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Tham khảo tài liệu 'robust control theory and applications part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Robust Controller Design New Approaches in the Time and the Frequency Domains 227 -0.5608 0.8553 0.5892 2.3740 0.7485 A1 0.6698 -1.3750 -0.9909 B1 1.3660 3.4440 3.1917 1.7971 -2.5887 0.9461 -9.6190 0.6698 -1.3750 -0.9909 0.1562 0.1306 A2 -2.8963 -1.5292 10.5160 B2 -0.4958 4.0379 -3.5777 2.8389 1.9087 -0.0306 0.8947 The uncertain system can be described by 4 vertices corresponding maximal eigenvalues in the vertices of open loop system are respectively -4.0896 2.1956i -3.9243 1.5014 -4.9595. Notice that the open loop uncertain system is unstable positive eigenvalue in the third vertex . The stabilizing optimal PD controller has been designed by solving matrix inequality 25 . Optimality is considered in the sense of guaranteed cost w.r.t. cost function 23 with matrices R I2x2 Q 0.001 I3 3 . The results summarized in Tab.2.1 indicate the differences between results obtained for different choice of cost matrix S respective to a derivative of x. S Controller matrices F proportional part Fd derivative part Max eigenvalues in vertices 1e-6 I F Fd -1.0567 -0.5643 -2.1825 -1.4969 -0.3126 -0.2243 -0.0967 0.0330 -4.8644 -2.4074 -3.8368 1.1165 i -4.7436 0.1 I F Fd -1.0724 -0.5818 -2.1941 -1.4642 -0.3227 -0.2186 -0.0969 0.0340 -4.9546 -2.2211 -3.7823 1.4723 i -4.7751 Table 2.1 PD controllers from Example 2.1. Example 2.2 Consider the uncertain system 1 2 where -2.9800 0.9300 0 -0.0340 -0.0320 -0.9900 -0.2100 0.0350 -0.0011 0 C 0 0 1 0 A 0 0 0 1 B 0 .0 0 0 1 0.3900 -5.5550 0 -1.8900 -1.6000J 0 1.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B 228 Robust Control Theory and Applications The results are summarized in Tab.2.2 for R 1 Q 0.0005 I4x4 for various values of cost function matrix S. As indicated in Tab.2.2 increasing values of S slow down the response as assumed max. eigenvalue of closed loop system is shifted to zero . S qmax Max. eigenvalue of closed loop system 1e-8 I 1.1 -0.1890 0.1 I 1.1 -0.1101 0.2 I 1.1 -0.0863 0.29 I 1.02 -0.0590 Table 2.2 Comparison of closed loop .
