tailieunhanh - RECENT ADVANCES IN ROBUST CONTROL – NOVEL APPROACHES AND DESIGN METHODSE Part 7

Tham khảo tài liệu 'recent advances in robust control – novel approaches and design methodse part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Integral Sliding-Based Robust Control 169 3. Sliding-mode control design The integral sliding-mode control completely eliminating the matched-type nonlinearities and uncertainties of 1 while keeping s 0 and satisfying 2-gain bound is designed in the following manner. Integral sliding-mode control Let the switching control law be s x t us t a t pM 15 The integral sliding surface inspired by Cao Xu 2004 is defined to be s x t Mx t S0 x t 16 where s0 x t is defined to be sq x t M xq Ị Ax t Bur r d x0 x 0 . 17 The switching control gain a t being a positive scalar satisfies 1 a t - 1 0 1 1 n x 1 Wur II 18 where N 0 11ME0IIII-HqII 11Mil et MBdII . 19 i 1 Ả is chosen to be some positive constant satisfying performance measure. It is not difficult to see from 16 and 17 that s x0 0 0 20 which in other words from the very beginning of system operation the controlled system is on the sliding surface. Without reaching phase is then achieved. Next to ensure the sliding motion on the sliding surface a Lyapunov candidate for the system is chosen to be Vs 1 sTs. 21 It is noted that in the sequel if the arguments of a function is intuitively understandable we will omit them. To guarantee the sliding motion of the sliding surface the following differentiation of time must hold . 7s sTs 0. 22 It follows from 16 and 17 that s Mx M Ax Bur 23 Substituting 1 into 23 and in view of 10 we have N s MAA t x I AB t u h x M gi x t MBdw Ur. 24 i 1 170 Recent Advances in Robust Control - Novel Approaches and Design Methods Thus the following inequality holds 7 N iZj sT MAA t x I AB t u h x M gi x t MBdW ur i 1 25 llsll 0 1 1 n x Mur II fi1 1 a t . By selecting a t as 18 we obtain V s A 0 26 which not only guarantees the sliding motion of 1 on the sliding surface . maintaining s 0 but also drives the system back to sliding surface if deviation caused by disturbances happens. To illustrate the inequality of 25 the following norm-bounded conditions must be quantified sT MAA t x s MAA t x