Tham khảo tài liệu 'adaptive control design and analysis part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 422 Chapter 9 Multivariable Adaptive Control for p G 0 where p sifUndAd. From - we have V er t o f e t - 2ơ í tr 0 i SKj 0r t M M 2 5 ei 0i 2 .Í 52 ei9i i l 2 1 for any p E 0 z . From and we have o t tr Ỗ í J 0T í 0 lim cr í tr 0 i SK 07 i oo. Hence we conclude that 0 t G L and e t G L and satisfies . From it follows that m i ai ỗi e áo t tễ t IICỈ7- Jo for some constant 0-1 0. From we obtain u t Gõ1 - d t - zAm s u t . From we can express Wi i as W1G ylyơõ s - d t - z Aro s u i . i k 8 2YI3 J From it follows that II Ạ Am s tz í Ci2m t for some constant a2 0. From and with we derive w t a3 w1 i tz4 gũa5m t ae a2a3p a5g0 ổi e ỉo í-T U T II dr Ja for some constants di 0 i 3 . 6. Using the Bellman-Gronwall lemma Lemma also see in the proof of Lemma we obtain tí i II a6 a6 e- o t-T a2a3M 08ffo ii t-T dr Jo Hence u t is bounded if a aM Osgo a2a3p Ci5 7o 5i 5o where p g li dA d as defined form . The condition is satisfied for g0 G 0 On where git . au v 5 O7 ao aaaamindÀod asgiPi Model Reference Adaptive Control 423 When d t 0 and 0 in we have 2eT t i d t - Kpfco ỉ e i M II -2 EkotteWi doi sat ie t i ef 0 i i 0i 2eT i íi w ỉ - pỡo e t m í M .Is .I -2 E5o 4ie t iAOi sat ie t jm t i m t 0 i i s0i see and so that from and we obtain V -er i o e i 0 that is e t e Lz so that with ẽ t e L c t 0. V When d t 0 and zATO s 0 the design parameter ko 0 can be arbitrary while the design parameter go needs to satisfy 0 go go In the SISO case see Section that is when M 1 we can choose ST signup Do Mo Aoi where Sp 0 is the lower bound for kp . In this case the plant observability index is equal to the plant order m s is any stable polynomial of degree 1 and s in is sign fcp . Remark The limit case of the design - with j 0 i 1 . M is presented as .
