ࡱ > m o l q q [ R bjbj ΐ ΐ ? t t $ P ! \ +b \ " $ $ $ $ ' ' ' >a @a @a @a @a @a @a $ d )g V da * x' |' * * da $ $ a ; ; ; * $ l $ >a ; * >a ; ; J d t , 8L $ V 7 8K *a a 0 +b LK g r9 g ( 8L 8L g L \ ' L ' 6 ; ( , .( ' ' ' da da : ' ' ' +b * * * * g ' ' ' ' ' ' ' ' ' t : WNޏ~S_idd!jWvvAm5u:g pbReP^c6R H=NT1 , 2 Y^R3 c/cPN3 ( 1 . -N*]NёWWSN:g5umS]zxvz-N_WSN 2 1 1 1 0 6 2 . -N*]N*zz:g5u|~~T*zzyb͑p[[WSN 2 1 1 1 0 6 3 . WSNt]'Yf[ :gh]zf[bWSN 2 1 0 0 9 4 ) XdiddT*g^!jR`/f5u:g:O g|~nfMX[(Wv^~'`[ُNNvqvAm5u:g:Nxvz[a^zNS+Tޏ~S_idd!jWv|~!jWǏ[*g^!jR`v NLuۏL^0ONpbRePhSyۏ NekǑ(uWNcNvSpeVR_hVNWNcNScN[pev!jWePyMNON|~ߍ*'`[KmϑjVXvOea^Ǒ(uL y a p u n o v Qpef3z['`Nw[k~gNc6RhV[NiddTpbRwQ g}Y0WePHeg0 sQ.͋vAm5u:g ޏ~S_idd!jW*g^!jR`^c6RWNcNvSpe^ -NVR{|ST P 3 9 1 e.sh_xA C o n t i n u o u s l y - d i f f e r e n t i a b l e - f r i c t i o n - m o d e l - b a s e d a d a p t i v e c o n t r o l o f D C m o t o r s w i t h d i s t u r b a n ce compensation Chen Lijun1,2, Yao Jianyong3, Dong Zhenle3 (1. Nanjing Engineering Institute of Aircraft Systems, AVIC Jincheng, Nanjing 211106, China; 2. Aviation Key Laboratory of Science and Technology on Aero Electromechanical System Integration, Nanjing 211106, China; 3. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China) Abstract: Friction and unmodeled dynamics are common nonlinearities existing in motor servo systems. For these problems, by taking direct-drive dc motor for instance, the mathematic model concluding a continuously differentiable friction model is conducted. The bound of the unmodeled dynamics is estimated and the robust disturbances compensation term is designed. Furthermore, a trajectory-based regressor is adopted and the model-based compensation term is designed based on the trajectory and the derivatives of trajectory, which can reduce the noise sensitivity. The stability is proved via the Lyapunov analysis. Simulation results illustr a t e t h a t t h e p r o p o s e d a p p r o a c h c a n c o m p e n s a t e t h e f r i c t i o n a n d d i s t u r b a n c e s w e l l . K e y w o r d s : d c m o t o r c o n t i n u o u s l y d i f f e r e n t i a b l e f r i c t i o n m o d e l ; u n m o d e l e d d y n a m i c s d i s t u r b a n c e c o m p e n s a t i o n ; t r a j e c t o r y - b a s e d p a r a m e t r i c a d a p t a t i o n 0 _ ؚ|^ЏRc6R(W]NW g'Yϑ BlOY:g^[ 1 ] 0lS[ 2 ] 0KmՋY[ 3 ] I{(WُKN-NvqvAm5u:gV:NSNMQ[ߍ*'`vq_TfN[sؚTؚR^NwQ g}Yv~'`5uAmlwyr'`f_0R^l^(u[ 4 - 5 ] 06q5u:g:O g|~X[(WYv!jW Nnx['`SbSpe Nnx['`Y5ulXv0)n^Sx_cSSviddyr'`SpeI{ T Nnx[^~'`Y*g^!jYr^pb0^~'`iddI{ ُN!jW Nnx['`vX[(W~c6RhVv&^eg_'Y^0 idd/f:g5u:O g|~-N gnfMv N{|^~'`saiddeP8^(uvidd!jW;N g^&Oidd!jW[ 6 ] 0|'`idd!jW[ 2 ] 0L u G r e idd!jW[ 3 ] I{vQ-NL u G r e idd!jW1uNYc'YYpeviddL:NOYS t r i b e c k He^0iddߏn09_'|yr'`I{ VdkO(u g:N^l6qL u G r e !jW_NX[(WY NHQL u G r e !jWv!jWSpev^0O_:N YBgvQ!kS_|~ؚЏLe!jWQR`kSb_ϑvKmǏzf1Y3z[ 5 ] dkYL u G r e !jWv Nޏ~yr'`~O_[E^(uX[(W N[P6RُN~iddeP&^egNΘi0e.s[ 7 ] -NcQ Nyޏ~S_idd!jW!jW NNKQ gNL u G r e !jW NTeSN}Y0Wh'YYpeiddsaVdk_0RNY\Ջ[ 4 - 5 ] 0 *g^!jR`Yr^pb0*g^!jiddI{ _N/fq_T|~ߍ*'`v͑V }[dk{|8^(uvel gn[ 1 ] 0^y~Q~[ 8 ] I{6qnc6R-N Nޏ~Qpef bc6Rϑb/c%N͑efoR|~ؚR`^y~Q~{ϑ'Y N[z^ NP6RN|~vT^^0e.s[ 8 ] cQ NyWNr^pb NLu0OvpbRePV{eu0O_-NǑ(uޏ~vSfckRQpeMQNc6Rϑvb/cN~QN}Yv3z['`fǏz0 ,geWNe.s[ 7 ] -Nޏ~S_idd!jWۏLiddePxvz~Te.s[ 8 ] -NvpbRePV{euTe:NNMNOKmϑjVX[|~'`vq_Tۏ NekTe.s[ 6 ] -NO(uWNcNvSpeVR_hVv^V{eucQ NyeWv5u:g:O g|~MOnߍ*c6RV{euv^ǏNwNc6RhVv gHe'`0 1 cSpef[!jW E M B E D V i s i o . D r a w i n g . 1 1 V1 vqvAm5u:g:O g|~St:yaV ,ge@bQvqvAm5u:g:O g|~StVYV1 @b:y1u:O gqRhVqR5u:gvc&^R`'`}ZPelЏR01uN|~5ulRT^^ؚN:ghREe,ge^!je\_eu5uAmsR`[ 6 ] 9hnc[r,{N[_|~RRf[ez:N E M B E D E q u a t i o n . D S M T 4 ( 1 ) _-Nm :N`'`}k i :N5uSRw8^pe:N*g^!jr^pbyF f ( E M B E D E q u a t i o n . D S M T 4 ) :N^~'`iddyvQwQSOb__YN E M B E D E q u a t i o n . D S M T 4 ( 2 ) _-NvQ-Nr 1 , r 2 , r 3 :Nh_iddyr'`vCg͑VP[s 1 , s 2 , s 3 :Nh_ NTiddRvb_rVP[0ޏ~idd!jWSN}Yv<я|~NOЏRevS t r i b e c k He^0iddyr'`Cg͑VP[SǏiddƋSe.s[ 5 ] -N~QN~0WSpeƋǏz0 [INr`Sϑx = [ x 1 , x 2 ] T = [ y , E M B E D E q u a t i o n . D S M T 4 ] T RRRf[ezlS:N E M B E D E q u a t i o n . D S M T 4 ( 3 ) _-N1 = m / k i 2 = r 1 / k i 3 = r 2 / k i 3 = r 3 / k i f 1 ( x 2 ) = t a n h ( s 1 x 2 ) - t a n h ( s 2 x 2 ) f 2 ( x 2 ) = t a n h ( s 3 x 2 ) d = / k i 0 (Wc6RhVKNMRHQ\ONNGPeS^~'`yd ( t ) gLuFO NLu*gwsSn E M B E D E q u a t i o n . D S M T 4 vQ-ND :N*gw8^pe0 2 c6RhV [INYNRSϑ E M B E D E q u a t i o n . D S M T 4 ( 4 ) _-Nx 1 d :NMOnߍ*cNz 1 = x 1 - x 1 d :N|~ߍ*]k 1 :NckvSXvz 2 :NR]ϑ01uz 2 v[INSwYgz 2 _\bяN1uNG ( s ) = z 1 ( s ) / z 2 ( s ) = 1 / ( s + k 1 ) /f3z[vHNߍ*]z 1 _N\_\bяN0 ~T( 3 ) _T( 4 ) _S_ E M B E D E q u a t i o n . D S M T 4 ( 5 ) _-N E M B E D E q u a t i o n . D S M T 4 ( 6 ) [N( 6 ) _1u-N