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Tham khảo tài liệu 'recent advances in robust control – novel approaches and design methodse part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Robust Control Using LMI Transformation and Neural-Based Identification for Regulating Singularly-Perturbed Reduced Order Eigenvalue-Preserved Dynamic Systems 79 -0.5967 0.8701 -1.4633 35.1670 x t -0.8701 -0.5967 0.2276 x t -47.3374 u t _ 0 0 -0.9809 _ -4.1652 -0.0019 0 -0.0139 -0.0025 y t -0.0024 -0.0009 -0.0088 x t -0.0025 u t -0.0001 0.0004 -0.0021 0.0006 where the objective of eigenvalue preservation is clearly achieved. Investigating the performance of this new LMI-based reduced order model shows that the new completely transformed system is better than all the previous reduced models transformed and nontransformed . This is clearly shown in Figure 9 where the 3rd order reduced model based on the LMI optimization transformation provided a response that is almost the same as the 5th order original system response. Fig. 9. Reduced 3rd order models . transformed without LMI -.-.-.- non-transformed transformed with LMI output responses to a step input along with the non reduced _ original system output response. The LMI-transformed curve fits almost exactly on the original response. Case 2. For the example of case 2 in subsection 4.1.1 for Ts 0.1 sec. 200 input output data learning points and n 0.0051 with initial weights for the Ad matrix as follows w 0.0332 0.0317 0.0745 0.0459 0.0706 0.0682 0.0610 0.0516 0.0231 0.0418 0.0476 0.0575 0.0040 0.0086 0.0633 0.0129 0.0028 0.0234 0.0611 0.0176 0.0439 0.0691 0.0247 0.0154 0.0273 80 Recent Advances in Robust Control - Novel Approaches and Design Methods the transformed A was obtained and used to calculate the permutation matrix P . The complete system transformation was then performed and the reduction technique produced the following 3rd order reduced model -0.6910 1.3088 -3.8578 -0.7621 x t -1.3088 -0.6910 -1.5719 x t -0.1118 u t _ 0 0 -0.3697 0.4466 0.0061 0.0261 0.0111 0.0015 y t -0.0459 0.0187 -0.0946 x t 0.0015 u t 0.0117 0.0155 -0.0080 0.0014 with eigenvalues preserved as desired. Simulating this reduced order .