Tham khảo tài liệu 'adaptive control design and analysis part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 502 Chapter 9 Multivariable Adaptive Control Advanced Topics State feedback design and its parametrization. To generalize the results of parametrizing a state feedback control law using plant input output measurements for the SISO case see Section to the MIMO case we consider the continuous-time linear time-invariant plant i t Ax t Bu t y i Cx t where A G Fnxn B G RnxM c G RMxn u t G RM and y t G RM. The multivariable version of the adaptive control problem solved in Section is to use the state feedback controller structure u t K t x t K2 t r t where A i t G Rn M and A2 t G are updated by a stable adaptive law to be derived to ensure that all closed-loop signals are bounded and the plant output y t tracks a reference output ym t asymptotically where ỉ m t wys r t wm s C s with m s being the modified left interactor matrix of G s C sl A 1B and r t being a bounded reference input. As in the SISO case the key step is to establish the existence of constant matrices K G Rn M and KỊ RMxM such that the plant-model matching C sl - A - BKfi BKi -x s is achieved. From this matching condition the error equation y i - ym t - Ktfx A2 - K2 r t t similar to that in can be derived. Based on this error equation adaptive laws for updating the parameter estimates Kỵự and K2 t can be derived similar to that in Section to solve the adaptive control problem. Analogous to that in Section to develop adaptive control schemes using output feedback we need to parametrize the state feedback term K Tx t as Kịrx t J w t 2Tw2 i where ĩ ĩi . ĩJT G RvM M 0 1 . e pyMxM Q. e i 1 2 j 1 . V for the observability index V of G s and i i F s u t w2 t F s y t Problems 503 F s A s IM sIM st -1IM T for a monic stable polynomial A s of degree V based on a full -order observer using input li t and output y t for K xli - or as K Tx t ĩTWi t ef w2 t e 20y t for 20 RM M and Q Wi t 2 and w2 i defined above but with V replaced by V 1 based
