ﻛﻨﺘﺮل ﻓﺮﻛﺎﻧﺲ ﺳﻴﺴﺘﻢ دوﻣﻨﻄﻘﻪ اي ﺑﺎ اﺳﺘﻔﺎده از ﻣﻨﻄﻖ ﻓﺎزي 1داود * ﻗﻨﺒﺮي 2 ،ﻧﻮﻳﺪرﺿﺎاﺑﺠﺪي 3 ،ﻋﺒﺎس ﻛﺎرﮔﺮ 1
داﻧﺸﮕﺎه ﺷﻬﺮ ﻛﺮد
[email protected] ، 2داﻧﺸﮕﺎه ﺷﻬﺮﻛﺮد
[email protected] ، 3
داﻧﺸﮕﺎه ﺷﻬﺮﻛﺮد
[email protected] ،
ﭼﻜﻴﺪه در اﻳﻦ ﻣﻘﺎﻟﻪ ﻛﻨﺘﺮل ﻛﻨﻨﺪه اﻧﺘﮕﺮاﻟﻲ ﺑﺎ ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﻓﺎزي ﺟﺎﻳﮕﺰﻳﻦ ﻣﻲ ﮔﺮدد اﻳﻦ ﻛﻨﺘﺮل ﻛﻨﻨﺪه اﻧﻌﻄﺎف ﭘﺬﻳﺮ ﺑﻮده و ﻋﻤﻠﻜﺮد ﻣﻘﺎوﻣﻲ در ﺑﺮاﺑﺮ ﺗﻐﻴﻴﺮ ﭘﺎراﻣﺘﺮﻫﺎي ﺳﻴﺴﺘﻢ و ﻋﻮاﻣﻞ ﻏﻴﺮ ﺧﻄﻲ ﻧﻈﻴﺮ ﻣﺤﺪودﻳﺖ ﺗﻮﻟﻴﺪ ژﻧﺮاﺗﻮر ﺗﺤﺖ ﺷﺮاﻳﻂ ﻣﺨﺘﻠﻒ ﺑﺎر از ﺧﻮد ﻧﺸﺎن ﻣﻲ دﻫﺪ .از اﻳﻦ رو ﭼﻨﻴﻦ ﺑﻪ ﻧﻈﺮ ﻣﻲ رﺳﺪ ﻛﻪ ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﭘﻴﺸﻨﻬﺎدي ﻣﻲ ﺗﻮاﻧﺪ در ﺳﻴﺴﺘﻢ ﻫﺎي واﻗﻌﻲ ﺑﻪ ﻛﺎر رود .ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﭘﻴﺸﻨﻬﺎدي ﺑﻪ ﺳﻴﺴﺘﻢ ﻗﺪرت دو ﻧﺎﺣﻴﻪ اي اﻋﻤﺎل ﺷﺪه و ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ از آن ﺑﺎ ﻛﻨﺘﺮل ﻛﻨﻨﺪه PI ﻛﻼﺳﻴﻚ ﻣﻘﺎﻳﺴﻪ ﻣﻲ ﮔﺮدد .ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ از ﺷﺒﻴﻪ ﺳﺎزي ﻧﺸﺎن ﻣﻲ دﻫﺪ ﻛﻪ رﻓﺘﺎر ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﭘﻴﺸﻨﻬﺎدي در ﻣﻘﺎﺑﻞ ﺗﻐﻴﻴﺮ ﭘﺎراﻣﺘﺮﻫﺎ و ﺗﻐﻴﻴﺮات ﺑﺎر و ﻣﺤﺪودﻳﺖ ﻧﺮخ ﺗﻮﻟﻴﺪ ﺑﻬﺘﺮ از ﻛﻨﺘﺮل ﻛﻨﻨﺪه PIﻛﻼﺳﻴﻚ اﺳﺖ و ﻋﻤﻠﻜﺮد ﻣﻘﺎوﻣﻲ را از ﺧﻮد ﻧﺸﺎن ﻣﻲ دﻫﺪ.
واژه ﻫﺎي ﻛﻠﻴﺪي :ﻛﻨﺘﺮل ﻓﺮﻛﺎﻧﺲ ،ﺳﻴﺴﺘﻢ دو ﻣﻨﻄﻘﻪ اي ،ﻛﻨﺘﺮل ﻓﺎزي
-1
ﻣﻘﺪﻣﻪ از ﻗﺒﻴﻞ ﻣﺤﺪودﻳﺖ ﻫﺎي ﺗﻮرﺑﻴﻦ -ﮔﺎورﻧﺮ -ﺳﻴﺴﺘﻢ ﻗﺪرت واﻏﺘﺸﺎﺷﺎت ﺑﺎر را ﺑﺮآورده ﺳﺎزد.
ﺑﻪ ﻣﻨﻈﻮر ﻋﻤﻠﻜﺮد رﺿﺎﻳﺖ ﺑﺨﺶ ﻳﻚ ﺳﻴﺴﺘﻢ ﻗﺪرت ،ﺛﺒﺎت ﻓﺮﻛﺎﻧﺲ ﺳﻴﺴﺘﻢ ﻗﺪرت اﻣﺮي ﺿﺮوري اﺳﺖ .زﻳﺮا ﻛﻪ ﻛﻨﺘﺮل ﻧﺴﺒﺘﺄ دﻗﻴﻖ ﻓﺮﻛﺎﻧﺲ ﺛﺒﺎت ﺳﺮﻋﺖ ﻣﻮﺗﻮرﻫﺎي ﺳﻨﻜﺮون و اﻟﻘﺎﻳﻲ را ﺑﻪ دﻧﺒﺎل دارد و ﺗﺜﺒﻴﺖ ﺳﺮﻋﺖ راه اﻧﺪازي ﻣﻮﺗﻮري ﺑﻪ ﻃﻮر وﻳﮋه در ﻋﻤﻠﻜﺮد رﺿﺎﻳﺖ ﺑﺨﺶ واﺣﺪﻫﺎي ﺗﻮﻟﻴﺪي اﻫﻤﻴﺖ دارد.ﺛﺒﺎت ﻓﺮﻛﺎﻧﺲ ﺳﻴﺴﺘﻢ ﻗﺪرت ﺑﺴﺘﮕﻲ ﺑﻪ ﺗﻌﺎدل ﺗﻮان اﻛﺘﻴﻮ دارد و از آﻧﺠﺎ ﻛﻪ ﻓﺮﻛﺎﻧﺲ ﻋﺎﻣﻞ ﻣﺸﺘﺮﻛﻲ در ﺳﺮﺗﺎﺳﺮ ﺳﻴﺴﺘﻢ اﺳﺖ ،ﻫﺮ ﺗﻐﻴﻴﺮي در ﺗﻌﺎدل ﺑﻴﻦ ﺗﻘﺎﺿﺎ و ﺗﻮﻟﻴﺪ ﺗﻮان اﻛﺘﻴﻮ ﻳﻚ ﺷﺒﻜﻪ ،ﺑﻪ ﺷﻜﻞ ﺗﻐﻴﻴﺮ ﻓﺮﻛﺎﻧﺲ در ﺳﺮﺗﺎﺳﺮ ﺷﺒﻜﻪ ﻣﻨﻌﻜﺲ ﻣﻲ ﺷﻮد. ﺑﻨﺎﺑﺮاﻳﻦ ﻛﻨﺘﺮل ﺑﺎر ﻓﺮﻛﺎﻧﺲ در ﺳﻴﺴﺘﻢ ﻗﺪرت ﺑﺰرگ ﺑﺮاي ﺗﺎﻣﻴﻦ اﻧﺮژي اﻟﻜﺘﺮﻳﻜﻲ ﺑﺎ ﻗﺎﺑﻠﻴﺖ اﻃﻤﻴﻨﺎن ﺑﺎﻻ و ﻛﻴﻔﻴﺖ ﻣﻄﻠﻮب اﻣﺮي ﺿﺮوري ﺑﻪ ﻧﻈﺮ ﻣﻲ رﺳﺪ .ﻫﺪف اﺻﻠﻲ ﻛﻨﺘﺮل ﺑﺎر ﻓﺮﻛﺎﻧﺲ ﺻﻔﺮ ﻧﮕﻪ داﺷﺘﻦ ﺧﻄﺎي ﻣﺎﻧﺪﮔﺎر ﻣﻲ ﺑﺎﺷﺪ.ﺑﺮاي ﻣﺴﺄﻟﻪ ﻛﻨﺘﺮل ﺑﺎر ﻓﺮﻛﺎﻧﺲ روش ﻫﺎي ﻣﺨﺘﻠﻔﻲ اراﺋﻪ ﺷﺪه اﺳﺖ از ﺟﻤﻠﻪ :ﻛﻨﺘﺮل ﻛﻨﻨﺪه PIﺳﺎده ﺷﺒﻜﻪ ﻫﺎي ﻋﺼﺒﻲ وﻳﻮﻟﺖ ﺷﺒﻜﻪ ﻫﺎي ﻋﺼﺒﻲ ،ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﻣﺪ ﻟﻐﺰﺷﻲ و ﻛﻨﺘﺮل ﻛﻨﻨﺪهPI ﺑﻬﻴﻨﻪ وﻏﻴﺮه اراﺋﻪ ﺷﺪه اﺳﺖ .در ﺑﻴﻦ روﺷﻬﺎي اراﺋﻪ ﺷﺪه ﻛﻨﺘﺮل ﻛﻨﻨﺪه PI ﺑﻴﺶ از ﻫﻤﻪ در ﺻﻨﻌﺖ ﻣﻮرد ﺗﻮﺟﻪ ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ .اﻳﻦ ﻛﻨﺘﺮل ﻛﻨﻨﺪه داراي ﮔﻴﻦ ﺛﺎﺑﺘﻲ ﻣﻲ ﺑﺎﺷﺪ ﻛﻪ در ﺷﺮاﻳﻂ ﻋﻤﻠﻜﺮد ﻧﺎﻣﻲ ﻃﺮاﺣﻲ ﻣﻲ ﮔﺮدد ﺑﻨﺎﺑﺮاﻳﻦ ﺑﻬﺮه ﺑﺮداري از آن ﺳﺎده ﺑﻮده وﻟﻲ ﻧﻮﺳﺎﻧﺎت ﻓﺮﻛﺎﻧﺲ در اﻳﻦ ﺣﺎﻟﺖ ﺑﺴﻴﺎر زﻳﺎد اﺳﺖ .ﺑﻨﺎﺑﺮاﻳﻦ ﺟﻬﺖ ﻛﻨﺘﺮل ﺑﺎر ﻓﺮﻛﺎﻧﺲ ﺑﻪ ﻛﻨﺘﺮل ﻛﻨﻨﺪه اي ﻧﻴﺎز اﺳﺖ ﺗﺎ ﺗﻤﺎﻣﻲ ﻣﺤﺪودﻳﺖ ﻫﺎي ﻣﻮﺟﻮد
- 2ﺳﻴﺴﺘﻢ ﻗﺪرت دو ﻣﻨﻄﻘﻪ اي ﺑﻪ ﻃﻮر ﻃﺒﻴﻌﻲ ﺳﻴﺴﺘﻢ ﻗﺪرت داراي ﺳﺎﺧﺘﺎر ﭼﻨﺪ ﻣﺘﻐﻴﺮه و ﭘﻴﭽﻴـﺪه اي داردو داراي ﺑﻠﻮك ﻫﺎي ﻛﻨﺘﺮل ﻣﺘﻔﺎوﺗﻲ اﺳﺖ ﻛـﻪ اﻏﻠـﺐ آن ﻫـﺎ ﻏﻴـﺮ ﺧﻄﻲ و ﻳﺎ ﻏﻴﺮ ﻣﻴﻨﻴﻤﻢ ﻓﺎز ﻫﺴﺘﻨﺪ.اﻣﺮوزه اﻏﻠﺐ ﺳﻴﺴﺘﻢ ﻫﺎي ﻗـﺪرت ﺑـﻪ ﻣﻨﺎﻃﻖ ﻣﺠﺎور ﺧﻮد ﻣﺘﺼﻞ ﻫﺴﺘﻨﺪ و اﺗﺼـﺎل اﻳـﻦ ﻣﻨـﺎﻃﻖ ﻛﻨﺘـﺮل ،ﻳـﻚ ﺳﻴﺴﺘﻢ ﻗﺪرت ﭼﻨﺪ ﻣﻨﻄﻘﻪ اي را ﺑـﻪ وﺟـﻮد ﻣـﻲ آورد.در ﻳـﻚ ﺳﻴﺴـﺘﻢ ﻗﺪرت ﭼﻨﺪ ﻣﻨﻄﻘﻪ اي ،ﻫﺮ ﻣﻨﻄﻘﻪ ﻛﻨﺘﺮل در ﺷﺮاﻳﻂ ﻛﺎر ﻋـﺎدي ﺑﺎرﻫـﺎي ﻣﻨﻄﻘﻪ ﺧﻮد را ﺗﺎﻣﻴﻦ ﻣﻲ ﻧﻤﺎﻳﺪ .ﻣﺎ در اﻳﻦ ﻣﻘﺎﻟﻪ ﺑﺮاي ﺷﺒﻴﻪ ﺳﺎزي از ﻳﻚ ﺳﻴﺴﺘﻢ ﻛﻨﺘﺮل دو ﻣﻨﻄﻘﻪ اي اﺳﺘﻔﺎده ﻛﺮده اﻳﻢ.
1-2ﺳﻴﺴﺘﻢ ﻗﺪرت دوﻣﻨﻄﻘﻪ اي ﻛﻨﺘﺮل ﻧﺸﺪه ﺷﻜﻞ 1ﻳﻚ ﺳﻴﺴﺘﻢ ﻗﺪرت دو ﻧﺎﺣﻴﻪ اي در ﺣﺎﻟﺖ ﻛﻨﺘﺮل ﻧﺸﺪه را ﻧﺸﺎن ﻛﻪ در آن Fﻓﺮﻛﺎﻧﺲ ﺳﻴﺴﺘﻢ ﺑﺮ ﺣﺴﺐ ﻫﺮﺗﺰ و Rﺿﺮﻳﺐ ﺗﻨﻈﻴﻢ ژﻧﺮاﺗﻮرﺑﺮﺣﺴﺐ ﻫﺮﺗﺰ ﺑﺮ ﭘﺮﻳﻮﻧﻴﺖ Tgﺛﺎﺑﺖ زﻣﺎﻧﻲ ژﻧﺮاﺗﻮر ﺑﺮ ﺣﺴﺐ ﺛﺎﻧﻴﻪ Ttﺛﺎﺑﺖ زﻣﺎﻧﻲ ﺗﻮرﺑﻴﻦ ﺑﺮ ﺣﺴﺐ ﺛﺎﻧﻴﻪ و T pﺛﺎﺑﺖ زﻣﺎﻧﻲ ﺳﻴﺴﺘﻢ ﻗﺪرت ﺑﺮ ﺣﺴﺐ ﺛﺎﻧﻴﻪ اﺳﺖ .ﻣﺘﻐﻴﺮﻫﺎي ﺣﺎﻟﺖ ﺳﻴﺘﻢ ﺑﻪ ﺻﻮرت زﻳﺮ اﺳﺖ : ) (1 ) x • (t ) = Ax(t ) + Bu (t ) + Ld (t ﻛﻪ Aﻣﺎﺗﺮﻳﺲ ﺳﻴﺴﺘﻢ و Bورودي ﺳﻴﺴﺘﻢ و Lورودي اﻏﺘﺸﺎش اﺳﺖ.
436
)(2
x(t ) = [∆f1 , Pg1 , ∆Pt1 , ∆Ptie1 , ∆f 2 , ∆Pg 2 , ∆Pt 2 ]T
)(3
u (t ) = [u1 , u 2 ]T
)(4
] d (t ) = [∆p d 1 , ∆p d 2
ﻛــﻪ در رواﺑــﻂ ﺑــﺎﻻ u1و u2ورودي ﻛﻨﺘــﺮل و ∆pd 1و ∆p d 2
ب ردار
اﻏﺘﺸﺎﺷﺎت ﺑﺎر ﻫﺴﺘﻨﺪ.
ﺷﻜﻞ)(3ﭘﺎﺳﺦ ﺧﻄﺎي ﺗﻮان اﻧﺘﻘﺎﻟﻲ ﺑﻴﻦ دو ﻣﻨﻄﻘﻪ
ﻫﻤﺎﻧﻄﻮر ﻛﻪ در ﺷﻜﻞ ﻫﺎي 2و 3ﻣﺸﺨﺺ اﺳﺖ ﺑﻪ ﻋﻠﺖ اﻳﻨﻜﻪ ﺳﻴﺴﺘﻢ در ﺣﺎﻟﺖ ﻛﻨﺘﺮل ﻧﺸﺪه اﺳﺖ ﺧﻄﺎ ﺑﻪ ﺻﻔﺮ ﻧﺮﺳﻴﺪه اﺳﺖ در ﺻﻮرﺗﻲ ﻛﻪ ﺗﻤﺎﻳﻞ دارﻳﻢ ﻛﻪ ﺧﻄﺎ ﺑﻪ ﺻﻔﺮ ﺑﺮﺳﺪ.
-3-2ﺳﻴﺴﺘﻢ ﻗﺪرت دوﻣﻨﻄﻘﻪ اي ﻛﻨﺘﺮل ﺷﺪه ﻫﻤﺎﻧﻄﻮرﻛﻪ ﻧﺘﺎﻳﺞ ﺷﻜﻞ ﻫﺎي 2و 3ﻧﺸﺎن ﻣﻲ دﻫﺪ ﺑﺮ اﺛﺮ ﺗﻐﻴﻴﺮ ﺑﺎر در ﻣﻨﺎﻃﻖ ﻛﻨﺘﺮل ،در ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎر ﺟﺪﻳﺪ ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ در
ﺷﻜﻞ) (1ﺳﻴﺴﺘﻢ ﻗﺪرت دوﻣﻨﻄﻘﻪ اي ﻛﻨﺘﺮل ﻧﺸﺪه
ﻛﻪ در ﺷﻜﻞ ﺑﺎﻻ Ttﺛﺎﺑﺖ زﻣﺎﻧﻲ ﺗﻮرﺑﻴﻦ Tgﺛﺎﺑﺖ زﻣﺎﻧﻲ ژﻧﺮاﺗﻮر
ﻣﻘﺪار ∆f 0ﺑﺎﻗﻲ ﻣﻲ ﻣﺎﻧﺪ و ﺑﻪ ﺻﻔﺮ ﻧﻤﻲ رﺳﺪ .ﻫﻤﭽﻨﻴﻦ ﻗﺪرت اﻧﺘﻘﺎﻟﻲ از
Rﺿﺮﻳﺐ ﺗﻨﻈﻴﻢ ژﻧﺮاﺗﻮر T12ﻇﺮﻳﺐ ﺳﻨﻜﺮوﻧﻴﺰاﺳﻴﻮن و T pﺛﺎﺑﺖ زﻣﺎﻧﻲ
ﻣﻨﻄﻘﻪ 1ﺑﻪ 2ﺑﻪ ﻣﻴﺰان ∆p120از ﺣﺪ ﻗﺪرت اﻧﺘﻘﺎﻟﻲ ﻣﻮرد ﺗﻮاﻓﻖ ﺑﻴﻦ دو ﻣﻨﻄﻘﻪ ﺗﺠﺎوز ﻣﻲ ﻛﻨﺪ ﺑﺮاي اﻳﻨﻜﻪ ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ و ﺗﻐﻴﻴﺮ ﻗﺪرت اﻧﺘﻘﺎﻟﻲ ﺑﻴﻦ دو ﻣﻨﻄﻘﻪ در ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎر ﺑﻪ ﺻﻔﺮ ﺑﺮﺳﺪ از ﺣﻠﻘﻪ ﻓﻴﺪﺑﻚ دوم ﺷﺎﻣﻞ اﻧﺘﮕﺮاﻟﮕﻴﺮ اﺳﺘﻔﺎده ﻣﻲ ﺷﻮد.
ﺳﻴﺴﺘﻢ ﻗﺪرت اﺳﺖ.
-2-2ﭘﺎﺳﺦ دﻳﻨﺎﻣﻴﻜﻲ ﺳﻴﺴﺘﻢ ﻗﺪرت دوﻣﻨﻄﻘﻪ اي ﻛﻨﺘﺮل ﻧﺸﺪه
ﺷﻜﻞ)(2ﭘﺎﺳﺦ ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﺳﻴﺴﺘﻢ دو ﻣﻨﻄﻘﻪ اي
437
ﺷﻜﻞ ﺑﺎﻻ ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﺳﻴﺴﺘﻢ دو ﻣﻨﻄﻘﻪ اي را ﻧﺸﺎن ﻣﻲ دﻫﺪ ﻫﻤﺎﻧﻄﻮر ﻛﻪ در ﺷﻜﻞ ﻣﺸﺨﺺ اﺳﺖ ﺑﺎ ﺑﻜﺎرﺑﺮدن اﻧﺘﮕﺮاﻟﮕﻴﺮ در ﻣﺴﻴﺮ ﻓﻴﺪﺑﻚ ﺗﻮاﻧﺴﺘﻴﻢ ﺧﻄﺎي ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎر ﺳﻴﺴﺘﻢ را ﺑﻪ ﺻﻔﺮ ﺑﺮﺳﺎﻧﻴﻢ.
ﺷﻜﻞ) (4ﺳﻴﺴﺘﻢ دو ﻣﻨﻄﻘﻪ اي ﻛﻨﺘﺮل ﺷﺪه
در ﺷﻜﻞ B ، 4ضريب گرايش فرکانس نام دارد.خطای کنترل منطقه ، ACEعبارتست از ترکيب خطی دو خطای سيستم يعنی ∆fو ∆p12که در سيستم کنترل بايد صفر گردند .در اينجا برای دو منطقه: )(5
ACE1 = ∆p12 + B1 ∆f 1
)(6
ACE 2 = ∆p 21 + B2 ∆f 2
وﺑﻨﺎﺑﺮاﻳﻦ ∆p c1و ∆p c 2ﻋﺒﺎرﺗﻨﺪ از : ) (7
∆p c1 = − ki1 ∫ ACE1 dt
)(8
∆p c 2 = −ki2 ∫ ACE 2 dt
در اﻳﻦ ﺣﺎﻟﺖ ﺑﺮاي ﺗﻌﻴﻴﻦ ﭘﺎﺳﺦ ﺳﻴﺴﺘﻢ در ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎر: ) (9 )(10
∆p120 + B1 ∆f 0 = 0 − ∆p120 + B1 ∆f 0 = 0
اﻳﻦ ﻣﻌﺎدﻻت ﻓﻘﻂ در ﺷﺮاﻳﻂ زﻳﺮ ﺑﺮﻗﺮار ﺧﻮاﻫﺪ ﺑﻮد :
ﺷﻜﻞ )(6ﺧﻄﺎي ﺗﻮان اﻧﺘﻘﺎﻟﻲ ﺑﻴﻦ دو ﻣﻨﻄﻘﻪ
∆f 0 = ∆p12 = 0 )(11 -4-2ﭘﺎﺳﺦ دﻳﻨﺎﻣﻴﻜﻲ ﺳﻴﺴﺘﻢ ﻗﺪرت دوﻣﻨﻄﻘﻪ اي ﻛﻨﺘﺮل
–3ﺳﻴﺴﺘﻢ ﻫﺎي ﻓﺎزي ﺳﻴﺴﺘﻢ ﻫﺎي ﻓﺎزي ،ﺳﻴﺴﺘﻢ ﻫﺎﻳﻲ ﻫﺴﺘﻨﺪﺑﺎ ﺗﻌﺮﻳﻒ دﻗﻴﻖ و ﻛﻨﺘﺮل ﻓﺎزي ﻧﻴﺰ ﻧﻮع ﺧﺎﺻﻲ از ﻛﻨﺘﺮل ﻏﻴﺮ ﺧﻄﻲ ﻣﻲ ﺑﺎﺷﺪ اﺳﺎﺳﺄ ﮔﺮﭼﻪ ﺳﻴﺴﺘﻢ ﻫﺎي ﻓﺎزي ﭘﺪﻳﺪه ﻫﺎي ﻏﻴﺮ ﻗﻄﻌﻲ و ﻧﺎﻣﺸﺨﺺ را ﺗﻮﺻﻴﻒ ﻣﻲ ﻛﻨﻨﺪ ،ﺑﺎ اﻳﻦ ﺣﺎل ﺧﻮد ﺗﺌﻮري ﻓﺎزي ﻳﻚ ﺗﺌﻮري دﻗﻴﻖ ﻣﻲ ﺑﺎﺷﺪ .ﺳﻴﺴﺘﻢ ﻫﺎي ﻓﺎزي اﻣﺮوزه ،در ﻃﻴﻒ وﺳﻴﻌﻲ از ﻋﻠﻮ م و ﻓﻨﻮن ﻛﺎرﺑﺮد ﭘﻴﺪا ﻛﺮده اﻧﺪ .از ﻛﻨﺘﺮل ،ﭘﺮدازش ﺳﻴﮕﻨﺎل ،ارﺗﺒﺎﻃﺎت ،ﺳﺎﺧﺖ ﻣﺪارﻫﺎي ﻣﺠﺘﻤﻊ و ﺳﻴﺴﺘﻢ ﻫﺎي ﺧﺒﺮه ﮔﺮﻓﺘﻪ ﺗﺎ ﺑﺎزرﮔﺎﻧﻲ ،ﭘﺰﺷﻜﻲ ،و ......ﺑﺎ اﻳﻦ ﺣﺎل ﺑﻪ ﻋﻨﻮان ﻳﻜﻲ از ﻣﻬﻤﺘﺮﻳﻦ ﻛﺎرﺑﺮدﻫﺎي آن ﺣﻞ ﻣﺴﺎﺋﻞ و ﻣﺸﻜﻼت ﻛﻨﺘﺮل را ﻣﻲ ﺗﻮان ﺑﻴﺎن ﻛﺮد ﺳﻴﺘﻢ ﻫﺎي ﻓﺎزي را ﻣﻲ ﺗﻮان ﺑﻪ ﻋﻨﻮان ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﺣﻠﻘﻪ ﺑﺎز و ﻳﺎ ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﺣﻠﻘﻪ ﺑﺴﺘﻪ ﻣﻮرد اﺳﺘﻔﺎده ﻗﺮار داد . ﻫﻨﮕﺎﻣﻲ ﻛﻪ ﺑﻪ ﻋﻨﻮان ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﺣﻠﻘﻪ ﺑﺎز اﺳﺘﻔﺎده ﻣﻲ ﺷﻮد ،ﺳﻴﺴﺘﻢ ﻓﺎزي ﻣﻌﻤﻮﻷ ﺑﻌﻀﻲ از ﭘﺎراﻣﺘﺮﻫﺎي ﻛﻨﺘﺮل را ﻣﻌﻴﻦ ﻛﺮده و آﻧﮕﺎه ﺳﻴﺴﺘﻢ ﻣﻄﺎﺑﻖ ﺑﺎ اﻳﻦ ﭘﺎراﻣﺘﺮﻫﺎي ﻛﻨﺘﺮل ﻛﺎر ﻣﻲ ﻛﻨﺪ .ﺑﺴﻴﺎري از ﻛﺎرﺑﺮدﻫﺎي ﺳﻴﺴﺘﻢ ﻓﺎزي در اﻟﻜﺘﺮوﻧﻴﻚ ﺑﻪ اﻳﻦ دﺳﺘﻪ ﺗﻌﻠﻖ دارﻧﺪ .ﻫﻨﮕﺎﻣﻴﻜﻪ ﻛﻪ ﺳﻴﺴﺘﻢ ﻓﺎزي ﺑﻪ ﻋﻨﻮان ﻳﻚ ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﺣﻠﻘﻪ ﺑﺴﺘﻪ اﺳﺘﻔﺎده ﻣﻲ ﺷﻮد ، در اﻳﻦ ﺣﺎﻟﺖ ﺧﺮوﺟﻲ ﻫﺎي ﻓﺮآﻳﻨﺪ را اﻧﺪازه ﮔﻴﺮي ﻛﺮده و ﺑﻪ ﻃﻮر ﻫﻤﺰﻣﺎن ﻋﻤﻠﻴﺎت ﻛﻨﺘﺮل را اﻧﺠﺎم ﻣﻲ دﻫﺪ .ﻛﺎرﺑﺮدﻫﺎي ﺳﻴﺴﺘﻢ ﻫﺎي ﻓﺎزي در ﻓﺮآﻳﻨﺪ ﻫﺎي ﺻﻨﻌﺘﻲ ﺑﻪ اﻳﻦ دﺳﺘﻪ ﺗﻌﻠﻖ دارﻧﺪ.
ﺷﺪه
ﺷﻜﻞ ) (5ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﺳﻴﺴﺘﻢ دو ﻣﻨﻄﻘﻪ اي ﻛﻨﺘﺮل ﺷﺪه
438
1-3روش ﻣﻤﺪاﻧﻲ در اﻳﻦ ﻣﻘﺎﻟﻪ 5ﭘﺎراﻣﺘﺮ ﺳﻴﺴﺘﻢ ﺗﻐﻴﻴﺮ ﻣﻲ ﻛﻨﺪ ﻛﻪ ﺑﻪ ﻋﻨﻮان ورودي
ﻫﺎي ﺳﻴﺴﺘﻢ ﻫﺎي ﻓﺎزي ﺗﻠﻘﻲ ﻣﻲ ﮔﺮدﻧﺪ .اﻳﻦ 5ﭘﺎراﻣﺘﺮ ﻋﺒﺎرﺗﻨﺪ از Tt ﺛﺎﺑﺖ زﻣﺎﻧﻲ ﺗﻮرﺑﻴﻦ k p ،ﮔﻴﻦ ﺳﻴﺴﺘﻢ ﻗﺪرت B ،ﺿﺮﻳﺐ ﮔﺮاﻳﺶ ﻓﺮﻛﺎﻧﺲ T12ﺿﺮﻳﺐ ﺳﻨﻜﺮوﻧﻴﺰاﺳﻴﻮن و T pﺛﺎﺑﺖ زﻣﺎﻧﻲ ﺳﻴﺴﺘﻢ ﻗﺪرت ﻛﻪ ﺑﺮاي 5ﭘﺎراﻣﺘﺮ ازﺗﻮاﺑﻊ ﻣﺜﻠﺜﻲ اﺳﺘﻔﺎده ﻛﺮدﻳﻢ .
ﺷﻜﻞ )(10ﺗﺎﺑﻊ ﺗﻌﻠﻖ ﺛﺎﺑﺖ زﻣﺎﻧﻲ ﺗﻮرﺑﻴﻦ
ﺷﻜﻞ ) (7ﺗﺎﺑﻊ ﺗﻌﻠﻖ ﺿﺮﻳﺐ ﺳﻨﻜﺮوﻧﻴﺰاﺳﻴﻮن
ﺷﻜﻞ ) (11ﺗﺎﺑﻊ ﺗﻌﻠﻖ ﮔﻴﻦ ﺳﻴﺴﺘﻢ ﻗﺪرت
ﺧﺮوﺟﻲ ﺳﻴﺴﺘﻢ ﻓﺎزي ﻛﻪ ﮔﻴﻦ اﻧﺘﮕﺮال ﮔﻴﺮ ﻣﻲ ﺑﺎﺷﺪ kﻧﺎﻣﻴﺪه ﺷﺪه اﺳﺖ ﻛﻪ ﺗﺎﺑﻊ ﺗﻌﻠﻖ آن در ﺷﻜﻞ زﻳﺮ ﻣﺸﺨﺺ اﺳﺖ :
ﺷﻜﻞ ) (8ﺗﺎﺑﻊ ﺗﻌﻠﻖ ﺛﺎﺑﺖ زﻣﺎﻧﻲ ﺳﻴﺴﺘﻢ ﻗﺪرت
ﺷﻜﻞ ) (12ﺗﺎﺑﻊ ﺗﻌﻠﻖ ﺧﺮوﺟﻲ
ﺷﻜﻞ)(9ﺗﺎﺑﻊ ﺗﻌﻠﻖ ﺿﺮﻳﺐ ﮔﺮاﻳﺶ ﻓﺮﻛﺎﻧﺲ
439
If (Tp is s) and (T12 is m) and (b is l) and (Tt is m) and (Kp is m) then (k is xs)
ﻗﻮاﻧﻴﻦ ﻓﺎزي2-3
If (Tp is s) and (T12 is m) and (b is l) and (Tt is m) and (Kp is l) then (k is vs))
ﺑﻪ دﻟﻴﻞ زﻳﺎد ﺑﻮدن ﻗﻮاﻧﻴﻦ از ذﻛﺮ ﺗﻤﺎﻣﻲ ﻗﻮاﻧﻴﻦ ﺧﻮدداري ﻧﻤﻮده و .ﻓﻘﻂ ﭼﻨﺪ ﻗﺎﻧﻮن را ذﻛﺮ ﻣﻲ ﻛﻨﻴﻢ
If (Tp is s) and (T12 is m) and (b is l) and (Tt is l) and (Kp is s) then (k is vs) ) If (Tp is s) and (T12 is m) and (b is l) and (Tt is l) and (Kp is m) then (k is vs) (1) If (Tp is s) and (T12 is m) and (b is l) and (Tt is l) and (Kp is l) then (k is vs) (1)
If (Tp is s) and (T12 is s) and (b is s) and (Tt is s) and (Kp is s) then (k is vm)
If (Tp is s) and (T12 is l) and (b is s) and (Tt is s) and (Kp is s) then (k is xl) (1)
If (Tp is s) and (T12 is s) and (b is s) and (Tt is s) and (Kp is m) then (k is l)
If (Tp is s) and (T12 is l) and (b is s) and (Tt is s) and (Kp is m) then (k is vl) (1)
If (Tp is s) and (T12 is s) and (b is s) and (Tt is s) and (Kp is l) then (k is xl)
If (Tp is s) and (T12 is l) and (b is s) and (Tt is s) and (Kp is l) then (k is vl) (1)
If (Tp is s) and (T12 is s) and (b is s) and (Tt is m) and (Kp is s) then (k is vm)
– ﻧﺘﺎﻳﺞ روش ﻣﻤﺪاﻧﻲ3-3
If (Tp is s) and (T12 is s) and (b is s) and (Tt is m) and (Kp is m) then (k is vm) If (Tp is s) and (T12 is s) and (b is s) and (Tt is m) and (Kp is l) then (k is vm)
در ﻧﻈﺮﮔﺮﻓﺘﻪ اﻳﻢ1 ﭘﺎراﻣﺘﺮﻫﺎي ﺳﻴﺴﺘﻢ ﻧﻤﻮﻧﻪ را ﻣﻄﺎﺑﻖ ﺟﺪول
If (Tp is s) and (T12 is s) and (b is s) and (Tt is l) and (Kp is s) then (k is m)
(1) ﺟﺪول
If (Tp is s) and (T12 is s) and (b is s) and (Tt is l) and (Kp is m) then (k is m) If (Tp is s) and (T12 is s) and (b is s) and (Tt is l) and (Kp is l) then (k is m) If (Tp is s) and (T12 is s) and (b is m) and (Tt is s) and (Kp is s) then (k is s) If (Tp is s) and (T12 is s) and (b is m) and (Tt is s) and (Kp is m) then (k is s) If (Tp is s) and (T12 is s) and (b is m) and (Tt is s) and (Kp is l) then (k is s) If (Tp is s) and (T12 is s) and (b is m) and (Tt is m) and (Kp is s) then (k is s) If (Tp is s) and (T12 is s) and (b is m) and (Tt is m) and (Kp is m) then (k is s) If (Tp is s) and (T12 is s) and (b is m) and (Tt is m) and (Kp is l) then (k is s) If (Tp is s) and (T12 is s) and (b is m) and (Tt is l) and (Kp is s) then (k is xs) If (Tp is s) and (T12 is s) and (b is m) and (Tt is l) and (Kp is m) then (k is xs If (Tp is s) and (T12 is s) and (b is m) and (Tt is l) and (Kp is l) then (k is vs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is s) and (Kp is s) then (k is xs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is s) and (Kp is m) then (k is xs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is s) and (Kp is l) then (k is vs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is m) and (Kp is s) then (k is vs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is m) and (Kp is m) then (k is vs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is m) and (Kp is l) then (k is vs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is l) and (Kp is s) then (k is vs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is l) and (Kp is m) then (k is vs) If (Tp is s) and (T12 is s) and (b is l) and (Tt is l) and (Kp is l) then (k is vs) If (Tp is s) and (T12 is m) and (b is s) and (Tt is s) and (Kp is s) then (k is xl) If (Tp is s) and (T12 is m) and (b is s) and (Tt is s) and (Kp is m) then (k is xl) If (Tp is s) and (T12 is m) and (b is s) and (Tt is s) and (Kp is l) then (k is vl) If (Tp is s) and (T12 is m) and (b is s) and (Tt is m) and (Kp is s) then (k is vm)
1 ( ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ13) ﺷﻜﻞ
If (Tp is s) and (T12 is m) and (b is s) and (Tt is m) and (Kp is m) then (k is xm) If (Tp is s) and (T12 is m) and (b is s) and (Tt is m) and (Kp is l) then (k is m) If (Tp is s) and (T12 is m) and (b is s) and (Tt is l) and (Kp is s) then (k is m) If (Tp is s) and (T12 is m) and (b is s) and (Tt is l) and (Kp is m) then (k is s) If (Tp is s) and (T12 is m) and (b is s) and (Tt is l) and (Kp is l) then (k is xs) If (Tp is s) and (T12 is m) and (b is m) and (Tt is s) and (Kp is s) then (k is xm) If (Tp is s) and (T12 is m) and (b is m) and (Tt is s) and (Kp is m) then (k is xm) If (Tp is s) and (T12 is m) and (b is m) and (Tt is s) and (Kp is l) then (k is xm) If (Tp is s) and (T12 is m) and (b is m) and (Tt is m) and (Kp is s) then (k is s) If (Tp is s) and (T12 is m) and (b is m) and (Tt is m) and (Kp is m) then (k is s If (Tp is s) and (T12 is m) and (b is m) and (Tt is m) and (Kp is l) then (k is xs) If (Tp is s) and (T12 is m) and (b is m) and (Tt is l) and (Kp is s) then (k is xs)) If (Tp is s) and (T12 is m) and (b is m) and (Tt is l) and (Kp is m) then (k is xs) If (Tp is s) and (T12 is m) and (b is m) and (Tt is l) and (Kp is l) then (k is vs)) If (Tp is s) and (T12 is m) and (b is l) and (Tt is s) and (Kp is s) then (k is s) (1) If (Tp is s) and (T12 is m) and (b is l) and (Tt is s) and (Kp is m) then (k is m) If (Tp is s) and (T12 is m) and (b is l) and (Tt is s) and (Kp is l) then (k is m) )
2 (ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ14)ﺷﻜﻞ
If (Tp is s) and (T12 is m) and (b is l) and (Tt is m) and (Kp is s) then (k is xs))
440
ﺷﻜﻞ )(15ﺧﻄﺎي ﺗﻮان اﻧﺘﻘﺎﻟﻲ ﺑﻴﻦ دو ﻣﻨﻄﻘﻪ
ﺷﻜﻞ)(18ﺧﻄﺎي ﺗﻮان اﻧﺘﻘﺎﻟﻲ ﺑﻴﻦ دو ﻣﻨﻄﻘﻪ
-4ﻣﻘﺎﻳﺴﻪ ﺳﻮﮔﻨﻮ و ﻣﻤﺪاﻧﻲ
- 4-3روش ﺳﻮﮔﻨﻮ ﺗﻮاﺑﻊ ﺗﻌﻠﻖ ورودي در اﻳﻦ ﺳﻴﺴﺘﻢ ﻓﺎزي ﻫﻤﺎﻧﻨﺪ روش ﻣﻤﺪاﻧﻲ اﺳﺖ ﺑﺎ اﻳﻦ ﺗﻔﺎوت ﻛﻪ ﻣﻘﺎدﻳﺮ ﺧﺮوﺟﻲ ﻫﺮ ﻗﺎﻧﻮن ﺑﻪ ﺻﻮرت ﺗﺮﻛﻴﺐ ﺧﻄﻲ از ورودي ﻫﺎا ﺳﺖ.
ﺷﻜﻞ)(19ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ 1
ﺷﻜﻞ )(16ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ 1
ﺷﻜﻞ)(20ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ2
-5ﻋﻤﻠﻜﺮد ﺳﻮﮔﻨﻮ و ﻣﻤﺪاﻧﻲ در ﺷﺮاﻳﻂ ﻧﺎﻣﻲ ﭘﺎراﻣﺘﺮ ﻫﺎي ﻧﺎﻣﻲ ﺳﻴﺴﺘﻢ در ﺟﺪول 2آﻣﺪه اﺳﺖ : ﺟﺪول )(2 KP=120 ﺷﻜﻞ)(17ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ 2
441
Tt=0.3
B=0.425
T12=0.545
Tp=20
ﻧﺘﻴﺠﻪ ﮔﻴﺮي-6 ﻫﺪف ﻧﻬﺎﻳﻲ ﻛﻨﺘﺮل ﺑﺎر – ﻓﺮﻛﺎﻧﺲ اﻳﺠﺎد ﺗﻌﺎدل ﺑﻴﻦ ﺗﻮﻟﻴﺪ و ﻣﺼﺮف ، ﻣﻲ ﺑﺎﺷﺪ و ﺑﻪ ﺧﺎﻃﺮ ﭘﻴﭽﻴﺪﮔﻲ و ﭼﻨﺪ ﻣﺘﻐﻴﺮه ﺑﻮدن ﺳﻴﺴﺘﻢ ﻗﺪرت روش ﻛﻨﺘﺮل ﺳﻨﺘﻲ ﻧﻤﻲ ﺗﻮاﻧﺪ راه ﺣﻞ ﻣﻨﺎﺳﺒﻲ ﺑﺎﺷﺪ ﺑﻪ ﻫﻤﻴﻦ ﺧﺎﻃﺮ ﻧﺘﺎﻳﺞ.ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﻫﺎي ﻣﻘﺎوم و ﻫﻮﺷﻤﻨﺪ ﻣﻮرد اﺳﺘﻔﺎده ﻗﺮار ﻣﻲ ﮔﻴﺮﻧﺪ ﻧﺸﺎن داده ﺷﺪه در ﺷﻜﻞ ﻫﺎ ﺣﺎﻛﻲ از اﻳﻦ اﺳﺖ ﻛﻪ ﺑﺎ ﺟﺎﻳﮕﺰﻳﻨﻲ ﻧﺘﺮل ﻛﻨﻨﺪه ﻓﺎزي در ﺷﺮاﻳﻄﻲ ﻛﻪ ﭘﺎراﻣﺘﺮﻫﺎي ﺳﻴﺴﺘﻢ ﺑﺪون ﺗﻐﻴﻴﺮ ﺑﻤﺎﻧﺪ ﻣﺎﻧﻨﺪ ﻛﻨﺘﺮل ﻛﻨﻨﺪه اﻧﺘﮕﺮاﻟﮕﻴﺮ ﻛﻼﺳﻴﻚ ﺟﻮاب ﺧﻮﺑﻲ ﺧﻮاﻫﺪ داد وﻟﻲ در ﺻﻮرﺗﻲ ﻛﻪ ﭘﺎراﻣﺘﺮﻫﺎي ﺳﻴﺴﺘﻢ ﺑﻨﺎ ﺑﺮ ﻫﺮ ﻋﻠﺘﻲ ﺗﻐﻴﻴﺮ ﻧﻤﺎﻳﺪ ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﻓﺎزي اﻳﻦ ﺗﻐﻴﻴﺮات را ﻟﺤﺎظ ﻛﺮده و ﺿﻤﻦ ﺻﻔﺮ ﻛﺮدن ﺧﻄﺎي ﺣﺎﻟﺖ ﺑﺎ ﻣﻘﺎﻳﺴﻪ ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ ﺷﺪه از. داﺋﻤﻲ ﭘﺎﺳﺦ ﮔﺬراي ﺧﻮﺑﻲ ﺧﻮاﻫﺪ داد روش ﻫﺎي ﻣﻤﺪاﻧﻲ و ﺳﻮﮔﻨﻮ ﻧﺸﺎن ﻣﻲ دﻫﺪ ﻛﻪ روش ﻣﻤﺪاﻧﻲ ﺗﻘﺮﻳﺒﺄ ﺳﺮﻳﻌﺘﺮ از روش ﺳﻮﮔﻨﻮ اﺳﺖ ﻛﻪ اﻳﻦ ﻧﺘﻴﺠﻪ ﺣﺎﻛﻲ از اﻳﻦ اﺳﺖ ﻛﻪ ﺧﺮوﺟﻲ ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﻣﻤﺪاﻧﻲ ﻛﻪ ﮔﻴﻦ اﻧﺘﮕﺮاﻟﮕﻴﺮ اﺳﺖ اﻧﺪازه ﺑﺰرﮔﺘﺮي ﻧﺴﺒﺖ ﺑﻪ ﺧﺮوﺟﻲ ﻛﻨﺘﺮل ﻛﻨﻨﺪه ﺳﻮﮔﻨﻮ دارد ﻛﻪ اﺧﺘﻼف ﻧﺎﺷﻲ از روش .ﻫﺎي ﻧﺎﻓﺎزي ﺳﺎز اﺳﺖ
در ﺷﺮاﻳﻂ ﻧﺎﻣﻲ1 ( ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ21)ﺷﻜﻞ
ﻣﺮاﺟﻊ-7 [1] Grul Ertu “A fuzzy gain scheduling PI controller application for an interconnection power system’’Electric power system Research(2005) [2] Ashraf Mohamad Hemeida“Wavelet neural network load frequency controller’’Energy Conversion and management2005 [3] Ahmed M. Kassem’’Neural predictive controller of a two-area load frequency control for interconnected power system’’Control Technology Dep., Industrial Education College,Peni-Suef Received 17 April 2010; accepted 6 May 2010 [4] Venkata.B ,Jayaram Kumar’’Robust Fuzzy Load frequency Controller For Two Area Interconnected Power System’’Journal of Theoretical and Applied informationTechnology2005-2009 [5]Grul،Ertu،ilhan،kocaarslan“ A fuzzy gain scheduling PI
در ﺷﺮاﻳﻂ ﻧﺎﻣﻲ2 ( ﺧﻄﺎي ﻓﺮﻛﺎﻧﺲ ﻣﻨﻄﻘﻪ22) ﺷﻜﻞ
controller application for an interconnected electrical power system’’Electric Power System Research2005 [6] Atre.A، Patile.Y.R’’Two Area Load Frequency Control with Fuzzy Gain Scheduling of PI’’emerging Trends in Engineering and Technology, 2008. ICETET [7] Lee Jae Ho، park Bae Jin’’Robust Load Frequency Control for uncertain nonlinear power system:A fuzzy logic approach’’nformation Sciences 176 (2006) 3520– 3537
( ﺧﻄﺎي ﺗﻮان اﻧﺘﻘﺎﻟﻲ در ﺷﺮاﻳﻂ ﻧﺎﻣﻲ23)ﺷﻜﻞ
442
