tailieunhanh - Recent Advances in Robust Control Theory and Applications in Robotics and Electromechanics Part 4

Tham khảo tài liệu 'recent advances in robust control theory and applications in robotics and electromechanics part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Spatially Sampled Robust Repetitive Control 79 The upper and lower bounds of p and Ộ are empirically determined based on a velocity variation from -80 to 100 around the nominal value of rev sec and a 10-to-1 saturation limit respectively. The parameter variation set T is not convex but can be shown to lie within a polytope T with four vertices located at ip1 10 1 10 2 10 1 t 3 1 1 1 and 4 1 see Fig. 10 . The polytope T will be used for the following design. Given that Ộ e 1 in T the parameters of the weighting filter W1 can be properly determined to reflect the different performance requirement for the unsaturated Ộ 1 and saturated Ộ 1 system. Fig. 11 shows the magnitude curves of W with k Ob 2kx12 b and e 5 3x Ob as Ộ e 1 . The magnitude curve of W2 is also shown in the figure. The low-pass filters Hj s and F s are selected as 1 H1 g H2 s H3 s F s 1 s 2 x 1000 1 Fig. 11. The parameter-dependent performance weighting W1 and uncertainty weighting W2. where the frequency value of 1000 cycles rev is specified to reflect the negligible sensor and actuator dynamics. The low-order attenuated repetitive controller can be expressed as RC S s 2 x200 1 II s 2 XxX lo oOO ỉ where the periodic disturbances are at 32 48 and 96 cycles rev. A feasible LPV controller is determined based on the above parameters which attains Y . The controller can be written as 80 Recent Advances in Robust Control - Theory and Applications in Robotics and Electromechanics y1 x K Ak v 0 - Xk - BK1 V BK2 V BKs v 0 - y - X rc J . 0 Arc J Xrc J . 0 0 0 Brc p2 y 31 y1 u Ck v 0 - Xk - DK 1 v DK 2 v DK 3 v 0 - y . 2 _ . 0 Crc J .Xrc J . 0 0 0 0 . y _ 32 where BK v BK1 V BK 2V BK3 V z DK y dk 1 v DK 2 v DK 3 v . 4 4 V aiVi a 0 ai 1ỉ i 1 i 1 We can view 31 and 32 as an LPV repetitive controller LPVRC . For practical implementation the vertex controllers need to be transformed into their discrete-position invariant counterparts . using bilinear .