tailieunhanh - Adaptive Control Design and Analysis Part 15

Tham khảo tài liệu 'adaptive control design and analysis part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 542 Chapter 10 Adaptive Control of Systems with Nonlinearities Multivariable Adaptive Compensation Consider the M-input Af-output nonlinear plant i t r g x u u N v z h x with state variables X xi . xn T input V . Vji T output z zi . ZM T hi r . hM xhr and actuator nonlinearities Ui Ni vi i 1 2 . M for u 1 . Ujvr T and A - diag 2Vi - . Ạỉif such as dead-zone backlash or hysteresis. The models of the actuator nonlinearity A - and its inverse NI - are described in - . Design for systems with relative degrees. We first assume that the plant has a relative degree that is a x in is nonsingular. With the control error given in the plant becomes X f x g x ud Qtw dw i . When the plant has a vector relative degree r l . Hi and ri rM p n we can use the feedback linearizing control law Ud oFl x w - p x UN where P x is in Un e RM is to compensate the bounded error term d G RM and r G RM is a signal to be designed. In this case there exists a transformation Ệ T x G Rp such that A Bw g x ẽTtjj dN Un where A G Rp p and B G RMxp are in the Brunowsky canonical form 157 A block diag Ai . Am B block diag B1 . Bm where Ai G Rri ri Bi G Rri in the form of A B in with different dimensions as the result of the feedback linearization Choose the design signal w F r where F G RMxn is such that A BF is stable and r is a reference input and define the reference model system ỹm A - BF ym Br. Designs for Nonlinear Dynamics 543 For the state error vector ỹ ym G Rp from and we obtain the error equation ffv y A- BF ỹ g x QTu dN UN . ux Define the positive definite function m ẽi . M 1 ỹTPỹ ẽĩ r í z Í 1 where p G Rpxp with p PT 0 satisfies P A - BF A - BF TP -2Q for a chosen p X p matrix Q QT 0 and Tị diag 7ii 7ins. with 7ij 0 j 1 2 . 71 0 i 1 2 . M. Choose the adaptive laws ới í -ríei t wí t f8i t i l 2 .M where foift is a parameter .

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