tailieunhanh - Advances in Robot Manipulators Part 2

Tham khảo tài liệu 'advances in robot manipulators part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 32 Advances in Robot Manipulators u 6k Ord h p 16 where h is an estimate of h . Substituting 16 into 8 we may have the system dynamics x p A m x p B m t d T d B p h - h 17 Together with 9 we may have the error dynamics e m A m e m B p h - h 18 er C m e m 19 If we may design an appropriate update law such that h h then 18 implies e m 0 as t n . This further implies T T d as t n . Since D C g and h are functions of time traditional adaptive controllers are not directly applicable. To design the update laws let us apply the function approximation representation15 21 D WD Zd sD C wp ZC sC g wTZg Sg h wT Zh Eh where Wd G np xn Wc G 2pCxn Wg G nPg xn and Wh G WPh xn are weighting matrices ZD G ffl1 Pdxn ZC G n Pcxn Zg G Pe and Zh G nPhx1 are matrices of basis functions and s . are approximation error matrices. The number jB . represents the number of basis functions used. Using the same set of basis functions the corresponding estimates can also be represented as D Wdt Zd g WT Zg C WT zc h wT Zh 20b Define W . W . W . then equation 15 and 18 becomes Ds Cs K d s T T d WD ZDv VT ZC v WT Z s1 21 D g g 33 A Regressor-free Adaptive Control for Flexible-joint Robots based on Function Approximation Technique é A e -B WTZ B E m mm p hh p 2 22 where E1 E1 E D E C E g s q d and E 2 E 2 E h e m are lumped approximation errors. Since Wo are constant vectors their update laws can be easily found by proper selection of the Lyapunov-like function. Let us consider a candidate 1 V s e m Wd Wc Wg Wh 1 sT Ds eTm P e m 1 23 I - Tr WT Q W WT . WT Q w WT Q W 2 1 DqD D CQC C g Qg g h Qh h where P PT G 2 x2 is a positive definite matrix satisfying the Lyapunov equation AmP PAm -CTmCm . The matrices Qd G npx 2pD Qc G n Pcx 2pc Qg G Pg Pg and Qh G i V P nPh are positive definite. The notation Tr . denotes the trace operation of matrices. The time derivative of V along the trajectory of 21 and 22 can be computed as V sT Ds 1 sT Ds eT Pe eT Pem 2 m t m m t m - Tr WTQ W WTOAV WTQW WTOAV r DqD D .

TỪ KHÓA LIÊN QUAN
crossorigin="anonymous">
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.