Tham khảo tài liệu 'bishop, robert h. - the mechatronics handbook [crc press 2002] part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | for all w. This in turn implies that the associated sensitivity singular values satisfy Smax SKF jw 1 - 1 0dB Smin SKF jw for all w where Skf jw I GkfO w -1 From the above sensitivity singular value relationship we obtain the follow celebrated KBF loop margins infinite upward gain margin at least 1 6 dB downward gain margin at least 60 phase margin. The above gain margins apply to simultaneous and independent gain perturbations when the loop is broken at the output. The same holds for the above phase margins. The above margins are NOT guaranteed for simultaneous gain and phase perturbations. It should be noted that these margins can be easily motivated using elementary SISO Nyquist stability arguments 2 8 . From the above sensitivity singular value relations we obtain the following complementary sensitivity singular value relationship Smax Tkf jw ơmax I - Skf jw 1 Smax Skf j w 2 6dB for all w where TKF 1 Skf GKF 1 gkf 2. Recovery of Target Loop Lo Using Mođel-Baseđ Compensator. The second step is to use a modelbased compensator Kopt A - BGC - HfC Hf Gc where Gc is found by solving the CARE with A B M C R pIn x n with p a small positive scalar. Since p is small we call this a cheap control problem. If the plant P A B C is minimum phase then it can be shown that lim X 0 p 0 - lim JpGc WC p 0 for some orthonormal W . WTW WWT I lim PKopt Lo In such a case PKopt Lo for small p and hence PKopt will possess stability margins that are close to those of Lo at the plant output whatever method was used to design Lo. It must be noted that the minimum phase condition on the plant P is a suficient condition. It is not necessary. Moreover Gc need not be computed using a CARE. In fact any Gc which 1 satisfies a limiting condition plim pGc WC for some invertible matrix W and which 2 ensures that A - BGc is stable for small p will result in LTR at the plant output. This result 2002 CRC Press LLC 31 Adaptive and Nonlinear Control .
