Tham khảo tài liệu 'robot manipulators trends and development 2010 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 152 Robot Manipulators Trends and Development diagnose sensor biases in nonlinear systems such as Vemuri 2001 Wang et al. 1997 is the ability to diagnose piecewise constant bias with the same observer. Moreover the proposed approach is not limited to sensor biases and can be used to diagnose measurement errors of any harmonics. 5. Measurement Error Identification for Low and High Frequencies We now consider measurement errors of low frequencies determined by a cutoff frequency Ml. The SISO weighting wl s as b Zhou Doyle 1998 emphasizes this range with b selected as Ml and a as an arbitrary small number for the magnitude of wI jM as M TO. With a diagonal transfer matrix w s that consists of these SISO weightings and similar to the approach adopted in section the detection and identification objectives can be combined in the unified framework represented by the weighted setup of Fig. 5. In this case the augmented plant G is given by A 81 2 1 G C D11 D12 . C2 D21 D22 Ag 0np 0pn A 0 pn ỈH Bg 0np l 0 pn In 0np cCg In C 0n 0pn 0np CẺD 0n 0 pn 41 where Ag 0p Bg Ip Cg diagp b and Dg diagp a . This form also violates the assumptions of Theorem 1 note that A B 2 is not stabilizable . Similar to Section 4 we introduce the modified weighting ứjỊmod s a b with arbitrary small positive A . The augmented plant G is then the same as 41 except for Ag which is now given by the stable matrix diagp A and Cg given by diagp b aA . Similar to the narrow frequency band case the assumptions of Theorem 1 are now satisfied and the LMI approach in Gahinet Apkarian 1994 can be used to solve the HTO problem. To this end we define the HTO problem associated with the low frequency range as follows Definition 7. Low frequency HTO Given A 0 e 0 find S the set of admissible controllers K satisfying II Tzt IIto Y for the setup in Fig. 5 where G has the state space representation 41 with Ag diagp A Bg Ip Cg diagp b aA and Dg diagp a . Based on all the above we now present the main result of this .
