ﻃﺮاﺣﯽ رؤﯾﺘﮕﺮ ﺗﻄﺒﯿﻘﯽ ﭘﯿﺶ ﺑﯿﻦ ﺑﺮاي ﺳﯿﺴﺘﻢ ﻫﺎي داراي ﺗﺄﺧﯿﺮ ﻫﻢ زﻣﺎن در ورودي و ﺣﺎﻟﺖ ﻫﻤﺮاه ﺑﺎ ﻧﺎﻣﻌﯿﻨﯽ

Design of Predictive Adaptive Observer for Systems with Simultaneous Input and State Delays with Uncertainty

ﭼﮑﯿﺪه: در اﯾﻦ ﻣﻘﺎﻟﻪ، ﺟﺒﺮان ﺳﺎزي ﺗﺄﺧﯿﺮ ﺑﺮاي ﯾﮏ ﺳﯿﺴﺘﻢ داراي ﺗﺄﺧﯿﺮ ﻫﻢ زﻣﺎن در ﺣﺎﻟﺖ و ورودي ﻫﻤﺮاه ﺑﺎ ﻧﺎﻣﻌﯿﻨﯽ ﺑﺎ رؤﯾﺘﮕﺮ ﺗﻄﺒﯿﻘﯽ ﺑﺮرﺳﯽ ﻣﯽ ﺷﻮد. ﺑﺮاي ﭘﯿﺶ ﺑﯿﻨﯽ دﻗﯿﻖ ﺑﺎوﺟﻮد ﻋﺒﺎرت ﻧﺎﻣﻌﻠﻮم، اﺑﺘﺪا ﯾﮏ رؤﯾﺘﮕﺮ ﺗﻄﺒﯿﻘﯽ ﺑﺮاي ﺳﯿﺴﺘﻢ ﻃﺮاﺣﯽ ﻣﯽ ﺷﻮد. ﻧﺎﻣﻌﯿﻨﯽ ﺳﯿﺴﺘﻢ ﻫﻤﺮاه ﺑﺎ ﺗﺄﺧﯿﺮ ﻣﺘﻐﯿﺮ ﺑﺎزﻣﺎن ﺑﺎ ﯾﮏ ﺗﺎﺑﻊ ﻣﺤﺪودﺷﺪه ﮐﻪ ﻧﯿﺎز ﻧﯿﺴﺖ ﻣﻘﺪار ﺗﺄﺧﯿﺮ و ﺣﺪ ﺑﺎﻻي ﻧﺎﻣﻌﯿﻨﯽ ﺑﺮاي ﻃﺮاﺣﯽ ﻣﻌﻠﻮم ﺑﺎﺷﺪ. ﺳﭙﺲ رؤﯾﺘﮕﺮ دوم ﺑﻪ ﻣﻨﻈﻮر ﺟﺒﺮان ﺳﺎزي ﺗﺄﺧﯿﺮ ﻫﻢ زﻣﺎن در ﺣﺎﻟﺖ و ورودي ﻣﻌﺮﻓﯽ ﻣﯽ ﺷﻮد ﮐﻪ ﺗﺄﺧﯿﺮ در ورودي ﺑﻪ ﺻﻮرت اﺧﺘﯿﺎري ﻣﯽ ﺗﻮاﻧﺪ ﺑﺰرگ ﺗﺮ از ﺗﺄﺧﯿﺮ در ﺣﺎﻟﺖ ﺑﺎﺷﺪ. ﻣﺰﯾﺖ اﯾﻦ روش اﯾﻦ اﺳﺖ ﮐﻪ ﺑﺮاي ﺟﺒﺮان ﺗﺄﺧﯿﺮ در ورودي در ﺳﯿﺴﺘﻢ ﻧﺎﻣﻌﯿﻦ، از ﺣﻞ ﻋﺪدي اﺳﺘﻔﺎده ﻧﻤﯽ ﮐﻨﺪ. ﺑﺎ اﺳﺘﻔﺎده از ﺗﺌﻮري ﻟﯿﺎﭘﺎﻧﻮف اﺛﺒﺎت ﻣﯽ ﮔﺮدد ﮐﻪ ﺑﺎ رؤﯾﺘﮕﺮﻫﺎي ﻃﺮاﺣﯽ ﺷﺪه، ﺗﺄﺧﯿﺮ در ورودي ﺳﯿﺴﺘﻢ داراي ﻧﺎﻣﻌﯿﻨﯽ ﻏﯿﺮﺧﻄﯽ ﺑﻪ ﺧﻮﺑﯽ ﺟﺒﺮان ﺳﺎزي ﺷﺪه و ﺧﻄﺎي ﺗﺨﻤﯿﻦ ﻣﺤﺪود و ﮐﻮﭼﮏ ﺧﻮاﻫﺪ ﺑﻮد. ﻣﺰﯾﺖ و ﮐﺎراﯾﯽ روش ﭘﯿﺸﻨﻬﺎدي ﺑﺎ ﯾﮏ ﻣﺜﺎل ﻋﺪدي ﻧﺸﺎن داده ﻣﯽﺷﻮد.

In this paper, a delay compensation for a class of unknown systems with simultaneous state and input delays through the predictive adaptive observer is investigated. Despite the unknown term, an adaptive state observer is designed to have an exact prediction. The upper bounds of uncertainty with time varying delay are considered unknown, which do not require to be known for the design. Then, the second observer is introduced for simultaneous delay compensation in state and input that input delay can be optionally longer than the delay in the state. Besides, in this approach, the numerical solution is not implied for delay compensation of input in uncertainty system. Based on Lyapunov theory, it has been proved, the input delay in systems with the unknown term can compensate by means of designed observers, while the estimation error is small and bounded. For more details, we also show a numerical example that indicates the proposed approaches’ impact.