ردﯾﺎﺑﯽ زﻣﺎن-ﻣﺤﺪود ﻣﻘﺎوم دﺳﺘﻪاي از ﺳﯿﺴﺘﻢﻫﺎي ﻏﯿﺮﺧﻄﯽ ﮐﺎرﺑﺮدي ﻣﺘﺸﮑﻞ از زﯾﺮﺳﯿﺴﺘﻢﻫﺎي ﻣﺘﺼﻞ دواﻧﺘﮕﺮالﮔﯿﺮه ﻣﻄﺎﻟﻌﻪ ﻣﻮردي: ﺑﺎزوي رﺑﺎت

Robust Finite-Time Tracking for a Class of Nonlinear Systems Comprising Interconnected Double Integrator Subsystems (Case study:Robot Manipulator)

ﭼﮑﯿﺪه در اﯾﻦ ﻣﻘﺎﻟﻪ، ﻣﺴﺌﻠﻪي ردﯾﺎﺑﯽ زﻣﺎن-ﻣﺤﺪود ﻣﻘﺎوم دﺳﺘﻪاي از ﺳﯿﺴﺘﻢﻫﺎي ﻏﯿﺮﺧﻄﯽ ﻣﺘﺸﮑﻞ از زﯾﺮﺳﯿﺴﺘﻢﻫﺎي ﻣﺘﺼﻞ دواﻧﺘﮕﺮالﮔﯿﺮه ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار ﻣﯽﮔﯿﺮد. اﯾﻦ دﺳﺘﻪي ﺧﺎص از ﺳﯿﺴﺘﻢﻫﺎي ﻏﯿﺮﺧﻄﯽ، ﻗﺎﺑﻠﯿﺖ ﺗﻮﺻﯿﻒ ﺗﻌﺪادي از دﺳﺘﮕﺎهﻫﺎي ﻋﻤﻠﯽ از ﺟﻤﻠﻪ رﺑﺎتﻫﺎي ﺻﻨﻌﺘﯽ اﯾﺴﺘﺎ، وﺳﺎﯾﻞ درﯾﺎﯾﯽ و زﯾﺮدرﯾﺎﯾﯽ ﺧﻮدﮐﺎر، وﺳﺎﯾﻞ ﭘﺮﻧﺪهي ﺑﺪون ﺳﺮﻧﺸﯿﻦ و ﭘﺎﻧﺪول ﻣﻌﮑﻮس را دارد. ﺑﺎ ﺗﻌﻤﯿﻢ روش ﮐﻨﺘﺮل ﻣﺪ ﻟﻐﺰﺷﯽ ﺗﺮﻣﯿﻨﺎل و ﺗﻌﺮﯾﻒ ﺧﻤﯿﻨﻪﻫﺎي ﻟﻐﺰﺷﯽ ﻏﯿﺮﺧﻄﯽ اﺑﺘﮑﺎري، وروديﻫﺎي ﮐﻨﺘﺮﻟﯽ ﺑﻪ ﮔﻮﻧﻪاي ﻃﺮاﺣﯽ ﻣﯽﺷﻮﻧﺪ ﮐﻪ ﻣﺪل دﯾﻨﺎﻣﯿﮑﯽ ﺳﯿﺴﺘﻢ ﻣﺬﮐﻮر ﺑﻪ ﻓﺮم ﺳﯿﺴﺘﻢ ﻏﯿﺮﺧﻄﯽ ﮐﺎﻧﻮﻧﯿﮑﺎل ﺗﺒﺪﯾﻞ ﺷﺪه و ﻫﺪف ردﯾﺎﺑﯽ زﻣﺎن-ﻣﺤﺪود ﺑﺮآورده ﮔﺮدد. راهﮐﺎر ﮐﻨﺘﺮﻟﯽ ﭘﯿﺸﻨﻬﺎدي، ﭘﺎﯾﺪاري زﻣﺎن-ﻣﺤﺪود ﮐﻠّﯽ ﺳﯿﺴﺘﻢ ﻏﯿﺮﺧﻄﯽ ﺣﻠﻘﻪﺑﺴﺘﻪ را در ﺣﻀﻮر اﻏﺘﺸﺎش و ﻧﺎﻣﻌﯿﻨﯽ ﮐﺮاﻧﺪار و ﻏﯿﺮﮐﺮاﻧﺪار ﺗﻀﻤﯿﻦ ﻣﯽﮐﻨﺪ. ﻋﻼوه ﺑﺮاﯾﻦ، راﺑﻄﻪاي ﺑﺮاي ﺗﺨﻤﯿﻦ زﻣﺎن ﻣﺤﺪود ﻫﻤﮕﺮاﯾﯽ ﻣﺘﻐﯿﺮﻫﺎي ﺣﺎﻟﺖ ﺳﯿﺴﺘﻢ ﺑﻪ ﻣﺴﯿﺮﻫﺎي ﻣﻄﻠﻮب اﺳﺘﺨﺮاج ﻣﯽﮔﺮدد. راﺑﻄﻪي ﻣﺬﮐﻮر ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ ﺳﺮﻋﺖ ﻫﻤﮕﺮاﯾﯽ در ﻣﺴﺌﻠﻪ ردﯾﺎﺑﯽ، واﺑﺴﺘﮕﯽ ﺷﺪﯾﺪي ﺑﻪ ﭘﺎراﻣﺘﺮﻫﺎي اﺧﺘﯿﺎري ﻣﻮﺟﻮد در وروديﻫﺎي ﮐﻨﺘﺮﻟﯽ دارد. در اﻧﺘﻬﺎي ﻣﻘﺎﻟﻪ، ﺑﻪ ﻋﻨﻮان ﻣﻄﺎﻟﻌﻪ ﻣﻮردي، ﻃﺮح ﮐﻨﺘﺮﻟﯽ اراﺋﻪ ﺷﺪه ﺑﺮ روي رﺑﺎت داراي دو ﻟﯿﻨﮏ ﻣﻮرد ﺷﺒﯿﻪﺳﺎزي ﮐﺎﻣﭙﯿﻮﺗﺮي ﻗﺮار ﮔﺮﻓﺘﻪ و ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽدﻫﻨﺪ ﮐﻪ وروديﻫﺎي ﮐﻨﺘﺮﻟﯽ ﻏﯿﺮﺧﻄﯽ ﺑﻪ ﺧﻮﺑﯽ ﻗﺎدر ﺑﻪ ﺑﺮآورده ﺳﺎﺧﺘﻦ ﻫﺪف ردﯾﺎﺑﯽ زﻣﺎن-ﻣﺤﺪود ﻫﺴﺘﻨﺪ.

In this paper, the robust finite-time tracking for a class of nonlinear systems comprising interconnected double integrator subsystems is discussed. This particular class of nonlinear systems is able to describe and model a group of practical plants such as industrial robot manipulators, autonomous underwater vehicles (AUVs), autonomous marine vessels, unmanned aerial vehicles (UAVs), and inverted pendulums. By developing the nonsingular terminal sliding mode control (NTSMC) method and defining innovative nonlinear sliding manifolds, control inputs are designed in order to convert the aforementioned system to the canonical nonlinear form and, in consequence, two significant goals including the finite-time tracking objective and the global finite-time stabilization of the closed-loop system (subjected to unbounded disturbances and uncertainties) are provided and guaranteed. Furthermore, a remarkable relation is derived to estimate the convergence finite time regarding the mentioned tracking problem. This relation reveals that the convergence finite time extremely depends on the values of arbitrary constants of the designed control inputs. Finally, the proposed robust control scheme is numerically simulated onto two-link robot manipulator and simulation results illustrate that the designed control inputs properly fulfill the finite-time tracking objective