠﻧا ﺎﻫ يﺎﻫ5 ،10 و15 ﺮﺑاﺮﺑ ﺐﯿﺗﺮﺗ ﻪﺑ ﻪﻘﺒﻃ
26/0 ،17/0 و27/0 ﺐﯾاﺮﺿ .ﺪﺷ ﻪﺒﺳﺎﺤﻣ
A
،
،
ﺮﺑاﺮﺑ ﺐﯿﺗﺮﺗ ﻪﺑ ﺰﯿﻧ1 ،5/0 و5/0 هﺪﺷ دﺎﺨﺗا .ﺪﻧا
3,2 هدﺎﻔﺘﺳا درﻮﻣ ﻪﻟﺰﻟز
زا هزﺎﺳ يور ﺮﺑ ﻪﻟﺰﻟز يراﺬﮔرﺎﺑ لﺎﻤﻋا ﺖﻬﺟ5 % ﺖﺷﺬﮔاﺮﻓ لﺎﻤﺘﺣا ﺎﺑ ﻪﻟﺰﻟز10 رد50 هدﺎﻔﺘﺳا (حﺮﻃ ﻪﻟﺰﻟز) لﺎﺳ ﻦﯾا ﻪﺑ .ﺖﺳا هﺪﺷ
رﻮﻈﻨﻣ يداﺪﻌﺗدرﻮﮐر زايﺎﻫ هژوﺮﭘ هوﺮﮔ ﻂﺳﻮﺗ هﺪﺷ ﻪﯿﺻﻮﺗSAC ]14[، هزﺎﺳ ﯽﺣاﺮﻃ رد هدﺎﻔﺘﺳا ﺖﻬﺟيدﻻﻮﻓ يﺎﻫ، ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد
هﺪﺷﺪﻧاﮐر ﻦﯾا .درﺎﻫ رد ﻊﻗاوهﺪﺷ ﺶﯾاﺮﯾو ﻪﺨﺴﻧيا ﺴﻧ زادرﻮﮐر ﯽﻠﺻا ﻪﺨرﻮﮐﺬﻣ يﺎﻫ ﻪﮐ يﻮﺤﻧ ﻪﺑ ﺪﻨﺘﺴﻫﻮﺘﺤﻣ ﺮﻈﻧ زاا ﯽﺴﻧﺎﮐﺮﻓ ي
عﻮﻧ كﺎﺧ ﺎﺑ ﻖﺒﻄﻨﻣ
d
S ﻦﯿﯾآﻪﻣﺎ
4
ASCE ﭗﯿﺗ كﺎﺧ)3 ﻪﻣﺎﻧ ﻦﯿﯾآ2800 (ﺷﺎﺑدرﻮﮐر ﻦﯾا ،ﻦﯾاﺮﺑ هوﻼﻋ .ﺪﺎﻫ ﻪﻧﻮﮔ ﻪﺑ سﺎﯿﻘﻣ يا
هﺪﺷ ﺪﻧا ﯽﺣاﺮﻃ دراﺪﻧﺎﺘﺳا ﻒﯿﻃ ﺎﺑ ﻖﺒﻄﻨﻣ ﻪﮐASCE ﺲﻟ ﻪﻘﻄﻨﻣ ياﺮﺑ ﺲﻠﺠﻧآﺷﺎﺑ.ﺪ
لوﺪﺟ2ﻪﻟﺰﻟز تﺎﺼﺨﺸﻣ .هدﺎﻔﺘﺳا درﻮﻣ يﺎﻫ
PGA(g) )ماود نﺎﻣز تﺪﻣs( ﺎﮔرﺰﺑ هﺎﮕﺘﺴﯾا داﺪﺧر هژوﺮﭘ ﺲﯾﺪﻧاSAC ﻒﯾدر
0.675
39.38 6.9 Elcentro Imperial Valey,1940 L.A.02 1
0.478 39.38 6.5 Array #05 Imperial Valey,1979 L.A.04 2
0.417 79.98 7.3 Barstow Landers,1992 L.A.08 3
0.969 39.98 7.0 Gilroy Loma Prieta,1989 L.A.12 4
0.580 14.95 6.7 Rinaldi RS Northridge,1994 L.A.16 5
3,3 ﻢﺘﺴﯿﺳهدﺎﻔﺘﺳا درﻮﻣ لﺮﺘﻨﮐ يﺎﻫ
هدﺎﻔﺘﺳا لﺎﻌﻓ و لﺎﻌﻓﺮﯿﻏ لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣ ﻢﺘﺴﯿﺳ عﻮﻧ ود زا ﻖﯿﻘﺤﺗ ﻦﯾا ردﯽﻣ ﻢﺘﯾرﻮﮕﻟا زا لﺎﻌﻓ لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ درﻮﻣ رد .دﻮﺷ
LQR ﻪﺘﻓﺮﮔ هﺮﻬﺑﺖﺳا هﺪﺷ ﻢﺘﺴﯿﺳ ﻦﯿﺑ زا وي ﻌﻓﺮﯿﻏلﺎ ﺰﯿﻧ ﮑﺴﯾو ﺮﮔاﺮﯿﻣ هﺎﮕﺘﺳد عﻮﻧ ودﯽﻣ هدﺎﻔﺘﺳا ﺲﯾزﺮﺘﺴﯿﻫ ﺮﮔاﺮﯿﻣ و زﻮﻮﺷ .ﺪ
1 Plastic Stiffness
2 Elastic Stiffness
3 Push-Over Analysis
4 American Society of Civil Engineering
ﻦﯿﻣﻮﺳﻦﯿﺑ ﺲﻧاﺮﻔﻨﮐ تﺎﺷﺎﻌﺗرا و ﮏﯿﺘﺳﻮﮐآ ﯽﻠﻠﻤﻟا- 4 و5 هﺎﻤﯾد1392- ﯽﺳﻮﻃ ﻦﯾﺪﻟاﺮﯿﺼﻧ ﻪﺟاﻮﺧ ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧاد- ناﺮﻬﺗ- ناﺮﯾا
5
ﻢﺘﯾرﻮﮔا ردLQR، شور ﻦﯿﺑ رد ﺧﺎﺷ ﻢﺘﯾرﻮﮕﻟا ﮏﯾ ناﻮﻨﻋ ﻪﺑ ﻪﮐ يوﺮﯿﻧ ،ﺖﺳا حﺮﻄﻣ لﺎﻌﻓ لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣ يﺎﻫ لﺮﺘﻨﮐ
سﺎﺳاﺮﺑ ﻊﺑﺎﺗ ندﺮﮐ ﻪﻨﯿﻤﮐﺮﯾز ﯽﻣ ﺖﺳﺪﺑﺪﯾآ ]15[ .
)4(
0
[ ( ) ( ) ( ) ( )]
t
T T
J Z t QZ t U t RU t dt
 
ﻪﻄﺑار رد ﻪﮐ )4( Z رادﺮﺑnx1 ﻪﺑﺎﺟ زا ﻞﮑﺸﺘﻣ ﯽﯾﺎﺟ ﻢﺘﺴﯿﺳ ﺖﻋﺮﺳ وﺖﺳا .U ﺰﯿﻧﺎﻫراﺰﺑا لﺮﺘﻨﮐ يوﺮﯿﻧ رادﺮﺑ ،t يراﺬﮔرﺎﺑ نﺎﻣز تﺪﻣ و
R وQ ﻢﺘﺴﯿﺳ ﺦﺳﺎﭘ و لﺮﺘﻨﮐ يوﺮﯿﻧ ﯽﻧزو ﺐﯾاﺮﺿ ﺲﯾﺮﺗﺎﻣ ﺐﯿﺗﺮﺗ ﻪﺑ ﻢﻫﺪﻨﺘﺴﻫ . ﯽﻔﻠﺘﺨﻣ ﺮﯾدﺎﻘﻣ ﯽﺘﺴﯾﺎﺑ ﻪﻨﯿﻬﺑ حﺮﻃ ﻦﯿﯿﻌﺗ رﻮﻈﻨﻣ ﻪﺑ
ﺲﯾﺮﺗﺎﻣ ﻦﯾا زاﺪﻧﻮﺷ ﯽﺳرﺮﺑ ﯽﻧزو يﺎﻫ، ﺎﺘﺳار ﻦﯿﻤﻫ ردﺲﯾﺮﺗﺎﻣﯾز ترﻮﺻ ﻪﺑ ﺎﻫهﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد ﺮ.ﺪﻧا
)5(
n n
R I
)
6
(
10B
n n
Q I
ﻪﮐI ﯽﻣ ﻪﮑﯾ ﺲﯾﺮﺗﺎﻣ.ﺪﺷﺎﺑ ﻔﻠﺘﺨﻣ ﺮﯾاﺪﻘﻣ ﻪﻨﯿﻬﺑ حﺮﻃ ﻦﯿﯿﻌﺗ ﺖﻬﺟ ناﻮﺗ زاB ﯽﻣ ﯽﺳرﺮﺑ .ددﺮﻢﻬﻣ ﻪﺘﮑﻧ ﻢﺘﺴﯿﺳ ﯽﺣاﺮﻃ ردLQR
هزﺎﺳ ردﺧﺮﯿﻏ يﺎﻫ ﯽﻄﺖﺳا ﻦﯾا هزﺎﺳ ﻦﯾا رد ﻪﮐ فﺪﻫ ﻊﺑﺎﺗ يزﺎﺳ ﻪﻨﯿﻬﺑ ﺪﻨﯾآﺮﻓ ﯽﺘﺴﯾﺎﺑ ﺎﻫJ هزﺎﺳ تﺎﺼﺨﺸﻣ يازا ﻪﺑ و نﺎﻣز ﺮﻫ رد
،دﺮﯾﺬﭘ ترﻮﺻ ﻪﻈﺤﻟ نﺎﻤﻫ رد (ﯽﺘﺨﺳ)ﻪﮐ ﯽﻟﺎﺣ رد نﺎﻣز رﺎﯿﺴﺑ ﯽﻋﻮﺿﻮﻣ ﺮﻣا ﻦﯾاﻪﻧﺎﯾار ﺎﺑ و ﺖﺳا ﺮﺑزوﺮﻣا يﺎﻫي رﺎﯿﺴﺑ رﺎﮐ ﻦﯾا مﺎﺠﻧا
ﻦﯿﻨﭽﻤﻫ .ﺖﺳا راﻮﺷد تﺎﺼﺨﺸﻣ ﻂﺧﺮﺑ ﯽﻧﺎﺳرزوﺮﺑ هزﺎ ﯽﻧﺎﻣز ﺮﯿﺧﺎﺗ هﺪﯾﺪﭘ دﺎﺠﯾا ﻪﺑ ﺮﺠﻨﻣ
1
ﻢﺘﺴﯿﺳ رد ﯽﻣ ﺶﻫﺎﮐ ﻪﺑ دﻮﺧ ﻪﮐ دﻮﺷ
نآ ﯽﯾارﺎﮐ ﺢﻄﺳ ﺮﺠﻨﻣﯽﻣﯽﻣ ضﺮﻓ ﺶﻫوﮋﭘ ﻦﯾا رد ﻦﯾاﺮﺑﺎﻨﺑ .دﻮﺷدﻮﺷ فﺪﻫ ﻊﺑﺎﺗ ،ﯽﻄﺧ هزﺎﺳ ﯽﺘﺨﺳ ﺲﯾﺮﺗﺎﻣ يازا ﻪﺑ و رﺎﺑ ﮏﯾ ﺎﻬﻨﺗ ﻪﮐ
J لﺮﺘﻨﮐ هﺮﻬﺑ ﺲﯾﺮﺗﺎﻣ سﺎﺳاﺮﺑ و دﻮﺷ ﻪﻨﯿﻬﺑ
2
نآ زا هﺪﻣآ ﺖﺳﺪﺑ، ﺎﻫﺰﯿﻟﺎﻧآ ﺮﯾﺎﺳ ﯽﻣ ترﻮﺻ .دﺮﯿﮔﮏﯾدﺰﻧ رﻮﻈﻨﻣ ﻪﺑندﻮﺑ ﺮﺗ ﺞﯾﺎﺘﻧ ﺶﻫوﮋﭘ
ﯽﻣﺎﻤﺗ رد ﻪﮐ ﺖﺳا هﺪﺷ ضﺮﻓ ﺖﯿﻌﻗاو ﻪﺑﺘﺷاد دﻮﺟو لﺎﻌﻓ لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ تﺎﻘﺒﻃﯽﮑﯿﻟورﺪﯿﻫ يﺎﻫوزﺎﺑ و ﺪﺷﺎﺑ ﻪ
3
يور ﺮﺑ هﺪﺷ ﺐﺼﻧ
هزﺎﺳﺎﻫ ياراد ﯽﮕﻤﻫهزﺎﺳ رد ﻪﮐ ترﻮﺻ ﻦﯾا ﻪﺑ ﺪﻨﺷﺎﺑ وﺮﯿﻧ لﺎﻤﻋا ﺖﯾدوﺪﺤﻣ يﺎﻫ5 ،10 و15 ﺐﯿﺗﺮﺗ ﻪﺑ ﻪﻘﺒﻃ ﺮﯾدﺎﻘ750000 ،
1500000 و2250000 ضﺮﻓ ﻦﺗﻮﯿﻧهﺪﺷاﺪﻧ هزﺎﺳ ﻪﻧﻮﮕﻨﯾا رد ﯽﻠﻤﻋ ﺮﯾدﺎﻘﻣ ﻪﺑ ﮏﯾدﺰﻧ ﻪﮐﺖﺳﺎﻫ . ردﯾا يﺮﯿﮔراﺮﻗ ﺖﯿﻌﻗﻮﻣ ﺖﯾﺎﻬﻧ
رد ﻢﺘﺴﯿﺳ ﻞﮑﺷ2 ..ﺖﺳا هﺪﻣآرد ﺶﯾﺎﻤﻧ ﻪﺑ
ﻢﺘﺴﯿﺳ ﯽﻣ راﺮﻗ ﯽﺳرﺮﺑ درﻮﻣ ﻪﮐ يﺪﻌﺑدﺮﯿﮔ زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ ﺖﺳا. ﻢﺘﺴﯿﺳ ﻦﯾاِيراﺬﮔرﺎﺑ ﺖﻋﺮﺳ سﺎﺳاﺮ دراو نآ ﻪﺑ ﻞﻤﻋ
ﯽﻣﺪﻨﮐ ﯽﻣ ﻢﯿﺴﻘﺗ ﯽﻄﺧﺮﯿﻏ و ﯽﻄﺧ ﻪﺘﺳد ود ﻪﺑ يراﺬﮔرﺎﺑ ﺖﻋﺮﺳ و هﺎﮕﺘﺳد رد هﺪﺷ ﺪﯿﻟﻮﺗ يوﺮﯿﻧ ﻦﯿﺑ ﻪﻄﺑار عﻮﻧ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ودﻮﺷ، ﻪﮐ
.ﺖﺳا ﺮﻈﻧﺪﻣ نآ ﯽﻄﺧ عﻮﻧ ﺶﻫوﮋﭘ ﻦﯾا رد زﻮﮑﺴﯾو يﺎﻫﺮﮔاﺮﯿﻣ ﯽﺣاﺮﻃ رداﺪﻘﻣ ﯽﮑﯾ ﺖﺳا حﺮﻄﻣ ﯽﻠﺻا و ﻢﻬﻣ ﺮﺘﻣارﺎﭘ ود ﯽﯾاﺮﯿﻣ ﺐﯾﺮﺿ ر
ﺳد ﻪﮐ يﺪﻨﺑرﺎﻬﻣ ﯽﺘﺨﺳ يﺮﮕﯾد و هﺎﮕﺘﺳدﯽﻣ ﻞﺼﺘﻣ هزﺎﺳ ﻪﺑ ار هﺎﮕﺘ .ﺪﻨﮐ ﺮﺘﻣارﺎﭘ ود ﻦﯾا ﻦﯿﯿﻌﺗ رﻮﻈﻨﻣ ﻪﺑ ،ﻪﻨﯿﻬﺑ ترﻮﺻ ﻪﺑ شور زا
نﻮﻣزآ ﯽﻣ هدﺎﻔﺘﺳا ﺎﻄﺧ و .ددﺮﮔﺪﺘﺑا ﻪﮐ ﻮﺤﻧ ﻦﯾا ﻪﺑا ) ﺪﻨﺑرﺎﻬﻣ ﯽﺘﺨﺳ ياﺮﺑ ﻒﻠﺘﺨﻣ راﺪﻘﻣ ﻪﺳ1 ،2 و3 ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد (ﻪﻘﺒﻃ ﯽﺘﺨﺳ ﺮﺑاﺮﺑ
ﯽﻣدﻮﺷﯽﻣ ﻪﺒﺳﺎﺤﻣ ﻪﻨﯿﻬﺑ ﯽﯾاﺮﯿﻣ ﺐﯾﺮﺿ راﺪﻘﻣ ﺎﻬﻧآ زا ماﺪﮐ ﺮﻫ ياﺮﺑ ﺲﭙﺳ . .ددﺮﮔﺖﺳا ﺮﮐذ ﻪﺑ مزﻻ هﺎﮕﺘﺳد ﯽﯾاﺮﯿﻣ ﺐﯾﺮﺿ راﺪﻘﻣ ﻪﮐ ﺎﻫ
و ﺖﺳا نﺎﺴﮑﯾ تﺎﻘﺒﻃ مﺎﻤﺗ رد ﺖﯾدوﺪﺤﻣ ﺰﯿﻧ زﻮﮑﺴﯾو يﺎﻫﺮﮔاﺮﯿﻣ ياﺮﺑ هﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد وﺮﯿﻧ لﺎﻤﻋا ﺖﯾدوﺪﺤﻣ ﻪﺑﺎﺸﻣ ﺎﻨﯿﻋ ﻪﮐ يﺎﻫ
ﯽﮑﯿﻟورﺪﯿﻫ يﺎﻫوزﺎﺑﺖﺳا. د ﯽﮑﯾ رد ﻪﮐ ﺖﺳا هزﺎﺳ رد ﺎﻬﻧآ ﺐﺼﻧ ﺖﯿﻌﻗﻮﻣ زﻮﮑﺴﯾو يﺎﻫﺮﮔاﺮﯿﻣ ﯽﺣاﺮﻃ رد ﻢﻬﻣ تﺎﮑﻧ زا ﺮﮕﯾ ﻞﮑﺷ2
هﺪﺷ هداد ﺶﯾﺎﻤﻧ ﺖﺳا .
ﻦﯾﺮﺧآ ﻢﺘﺴﯿﺳﯽﺳرﺮﺑ درﻮﻣ، ﯿﻣاﺮ ﺲﯾزﺮﺘﺴﯿﻫ ﺮﮔﺳا ﺰﯿﻧﺎﮑﻣ ﻪﮐم ﻖﯾﺮﻃ زا هزﺎﺳ ﻪﺑ يدورو يژﺮﻧا ندﺮﮐ ﮏﻠﻬﺘﺴﻣ نآ رﺎﮐ ﯽﻠﺻا
ﺎﯾ و تﺎﻌﻄﻗ ﻢﯿﻠﺴﺗﻮﻗو ع شﺰﻐﻟ ردﺖﺳا ﯽﮐﺎﮑﻄﺻا حﻮﻄﺳ يوﺮﯿﻧ راﺪﻘﻣ ﯽﻠﺻا ﻪﺼﺧﺎﺷ ود زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ ﺪﻨﻧﺎﻤﻫ ﻢﻫ ﻢﺘﺴﯿﺳ ﻦﯾا رد .
ﺨﺳ و (كﺎﮑﻄﺻا شﺰﻐﻟ) ﻢﯿﻠﺴﺗ،هزﺎﺳ ﻪﺑ ﺮﮔاﺮﯿﻣ لﺎﺼﺗا يﺪﻨﺑرﺎﻬﻣ ﯽﺘ ﯽﻣ ﻢﺘﺴﯿﺳ تﺎﯿﺻﻮﺼﺧ هﺪﻨﻨﮐ ﻦﯿﯿﻌﺗ ﻦﯾا ﻦﯿﯿﻌﺗ رﻮﻈﻨﻣ ﻪﺑ .ﺪﻨﺷﺎﺑ
ﯿﻗد ﺰﯿﻧ ﺮﯾدﺎﻘﻣﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ ياﺮﺑ هﺪﺷ ﺮﮐذ شور ﻖﺑﺎﻄﻣ ﺎ ﻞﻤﻋ زﯽﻣ ﺪﻨﺑرﺎﻬﻣ ﯽﺘﺨﺳ ياﺮﺑ ﯽﻔﻠﺘﺨﻣ ﺮﯾدﺎﻘﻣ اﺪﺘﺑا ﻪﮐ ترﻮﺻ ﻦﯾا ﻪﺑ دﻮﺷ
)1 ،2 و3 ﯽﻣ ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد (ﻪﻘﺒﻃ ﯽﺘﺨﺳ ﺮﺑاﺮﺑ .دﻮﺷﮏﯾ ﺮﻫ يازا ﻪﺑ ﺲﭙﺳ، ﯽﻣ ﻪﺒﺳﺎﺤﻣ ﻢﯿﻠﺴﺗ يوﺮﯿﻧ ﻪﻨﯿﻬﺑ راﺪﻘﻣ ضﺮﻓ ﻦﯿﻨﭽﻤﻫ .ددﺮﮔ
ﯽﻣهﺎﮕﺘﺳد ﻢﯿﻠﺴﺗ يوﺮﯿﻧ راﺪﻘﻣ ﻪﮐ دﻮﺷ.ﺪﺷﺎﺑ نﺎﺴﮑﯾ ﻒﻠﺘﺨﻣ تﺎﻘﺒﻃ رد هﺪﺷ ﺐﺼﻧ يﺎﻫ رد ﺰﯿﻧ هزﺎﺳ رد ﻢﺘﺴﯿﺳ ﻦﯾا ﺐﺼﻧ ﺖﯿﻌﻗﻮﻣ
ﻞﮑﺷ2 .ﺖﺳا هﺪﻣآ رد ﺶﯾﺎﻤﻧ ﻪﺑ
1 Time Delay
2 Gain Control Matrix
3 Actuator
ﻦﯿﻣﻮﺳﻦﯿﺑ ﺲﻧاﺮﻔﻨﮐ تﺎﺷﺎﻌﺗرا و ﮏﯿﺘﺳﻮﮐآ ﯽﻠﻠﻤﻟا- 4 و5 هﺎﻤﯾد1392- ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧادﺳﻮﻃ ﻦﯾﺪﻟاﺮﯿﺼﻧ ﻪﺟاﻮﺧ- ناﺮﻬﺗ- ناﺮﯾا
6
(ﻒﻟا)
(ب)
(ج)
ﻞﮑﺷ2 .ﻢﺘﺴﯿﺳ يﺮﯿﮔراﺮﻗ ﺖﯿﻌﻗوهزﺎﺳ رد لﺮﺘﻨﮐ يﺎﻫﺲﯾزﺮﺘﺴﯿﻫ ﺮﮔاﺮﯿﻣ (ج ،زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ (ب ،لﺎﻌﻓ لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ (ﻒﻟا ،
3,4 ﻤﻋ ﺲﯾﺪﻧادﺮﮑﻠ
تﺎﻘﺒﻃ ﯽﺒﺴﻧ نﺎﮑﻣ ﺮﯿﯿﻐﺗ لﺮﺘﻨﮐ ،ﯽﻠﺻا فﺪﻫ هزﺎﺳ ﯽﺣاﺮﻃ رد لﻮﻤﻌﻣ رﻮﻃ ﻪﺑﺖﺳاﺪﺷﺎﺑ ﺮﺘﺸﯿﺑ نآ راﺪﻘﻣ ﻪﭼﺮﻫ اﺮﯾز . ﺐﯾﺮﺨﺗ
زﺎﺳ ﺮﯿﻏ يﺎﻀﻋا ﺺﺧﻻﺎﺑ و هزﺎﺳ رد ﺮﺘﺸﯿﺑهﻪﺑﺎﺟ ﻪﺑ سﺎﺴﺣ ياﯽﯾﺎﺟ دﺎﺠﯾا مزﻻ و ﺖﺴﯿﻧ ﯽﻓﺎﮐ ﯽﯾﺎﻬﻨﺗ ﻪﺑ فﺪﻫ ﻦﯾا هراﻮﻤﻫ ﺎﻣا .دﻮﺷ
ﺮﺘﻨﮐ ﺰﯿﻧ هزﺎﺳ بﺎﺘﺷ ﺎﺗ ﺖﺳانﺎﻤﺘﺧﺎﺳ ﺮﯿﻈﻧ ،ددﺮﮔ ل ﺪﻨﻧﺎﻣ) دراد دﻮﺟو بﺎﺘﺷ ﻪﺑ سﺎﺴﺣ تاﺰﯿﻬﺠﺗ ﺎﻬﻧآ رد ﻪﮐ ﯽﯾﺎﻫنﺎﻤﺘﺧﺎﺳ يﺎﻫ
لﺮﺘﻨﮐ ﺰﯿﻧ نآ تﺎﻘﺒﻃ بﺎﺘﺷ هزﺎﺳ تﺎﻘﺒﻃ ﯽﺒﺴﻧ ﺰﯾﺮﮔ ﺮﺑ هوﻼﻋ ﻪﮐ ﺖﺳا مزﻻ ﻦﯾاﺮﺑﺎﻨﺑ .(ﯽﺗاﺮﺑﺎﺨﻣدﻮﺷ ﺶﻫوﮋﭘ ﻦﯾا رد رﻮﻈﻨﻣ ﻦﯾا ﻪﺑ .
ﻋ ﺲﯾﺪﻧا دﺮﮑﻠﻤﺮﮔ راﺮﻗ ﺮﻈﻧﺪﻣ تﺎﻘﺒﻃ ﺰﯾﺮﮔ و بﺎﺘﺷ ﻦﯿﮕﻧﺎﯿﻣ.ﺖﺳا ﻪﺘﻓ
)7(
{ ( )} { ( )}
1 1
2 { ( )} 2 { ( )}
controlled controlled
Uncontrolled Uncontrolled
norm A norm D
PI norm A norm D
 
ر رد ﻪﮐ قﻮﻓ ﻪﻄﺑاA وD ﻠﻄﻣ بﺎﺘﺷ ﻪﻨﯿﺸﯿﺑ رادﺮﺑ ﺐﯿﺗﺮﺗ ﻪﺑتﺎﻘﺒﻃ ﯽﺒﺴﻧ ﺰﯾﺮﮔ ﻪﻨﯿﺸﯿﺑ و تﺎﻘﺒﻃ ﻖﺪﻧا. ﻒﯾﺮﻌﺗ norm ﺎﺑ رادﺮﺑ ﮏﯾ ياﺮﺑ
n ﺮﯾز ترﻮﺻ ﻪﺑ ﻪﯾاردﺖﺳا.
)8(
2 2
1
( ) ...
n
norm A A A
 
4.
ﯽﺳرﺮﺑﺞﯾﺎﺘﻧ ﻞﯿﻠﺤﺗﺎﻫ
ﺶﺨﺑ ﻦﯾا ردﻞﯿﻠﺤﺗ ﺪﻨﯾآﺮﻓ اﺪﺘﺑا ﻪﺋارا نآ ﺞﯾﺎﺘﻧ ﺲﭙﺳ و ﺢﯾﺮﺸﺗ ﻪﺘﻓﺮﮔ ترﻮﺻ يﺎﻫﺖﺳا هﺪﺷ.
نﺎﻤﺘﺧﺎﺳ ﻪﺳ ﺪﺷ ﺮﮐذ ﻪﮐ رﻮﻄﻧﺎﻤﻫ ﺶﻫوﮋﭘ ﻦﯾا رد5 ،10 و15 ﺪﻣ ﻪﻘﺒﻃ ﻪﺘﻓﺮﮔ راﺮﻗ ﺮﻈﻧﺪﻧا ﻦﯾا .نﺎﻤﺘﺧﺎﺳ ﺖﺤﺗ ﯽﮕﻤﻫ ﺎﻫ
زا ﯽﻫوﺮﮔﻪﻟﺰﻟز حﺮﻃ يﺎﻫﺰﯿﻟﺎﻧآ هﺪﺷ ﻣآ ﺖﺳﺪﺑ ﺞﯾﺎﺘﻧ وﺖﺳا ههزﺎﺳ ﻦﯾا ﺲﭙﺳ .ﺎﻫ و زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ ،لﺎﻌﻓ لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ ﻪﺳ ﻂﺳﻮﺗ
دﺮﮑﻠﻤﻋ ﺲﯾﺪﻧا ياﺮﺑ ﺲﯾزﺮﺘﺴﯿﻫ ﺮﮔاﺮﯿﻣﺮﻈﻧدرﻮﻣ ﻪﻧﺎﮔاﺪﺟ ترﻮﺻ ﻪﺑ موﺎﻘﻣ .ﺪﻧﺪﺷ يزﺎﺳ ترﻮﺻ ﻪﺑ لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ تﻻﺎﺣ ﻦﯾا ﯽﻣﺎﻤﺗ رد
هزﺎﺳ نﺎﻤﻫ ادﺪﺠﻣ ﺰﯿﻧ ﺮﺧآ مﺎﮔ رد .ﺖﺳا هﺪﺷ ﯽﺣاﺮﻃ هزﺎﺳ ﯽﻄﺧ رﺎﺘﻓر ضﺮﻓ ﺎﺑ و ﻪﻨﯿﻬﺑﻢﺘﺴﯿﺳ نﺎﻤﻫ ﺎﺑ ،ﺎﻫ ﻪﻠﺣﺮﻣ رد هﺪﺷ ﯽﺣاﺮﻃ يﺎﻫ
ﻪﻟﺰﻟز ضﺮﻌﻣ رد ادﺪﺠﻣ ﻞﺒﻗﺎﻫ ﯽﻣ راﺮﻗهزﺎﺳ رﺎﺑ ﻦﯾا ﻪﮐ توﺎﻔﺗ ﻦﯾا ﺎﺑ ﺪﻧﺮﯿﮔﻄﺧﺮﯿﻏ رﺎﺘﻓر ياراد ﺎﺪﻧا دراﻮﻣ ﺎﺑ و ﯽﺑﺎﯾزﺎﺑ ﺞﯾﺎﺘﻧ ﺎﺘﯾﺎﻬﻧ .
زا ﻞﺻﺎﺣﯽﻣ ﻪﺴﯾﺎﻘﻣ ﻞﺒﻗ ﻪﻠﺣﺮﻣﻧﻮﺷ.ﺪ
د ﺶﺨﺑ ﻦﯾا ردﯽﻣ هداد راﺮﻗ شﺎﮑﻨﮐ درﻮﻣ عﻮﺿﻮﻣ ودﻮﺷ، ﯽﮑﯾ ﺚﺤﺑﻢﺘﺴﯿﺳ رﻮﻀﺣ رد دﻮﺧ ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر زﺎﻓ ﻪﺑ هزﺎﺳ دورو يﺎﻫ
ﺖﺳا لﺮﺘﻨﮐ و ﻢﺘﺴﯿﺳ ﺖﯿﺳﺎﺴﺣ و دﺮﮑﻠﻤﻋ ﻪﺴﯾﺎﻘﻣ يﺮﮕﯾد.هزﺎﺳ نﺪﺷ ﯽﻄﺧﺮﯿﻏ ﻪﺑ ﺎﻫ ﯽﺳرﺮﺑ رد رﺎﺘﻓر زوﺮﺑ ﯽﻄﺧﺮﯿﻏهزﺎﺳ ردﺎﻫ ﻪﺑ
ﻪﻟﺰﻟز ﻦﯿﮕﻧﺎﯿﻣ ﺞﯾﺎﺘﻧ ﯽﺳرﺮﺑ ﻪﮑﻨﯾا ﻞﯿﻟد ياﺮﺑ ﻪﻧﻮﻤﻧ ترﻮﺻ ﻪﺑ ﺞﯾﺎﺘﻧ ﺖﺴﯿﻧ ﺮﯾﺬﭘ نﺎﮑﻣا ﺎﻫﻣ درﻮﮐر هﺪﺷ سﺎﯿﻘلاﯽﻣ ﺮﮐذ وﺮﺘﻨﺳ رد ﺎﻣا دﻮﺷ
ﯽﻣ راﺮﻗ ﯽﺳرﺮﺑ درﻮﻣ ﻦﯿﮕﻧﺎﯿﻣ ﺞﯾﺎﺘﻧ دراﻮﻣ ﺮﯾﺎﺳ .دﺮﯿﮔ
رد ﻪﮐ رﻮﻄﻧﺎﻤﻫ ﻞﮑﺷ3 ﯽﻣ هﺪﻫﺎﺸﻣهزﺎﺳ ،دراﻮﻣ مﺎﻤﺗ رد (لوا ﻪﻘﺒﻃ) ﻪﻘﺒﻃ ﮏﯾ رد ﻞﻗاﺪﺣ دﻮﺷ ﻢﺘﺴﯿﺳ ﻪﺑ هﺪﺷ ﺰﯿﻬﺠﺗ يﺎﻫ
ﯿﺣﺎﻧ دراو ﻢﻫزﺎﺑ (لﺎﻌﻓﺮﯿﻏ و لﺎﻌﻓ) لﺮﺘﻨﮐهﺪﺷ دﻮﺧ ﺦﺳﺎﭘ ﯽﻄﺧﺮﯿﻏ ﻪﻪﻟﺰﻟز يﺎﻫدرﻮﮐر ﺮﯾﺎﺳ رد عﻮﺿﻮﻣ ﻦﯾا .ﺪﻧا ﺶﻫوﮋﭘ ﻦﯾا رد ﻪﮐ يا
هﺪﺷ هدﺎﻔﺘﺳا رﻮﻀﺣ رد هزﺎﺳ ﯽﻄﺧ رﺎﺘﻓر ضﺮﻓ ﺐﯿﺗﺮﺗ ﻦﯾا ﻪﺑ .ﺪﺷ هﺪﻫﺎﺸﻣ ﺰﯿﻧ ﺪﻧاﻢﺘﺴﯿﺳلﺮﺘﻨﮐ يﺎ ﻪﻟﺰﻟز ياﺮﺑ ﯽﺘﺣ ﯽﺣاﺮﻃ ﺢﻄﺳ يﺎﻫ
.دور ﯽﻤﻧ رﺎﻤﺷ ﻪﺑ ﯽﻘﯿﻗد ضﺮﻓ ﻢﻫ
ﻦﯿﻣﻮﺳﻦﯿﺑ ﺲﻧاﺮﻔﻨﮐ تﺎﺷﺎﻌﺗرا و ﮏﯿﺘﺳﻮﮐآ ﯽﻠﻠﻤﻟا- 4 و5 هﺎﻤﯾد1392- ﯽﺳﻮﻃ ﻦﯾﺪﻟاﺮﯿﺼﻧ ﻪﺟاﻮﺧ ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧاد- ناﺮﻬﺗ- ناﺮﯾا
7
ﺲﯾزﺮﺘﺴﯿﻫ ﺮﮔاﺮﯿﻣ
زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ
لﺎﻌﻓ لﺮﺘﻨﮐ
هزﺎﺳ5 ﻪﻘﺒﻃ
هزﺎﺳ10 ﻪﻘﺒﻃ هزﺎﺳ15 ﻪﻘﺒﻃ
ﻞﮑﺷ3 .شﺮﺑ رادﻮﻤﻧ - ِﺰﯾﺮﮔ هزﺎﺳ لوا ﻪﻘﺒﻃ يﺎﻫ5 ،10 و15 ﻢﺘﺴﯿﺳ رﻮﻀﺣرد ﻪﻘﺒﻃﺮﮔاﺮﯿﻣ و زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ ،لﺎﻌﻓ لﺮﺘﻨﮐ يﺎﻫ
هزﺎﺳ رد ﺲﯾزﺮﺘﺴﯿﻫيﺎﻫ رﺎﺘﻓر ﺖﯿﻫﺎﻣ ﺎﺑ ﯽﻄﺧﺮﯿﻏ
ﻠﺌﺴﻣ دﺮﮑﻠﻤﻋ ﻪﺴﯾﺎﻘﻣ يﺪﻌﺑ ﻪﻢﺘﺴﯿﺳ ﺖﯿﺳﺎﺴﺣ و رد ﻪﮐ ﺖﺳا نﺪﺷ ﯽﻄﺧﺮﯿﻏ ﻪﺑ ﻒﻠﺘﺨﻣ يﺎﻫ ﻞﮑﺷ4 ﯽﺳرﺮﺑﯽﻣ .ددﺮﮔ
ﻞﮑﺷ4 .ﯽﯾﺎﻬﻧ حﺮﻃ دﺮﮑﻠﻤﻋ ﺲﯾﺪﻧا راﺪﻘﻣ(ﻒﻟا ،هزﺎﺳيﺎﻫ ﯽﻄﺧ(ب ، هزﺎﺳ يﺎﻫﯽﻄﺧﺮﯿﻏ
ﻪﺑ ﻪﺟﻮﺗ ﺎﺑرد ﻪﭽﻧآ ﻞﮑﺷ4 و لوﺪﺟ3 ﯽﻣ ﺖﺳا هﺪﻣآﻪﮐ ﺖﻓﺮﮔ ﻪﺠﯿﺘﻧ ناﻮﺗ ﻢﺘﺴﯿﺳ ﻦﯿﺑ ردهزﺎﺳ رد ﻪﭼ ﻒﻠﺘﺨﻣ يﺎﻫ ﯽﻄﺧ يﺎﻫ
و ﻪﭼﯽﻄﺧﺮﯿﻏﻢﺘﺴﯿﺳ ، ﻢﺘﺴﯿﺳ ﻦﯾﺮﺗﺮﺑ لﺎﻌﻓ لﺮﺘﻨﮐﺖﺳا ﺮﮔاﺮﯿﻣ ﺐﯿﺗﺮﺗ ﻪﺑ نآ زا ﺲﭘ و.ﺪﻧراد راﺮﻗ ﺲﯾزﺮﺘﺴﯿﻫ و زﻮﮑﺴﯾو يﺎﻫ عﻮﺿﻮﻣ
،ﺖﺳا حﺮﻄﻣ ﻪﮐ يﺮﮕﯾد ﺖﯿﺳﺎﺴﺣ ناﺰﯿﻢﺘﺴﯿرد ﻪﺖﺳا هزﺎﺳ نﺪﺷ ﯽﻄﺧﺮﯿﻏ ﻪﺑ ﺎﻫ لوﺪﺟ3 ﺲﯾﺪﻧا ﻦﯿﮕﻧﺎﯿﻣدﺮﮑﻠﻤﻋ يﺎﻫ و
نآ تاﺮﯿﯿﻐﺗ نﺎﻤﺘﺧﺎﺳ ياﺮﺑ يﺎﻫ5 ،10 و15 هﺪﻣآ رد ﺶﯾﺎﻤﻧ ﻪﺑ ﻪﻘﺒﻃاﺪﻧ. ﺖﺳا ﺺﺨﺸﻣ ﻪﮑﻧﺎﻨﭽﻧآﻏ ﺮﺛا ﺮﺑ،هزﺎﺳ نﺪﺷ ﯽﻄﺧﺮﯿ ﻪﻤﻫ رد
هزﺎﺳﻢﺘﺴﯿﺳ ﺎﻫﯾﺮﺘﻤﮐ لﺎﻌﻓﺮﯿﻏ يﺎﻫ.ﺪﻧداد نﺎﺸﻧ دﻮﺧ زا ار ﯽﮕﺘﺴﺑاو ﻦ ﯽﻣ ﻦﯾاﺮﺑﺎﻨﺑ دﺮﮑﻠﻤﻋ هزﺎﺳ نﺪﺷ ﯽﻄﺧﺮﯿﻏ ﺎﺑ ﻪﮐ ﺖﻔﮔ ناﻮﺗ
ﻢﺘﺴﯿﺳلﺎﻌﻓ ﺮﯿﻏ و لﺎﻌﻓ لﺮﺘﻨﮐ يﺎﻫ (زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ) ﮏﯾدﺰﻧ ﻢﻫ ﻪﺑﯽﻣ ﺮﺗ.ﺪﻧﻮﺷ رد يﺮﺘﺸﯿﺑ تﺪﺷ ﺎﺑ قﺎﻔﺗا ﻦﯾا ﻪﮐ ﺖﺳا ﺮﮐذ ﻪﺑ مزﻻ
ﻪﻟﺰﻟزﯽﻣ ﻒﯾﺮﻌﺗ ﺮﺗﻻﺎﺑ ﺮﻄﺧ حﻮﻄﺳ ياﺮﺑ ﻪﮐ ﺮﺘﯾﻮﻗ يﺎﻫﯾد ﺪﻧﻮﺷ ،ﺖﺳا هﺪﺷ هﺪ ﻪﮐﻧآ ﺞﯾﺎﺘﻧﺎﻬ ياﺮﺑ ﻪﺋارا ﻪﻟﺎﻘﻣ ﻢﺠﺖﯾدوﺪﺤﻣ ﺖﯾﺎﻋر
هﺪﺸﻧ.ﺪﻧا رد ﻪﮐ يﺮﮕﯾد عﻮﺿﻮﻣ ﻞﮑﺷ4 ﯽﻣ هﺪﯾد طﺎﺒﺗرا دﻮﺟو مﺪﻋ دﻮﺷ راد ﯽﻨﻌﻣﻢﺘﺴﯿﺳ ﯽﯾارﺎﮐ ﻦﯿﺑ.ﺖﺳا هزﺎﺳ عﺎﻔﺗرا و ﺎﻫ
ﻦﯿﻣﻮﺳﻦﯿﺑ ﺲﻧاﺮﻔﻨﮐ تﺎﺷﺎﻌﺗرا و ﮏﯿﺘﺳﻮﮐآ ﯽﻠﻠﻤﻟا- 4 و5 هﺎﻤﯾد1392- ﯽﺘﻌﻨﺻ هﺎﮕﺸﻧاد ﯽﺳﻮﻃ ﻦﯾﺪﻟاﺮﯿﺼﻧ ﻪﺟاﻮﺧ- ناﺮﻬﺗ- ناﺮﯾا
8
لوﺪﺟ3 ﻪﻨﯿﻬﺑ دﺮﮑﻠﻤﻋ ﺲﯾﺪﻧا ﻦﯿﮕﻧﺎﯿﻣ .ﻢﺘﺴﯿﺳهزﺎﺳ رد لﺮﺘﻨﮐ يﺎﻫﯽﻄﺧ يﺎﻫ ﯽﻄﺧﺮﯿﻏ و
لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ ﯽﻄﺧ هزﺎﺳ ﯽﻄﺧﺮﯿﻏ هزﺎﺳ ) نﺪﺷ ﯽﻄﺧﺮﯿﻏ ﺮﺛا ﺮﺑ دﺮﮑﻠﻤﻋ تاﺮﯿﯿﻐﺗ%(
لﺎﻌﻓ 0.379 0.454 19.8
زﻮﮑﺴﯾو 0.463 0.525 13.4
ﺲﯾزﺮﺘﺴﯿﻫ 0.578 0.715 23.7
5.
ﻊﻤﺟيﺪﻨﺑ يﺮﯿﮔ ﻪﺠﯿﺘﻧ و
ﯽﻣ ﺎﻬﺘﻧا رد ﺞﯾﺎﺘﻧ ناﻮﺗﺶﻫوﮋﭘ ﻦﯾا زا هﺪﻣآ ﺖﺳد ﻪﺑ ﻊﻤﺟ و ﻪﺻﻼﺧ ﺮﯾز ترﻮﺻ ﻪﺑ ار :دﺮﮐ يﺪﻨﺑ
- ﻢﺘﺴﯿﺳ رﻮﻀﺣ رد هزﺎﺳ ﯽﻄﺧ رﺎﺘﻓر ضﺮﻓلﺮﺘﻨﮐ يﺎﻫ رﺎﺘﻓر ناﺰﯿﻣ ﻪﮐ ﺪﻨﭼﺮﻫ ،ﺖﺴﯿﻧ ﯽﻘﯿﻗد ضﺮﻓ حﺮﻃ ﻪﻟﺰﻟز رد ﯽﺘﺣ
.ﺖﺳا دوﺪﺤﻣ ﺢﻄﺳ ﻦﯾا رد ﯽﻄﺧﺮﯿﻏ
- ﺘﺴﯿﺳ ﻪﻤﻫ ﻪﮐ ﺪﺷ هﺪﻫﺎﺸﻣ ﺶﻫوﮋﭘ ﻦﯾا رد زا ﯽﺸﺨﺑ هﺪﺷ ﯽﺳرﺮﺑ لﺮﺘﻨﮐ يﺎﻫ ﯽﯾارﺎﮐرﺎﺘﻓر ﺮﺛا رد ار دﻮﺧ ﺖﺳد زا ﯽﻄﺧﺮﯿﻏ
ﯽﻣ ﺎﻣا .ﺪﻨﻫدرد ﻦﯾا ﻦﯿﻢﺘﺴﯿﺳ ، لﺮﺘﻨﮐ لﺎﻌﻓﺮﯿﻏ زﻮﮑﺴﯾو ﺮﮔاﺮﯿﻣ زا هدﺎﻔﺘﺳا ﺎﺑ زا هزﺎﺳ رﺎﺘﻓر ﺮﯿﯿﻐﺗ ﻪﺑ يﺮﺘﻤﮐ ﯽﮕﺘﺴﺑاو
هدوﺪﺤﻣهداد نﺎﺸﻧ ﯽﻄﺧﺮﯿﻏ ﻪﺑ ﯽﻄﺧ .ﺪﻧايرﺎﺘﻓر ﻢﯾژر ﺮﯿﯿﻐﺗ ﺎﺑ دور ﯽﻣ رﺎﻈﺘﻧا ﻪﺠﯿﺘﻧ رد ﻢﺘﺴﯿﺳ ﯽﯾارﺎﮐ ﺮﯿﻏ لﺮﺘﻨﮐ يﺎﻫ
ﻢﺘﺴﯿﺳ ﻪﺑ لﺎﻌﻓﻧ لﺎﻌﻓ يﺎﻫﮑﯾدﺰﺮﺘ دﻮﺷ ،.ﺪﺷﺎﺑ ﻪﺘﺷاد يﺮﺗﺪﯾﺪﺷ ﯽﻄﺧﺮﯿﻏ رﺎﺘﻓر هزﺎﺳ ﻪﮐ ﯽﻧﺎﻣز هﮋﯾﻮﺑ
- هزﺎﺳ ﯽﺳرﺮﺑ دﻮﺟو ﺎ ﻪﻌﻟﺎﻄﻣ ﻦﯾا رد ،ﻒﻠﺘﺨﻣ عﺎﻔﺗرا ﺎﺑ ﯽﯾﺎﻫﻨﻌﻣ طﺎﺒﺗراﻢﺘﺴﯿﺳ ﯽﯾارﺎﮐ و هزﺎﺳ عﺎﻔﺗرا ﻦﯿﺑ ﯽﺼﺨﺸﻣ و راد يﺎﻫ
لﺮﺘﻨﮐ ﻒﻠﺘﺨﻣﺪﺸﻧ هﺪﯾد.
ﻊﺟاﺮﻣ
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Article
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Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.
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Semiactive control systems combine the features of active and passive control to reduce the response of structures to various dynamic loadings. They include: (1)Active variable stiffness, where the stiffness of the structure is adjusted to establish a nonresonant condition between the structure and excitation; and (2) active variable damper, where the damping coefficient of the device is varied to achieve the most reduction in the response. This study is concerned with examining the effectiveness of variable dampers for seismic applications. Three algorithms for selecting the damping coefficient of variable dampers are presented and compared. They include a linear quadratic regulator algorithm; a generalized linear quadratic regulator algorithm with a penalty imposed on the acceleration response; and a displacement-acceleration domain algorithm, where the damping coefficient is selected by examining the response on the displacement-acceleration plane and assigning different damping coefficients accordingly. Two-single-degree-of-freedom structures subjected to 20 ground excitations are analyzed using the three algorithms. The analyses indicate that, unlike passive dampers (where for flexible structures, an increase in damping coefficient decreases displacement but increases the acceleration response), variable dampers can be effective in reducing both the displacement and acceleration responses. The algorithms are used to compute the seismic response of two structures: (1) An isolated bridge modeled as a single-degree-of-freedom system; and (2) a base-isolated six-story frame modeled as a multi-degree-of-freedom system. The results indicate that variable dampers significantly reduce the displacement and acceleration responses.
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t has been shown recently that a combined use of active and passive control systems, referred to as the hybrid control system, is more effective, beneficial, and practical, in some cases, for reducing the building response under strong earthquakes than an active or passive system used alone. However, the use of hybrid control systems involves active control of nonlinear or hysteretic structural systems. A refined version of the instantaneous optimal control algorithms for nonlinear or hysteretic structural systems is presented herein. The main advantage of the proposed algorithms is that the control vector is determined directly from the measured response state vector without the necessity of tracking a time-dependent system matrix, as suggested previously. A method of simulating the controlled response of the hysteretic system using the present algorithm is presented. Applications of the control algorithm to various types of aseismic hybrid control systems are emphasized. The performances of various control systems are evaluated and compared numerically, and the advantages of the aseismic hybrid control systems are demonstrated. It is shown that the proposed control algorithm is simple and reliable for on-line operations and that it is effective for practical applications.
Article
Linear quadratic regulator (LQR)-based control force is composed of an elastic restoring force component and a damping force component. According to the analysis of the proportions of the elastic restoring force and the damping force to the total active control force, two indices are defined to quantify the damping characteristics and negative stiffness characteristics of an active control force. Because a semi-active damping system behaves like a damping device with adjustable parameters, these two indices can be used to quantify the capability of a semi-active damping system and a passive damping system achieving the performance of a fully active control system. Numerical studies are conducted to investigate the damping characteristics and negative stiffness characteristics of an active control force in an active control system. Semi-active damping systems and passive damping systems are designed to replace the active control systems and then the capability of the semi-active control and passive control achieving the performance of fully active control is further studied through the numerical study. Finally, the negative stiffness characteristics realized by semi-active magnetorheological (MR) damping systems are demonstrated through an in situ field test of a stay cable in the Binzhou Yellow River Highway Bridge. Copyright © 2010 John Wiley & Sons, Ltd.
Article
Investigated is the accuracy in estimating the response of asymmetric one-storey systems with non-linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non-linear VE dampers are replaced by their energy-equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non-classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the ‘pseudo-velocity’ of non-linear VE dampers, the peak force of the non-linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude- and frequency-dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one-storey systems with non-linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non-linear supplemental damping systems that satisfy given design criteria for a given design spectrum. Copyright © 2003 John Wiley & Sons, Ltd.
Article
A design strategy for control of buildings experiencing inelastic deformations during seismic response is formulated. The strategy is using weakened, and/or softened, elements in a structural system while adding passive energy dissipation devices (e.g. viscous fluid devices, etc.) in order to control simultaneously accelerations and deformations response during seismic events. A design methodology is developed to determine the locations and the magnitude of weakening and/or softening of structural elements and the added damping while insuring structural stability. A two-stage design procedure is suggested: (i) first using a nonlinear active control algorithm, to determine the new structural parameters while insuring stability, then (ii) determine the properties of equivalent structural parameters of passive system, which can be implemented by removing or weakening some structural elements, or connections, and by addition of energy dissipation systems. Passive dampers and weakened elements are designed using an optimization algorithm to obtain a response as close as possible to an actively controlled system. A case study of a five-story building subjected to El Centro ground motion, as well as to an ensemble of simulated ground motions, is presented to illustrate the procedure. The results show that following the design strategy, a control of both peak inter-story drifts and total accelerations can be obtained. Copyright © 2008 John Wiley & Sons, Ltd.
Article
In this paper, the capabilities of passive control of structures using hydraulic fluid dampers are compared to those of semi-active control. It is demonstrated that, in most cases, the performance achieved by a properly designed passive control system can be comparable to that of semi-active systems that use the state-of-the-art control algorithms. It is also shown that the optimum damping coefficients for passive control may be much smaller than the maximum values considered in semi-active control. These conclusions are supported by numerical simulations of several structures, including a case of actual implementation of semi-active control in a building structure. Copyright © 2006 John Wiley & Sons, Ltd.
A Study of Applicability of Vibration Control to Nonlinear Structure for Seismic Excitation
  • S Shimada
  • T Fujinami
  • S Nakanowatary
  • S Jodai
S. Shimada, T. Fujinami, S. Nakanowatary, S.Jodai, "A Study of Applicability of Vibration Control to Nonlinear Structure for Seismic Excitation", Proceeding of Tenth World Conference on Earthquake Engineering, Madrid, Spain, July 19-24 (1992).
Generalized Optimal Active Control Algorithm for Nonlinear Seismic Structures
  • F Y Cheng
  • P Tian
F.Y. Cheng, and P. Tian, "Generalized Optimal Active Control Algorithm for Nonlinear Seismic Structures", Proceeding of Tenth World Conference on Earthquake Engineering, Madrid, Spain, July 19-24 (1992).