Tham khảo tài liệu 'frontiers in adaptive control part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | A Design of Discrete-Time Indirect Multivariable MRACS with Structural Estimation of Interactor 291 T- 11 1 1. -C- 1 1 Finally calculate X t by X t -ỹ t 0mxm v-1 Tv-2 t - L t V t 36 where C t Av t B t C t A t B t V t C t A2v -2 t B t c t Av w-2 t B t 37 mt T -Ô- 1 AZ .1 1 . .1- . 1 Then using L t X t and Y t the adaptive control input is given by u t -1 y t ym t 1 u t X t M Y t M L M . 38 u t-v 1 _y t-v 1 _ym t w . The global stability of the over-all system may be proved under the assumption 5. However the details are under studying. 4. Numerical Examples Consider the following plant a 1 G z z z 11 z b z J z2 0 1 a z z 0 z2 b z 1_ z z b Although the plant seems simple enough there exist three variations of the interactor depend on the values of a and b . Case 1 a b In this case the interactor of the plant is 2 L z z -2 - 2 3 Case 2 a 1 b In this case the interactor of the plant is L z z -10z 5 10z 5 10z - 4 292 Frontiers in Adaptive Control Case 3 a 1 b In this case the interactor of the plant is L z z 10z2 - - 10z2 - - 10z2 - 10z2 - For the above three cases the interactor can be obtained by solving L t T2 t J 2. Using the above L t Y t can be obtained by solving Y t C CA t -L t CÂ2 t CA3 t CA4 t Since C -matrix does not depend on t in this example and C A is observable independent on t O1 t always has column-full rank and thus the above equation has a solution. Finally X t can be calculated by X t -Y 0 CB t - L t CA t B t CA2 t B t CA3 t B t The reference signal vector was given by ym t Gm z r t sin nt 15 sin 2nt 25 The least square algorithm with constant trace was used to estimate the parameters where the initial values of the covariance matrix is 106 and min . 3 and 5 show the tracking errors of the proposed indirect MRACS for Case 1-3 respectively. 4 and 6 show the tracking errors of the proposed indirect MRACS for Case 1-3 without modification .
