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Recent Advances in Robust Control Theory and Applications in Robotics and Electromechanics Part 7

Tham khảo tài liệu 'recent advances in robust control theory and applications in robotics and electromechanics part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modelling of Bound Estimation Laws and Robust Controllers for Robot Manipulators Using Functions and Integration Techniques 169 p t 1 p t 2 P t p J 1YTodt 1 p1 a1 2a fyCt arctan eJ a t 1 1 e 2 1 J Y odt 1 J 2YTodt 2 p2 2 e 2a fYT dtk arctan eJ o t 2 1 e 2 2 JY odt 2 P2 C eJ pYTOdt p e p a ------ F-7T- p p 1 e 2 pJYTodt p arctan eJ pY odt p If p 0 p is taken as initial condition constant C is estimation law for the uncertainty bound is derived as. p t 1 p t 2 p t p Pp J 1YTodt 1 p1 . T 1 e 2 1 J YTodt 1 J 2 YT odt 2 P2 A f T . 2 1 e 2 2 J d . eJ pYTodt p a e ------ p 1 e J yT odt p 32 equivalent to -arctan 1 . So the J 1YTơdt 1 p2 1 1 Z jZt 1arctan e odt 1 J 2YTơdt 2 p22 2 -2 íytL arctan eJ 2Y 1 e 2 2 J Y odt 2 P2 - arctan 1 J 1YTodt 1 P1 1 e 2 1 J YTodt 1 J 2YT odt 2 p2 A 2 1 e2 2 J Yodụ 33 i YTodt eJ p p J pYTodt p ------- . _ . arctanle1 p p 1 e 2ar J YT dt p 2.3 Third choice of O t 1 For the third derivation of p t O t -1 is defined as L pp J eJ pYT dt p p e r ------- p 1 e 2ar J YT dt p O t 1 diag PiSin2 ai J YTodt iCos ai J YTodt i 34 Substitution of Equation 34 into Equation 23 yields p t 1 p t 2 p t p P1Sin2 1 J Yt odt 1Cos 1 J YT odt 1 Yĩ a 1 r P11 O t -1f J P2Sin2 2 JYtodt 2Cos 2 JYTodt 2 YTa 2 dt PpSin2 p J Yt odt pCos p J YT odt p YTơ p _ pp J 1 35 O t -1C 1 After integration the result is 170 Recent Advances in Robust Control - Theory and Applications in Robotics and Electromechanics P t 1 P t 2 P t p t -1 Sin3 a1 YTodt 1 fi1 7 -------1 Sin3 72 f YTOdt 2 fi2 7 2 ---- 3--------- Sin3 a fYT odt fip 7p ------------- P1 1 P2 . t -1C 1 n Pp . 1 _ 36 If p 0 p is taken as initial condition constant C is equivalent to zero. So the estimation law for the uncertainty bound is derived as . p t 1 p t 2 Sin5 a1 f YTodt 1Cos a1 f YTodt 1 fii 7 ---------------3-------------- Sin5 a2 f YTodt 2Cos a2 f YTodt 2 fi2 72 ----------------- ----------1 Pl P2 37 3 p t p r. Sin5 ap fYTodt Cos ap fYTodt fi2 7p --------------- p pj-------------p Pp 3 If we substitute I i and p t