tailieunhanh - RECENT ADVANCES IN ROBUST CONTROL – NOVEL APPROACHES AND DESIGN METHODSE Part 9

Tham khảo tài liệu 'recent advances in robust control – novel approaches and design methodse part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | New Practical Integral Variable Structure Controllers for Uncertain Nonlinear Systems 229 V x xTPx P 0 43 The derivative of 43 becomes V x xT f x t TP Pf0 x t x u g x t Px xTPgo x t u 44 By means of the Lyapunov control theory Khalil 1996 take the control input as u -gT x t Py -Bly 45 and Q x t 0 and Q. x t 0 for all x e Rn and all t 0 is fT x t P Pf0 x t -Q x t 46 fT x t P PfOc x t -Qc x t 47 then 3 x -xTQ x t x - xTCTPBBTPx - xTPBBTPCx -xT Q x t CTPBBTP PBBTPC x -xT fl x t P Pf0c x t x 48 -xTQc_ x t x - - . Q x t x Therefore the stable gain is chosen as G y BTP or II CB Hfiffx t 49 Output feedback discontinuous control input A corresponding output feedback discontinuous control input is proposed as follows U0 -G y y - AGy - G - G1Sign S0 50 where G y is a nonlinear output feedback gain satisfying the relationship 37 and 49 AG is a switching gain of the state G1 is a feedback gain of the output feedback integral sliding surface and G2 is a switching gain respectively as AG Agi i 1 . q 51 f max H1CB -1 H1CAf Al H1CBỴ Hf x t ----------------------------------------------- sign S0y 0 min l Al Ag J - A 52 min H1CB -1 H Af Al HlCB -Hf x t c . n ------------------------------------------------ sign S0y 0 min l Al G1 0 53 230 Recent Advances in Robust Control - Novel Approaches and Design Methods max d x t min A 55 The real sliding dynamics by the proposed control 50 with the output feedback integral sliding surface 35 is obtained as follows So H1CB H1ỹ Ho y H1CB -1 H1Cf0 x t x H1CAf x t H1C B Ag x t u H1Cd x t H0y HCBnHfx t x - H1CBG y y H y H1CB -1 H1CAf x t H1CAg x t K y y H1CB -1 H1C B Ag x t -AGy - G1S0 - G2sign S0 H1Cd x t 56 H1CB -1 H1C Af x t Cx H1C Ag x t G y y - A AG y y A -G1S0 - G2Sign S0 d x t H1CB -1 H1CAf x t y A H1CB -1 H1 f0 x t y - A AG y y A -g1s0 - G2sign S0 d x t The closed loop stability by the proposed control input with the output feedback integral sliding surface together with the existence .