Hw06
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ﺑﻪ ﻧﺎم ﺧﺪا
ﺗﻤﺮﻳﻦ ﺷﺸﻢ درس ﺳﻴﺴﺘﻤﻬﺎي ﻛﻨﺘﺮل ﺧﻄﻲ -1در ﺳﻴﺴﺘﻢ ﻣﺪار ﺑﺴﺘﻪ زﻳﺮ ﺑﻪ ازاي ﭼﻪ ﻣﻘﺪار αﺳﻴﺴﺘﻢ ﭘﺎﻳﺪار اﺳﺖ؟
-2ﻣﺤﻞ ﻗﻄﺒﻬﺎي ﺳﻴﺴﺘﻤﻲ ﺑﺎ ﻣﻌﺎدﻟﻪ ﻣﺸﺨﺼﻪ زﻳﺮ را ﺑﻴﺎﺑﻴﺪ: s 6 + 3s 5 + 6 s 4 + 12s 3 + 11s 2 + 9 s + 6 = 0
-3ﺗﺎﺑﻊ ﺗﺒﺪﻳﻞ ﺣﻠﻘﻪ ﺑﺎز ﻳﻚ ﺳﻴﺴﺘﻢ ﺣﻠﻘﻪ ﺑﺴﺘﻪ ﺑﻪ ﺻﻮرت زﻳﺮ اﺳﺖ .ﻣﺤﺪودهاي از Kﻛﻪ ﺑﻪ ازاي آن ﺳﻴﺴﺘﻢ ﭘﺎﻳﺪار اﺳﺖ را ﺑﻴﺎﺑﻴﺪ: )K ( s + 2 )s ( s + 5)( s 2 + 2 s + 5
= ) GH ( s
-4ﻣﺤﺪودهاي از Kرا ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ ﻛﻪ ﺑﻪ ازاي آن ﻣﻴﺮاﻳﻲ )ﺗﻀﻌﻴﻒ( ﺳﻴﺴﺘﻢ ) ( ζω nاز ﻳﻚ ﺑﻴﺸﺘﺮ ﺑﺎﺷﺪ.
-5ﺳﻴﺴﺘﻤﻲ ﺑﺎ ﻣﻌﺎدﻟﻪ ﻣﺸﺨﺼﻪ s 4 + Ks 3 + s 2 + s + 1 = 0ﺗﻮﺻﻴﻒ ﻣﻲﺷﻮد .ﮔﺴﺘﺮه ﺗﻐﻴﻴﺮات Kﺑﺮاي ﭘﺎﻳﺪاري ﺳﻴﺴﺘﻢ ﻛﺪام اﺳﺖ؟
K -6را ﻃﻮري ﺗﻌﻴﻴﻦ ﻛﻨﻴﺪ ﻛﻪ ﺑﺮاي ﺳﻴﺴﺘﻢ زﻳﺮ دو ﻗﻄﺐ ﺳﻴﺴﺘﻢ روي ﻣﺤﻮر jωﻗﺮار ﮔﻴﺮﻧﺪ:
K )s ( s + 2)( s + 3
= )GH ( s
ﺗﻤﺮﻳﻦ ﺷﺸﻢ درس ﺳﻴﺴﺘﻤﻬﺎي ﻛﻨﺘﺮل ﺧﻄﻲ -1در ﺳﻴﺴﺘﻢ ﻣﺪار ﺑﺴﺘﻪ زﻳﺮ ﺑﻪ ازاي ﭼﻪ ﻣﻘﺪار αﺳﻴﺴﺘﻢ ﭘﺎﻳﺪار اﺳﺖ؟
-2ﻣﺤﻞ ﻗﻄﺒﻬﺎي ﺳﻴﺴﺘﻤﻲ ﺑﺎ ﻣﻌﺎدﻟﻪ ﻣﺸﺨﺼﻪ زﻳﺮ را ﺑﻴﺎﺑﻴﺪ: s 6 + 3s 5 + 6 s 4 + 12s 3 + 11s 2 + 9 s + 6 = 0
-3ﺗﺎﺑﻊ ﺗﺒﺪﻳﻞ ﺣﻠﻘﻪ ﺑﺎز ﻳﻚ ﺳﻴﺴﺘﻢ ﺣﻠﻘﻪ ﺑﺴﺘﻪ ﺑﻪ ﺻﻮرت زﻳﺮ اﺳﺖ .ﻣﺤﺪودهاي از Kﻛﻪ ﺑﻪ ازاي آن ﺳﻴﺴﺘﻢ ﭘﺎﻳﺪار اﺳﺖ را ﺑﻴﺎﺑﻴﺪ: )K ( s + 2 )s ( s + 5)( s 2 + 2 s + 5
= ) GH ( s
-4ﻣﺤﺪودهاي از Kرا ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ ﻛﻪ ﺑﻪ ازاي آن ﻣﻴﺮاﻳﻲ )ﺗﻀﻌﻴﻒ( ﺳﻴﺴﺘﻢ ) ( ζω nاز ﻳﻚ ﺑﻴﺸﺘﺮ ﺑﺎﺷﺪ.
-5ﺳﻴﺴﺘﻤﻲ ﺑﺎ ﻣﻌﺎدﻟﻪ ﻣﺸﺨﺼﻪ s 4 + Ks 3 + s 2 + s + 1 = 0ﺗﻮﺻﻴﻒ ﻣﻲﺷﻮد .ﮔﺴﺘﺮه ﺗﻐﻴﻴﺮات Kﺑﺮاي ﭘﺎﻳﺪاري ﺳﻴﺴﺘﻢ ﻛﺪام اﺳﺖ؟
K -6را ﻃﻮري ﺗﻌﻴﻴﻦ ﻛﻨﻴﺪ ﻛﻪ ﺑﺮاي ﺳﻴﺴﺘﻢ زﻳﺮ دو ﻗﻄﺐ ﺳﻴﺴﺘﻢ روي ﻣﺤﻮر jωﻗﺮار ﮔﻴﺮﻧﺪ:
K )s ( s + 2)( s + 3
= )GH ( s
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Hw06
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