250 工程科学学报，第44卷，第2期 100 Common control track (b) 250.10r(a) End theory trac 60 250.05 % 20 Common control track 250.00 0 职or 249.95 -20 249.90 40 100 50 600 -60 0 500 -50 -80 400 y/mm -100300 x/mm -100 300 350 400 450 500550 660 x/mm 250.10 250.10 (c) Common control track (d) 250.08 250.08 PID control track 250.06 End theory track 250.06 250.04 250.04 目250.02 目250.02 250.00 号250.00 249.98 249.98 249.96 249.96 Common control track 249.94 249.94 PID control track -End theory track 249.9 249.92 600 550 500450400 350300 -100 -60 -20 20 60 100 x/mm 图5进给速率为30000 mm-min'时不同控制下末端的平面圆形跟踪轨迹对比图.(a)三维图：(b)xy平面投影：(c)x-:平面投影；(d)y-:平面投影 Fig5 Comparison of the planar circular tracking trajectories at the ends under different controls when the feed rate is 30000 mmmin (a)three- dimensional figure;(b)x-y plane projection;(c)xplane projection,(d)y-=plane projection 100r (b) 80 250.10r(a) 6 -End theory tra % 250.05 Sommon control track 20 control track End theory track 250.00 0 249.95 -20 24980 -40 50 600 -60 0 500 -80 -50 y/mm 400 -100300 x/mm -100 00 350 400 450 500550660 x/mm 250.10 250.10 (c) (d)_ -Common control track 250.08 Common control track 250.08 PID control track PID control track -End theory track 250.06 End theory track 250.06 250.04 250.04 目250.02 =250.02 元250.00 i250.00 e 249.98 249.98 249.96 249.96 249.94 249.94 249.92 249.92 600 550 500450400350300 -100 -60 -2020 60100 x/mm y/mm 图6进给速率为15000 mm-min时不同控制下末端的平面圆形跟踪轨迹对比图.(a)三维图：(b)x-y平面投影：(c)x-平面投影：(d)-平面投影 Fig.6 Comparison of the planar circular tracking trajectories at ends under different controls when the feed rate is 15000 mm'min:(a)three- dimensional figure;(b)x-yplane projection;(c)x-plane projection,(d)y=plane projection250.10 250.05 250.00 249.95 249.90 100 50 −50 −100 300 400 500 600 0 (a) y/mm x/mm x/mm z/mm 40 20 −40 −20 −60 −80 −100 300 350 400 450 500 550 660 0 100 80 60 (b) y/mm 250.10 250.08 250.06 250.04 250.02 250.00 249.98 249.96 249.94 249.92 −100 −60 −20 20 60 100 z/mm y/mm (d) Common control track PID control track End theory track 250.10 250.08 250.06 250.04 250.00 250.02 249.98 249.96 249.94 249.92 600 550 500 450 400 350 300 z/mm x/mm (c) Common control track PID control track End theory track Common control track PID control track End theory track Common control track PID control track End theory track 图 5    进给速率为 30000 mm·min−1 时不同控制下末端的平面圆形跟踪轨迹对比图. （a）三维图；（b）x−y 平面投影；（c）x−z 平面投影；（d）y−z 平面投影 Fig.5     Comparison  of  the  planar  circular  tracking  trajectories  at  the  ends  under  different  controls  when  the  feed  rate  is 30000 mm·min−1:  (a)  three￾dimensional figure; (b) x−y plane projection; (c) x−z plane projection; (d) y−z plane projection 250.10 250.05 250.00 249.95 249.90 100 50 −50 −100 300 400 500 600 0 Common control track PID control track End theory track (a) y/mm x/mm x/mm z/mm 40 20 −40 −20 −60 −80 −100 300 350 400 450 500 550 660 0 100 80 60 (b) y/mm Common control track PID control track End theory track 250.10 250.08 250.06 250.04 250.00 250.02 249.98 249.96 249.94 249.92 600 550 500 450 400 350 300 z/mm x/mm (c) Common control track PID control track End theory track 250.10 250.08 250.06 250.04 250.02 250.00 249.98 249.96 249.94 249.92 −100 −60 −20 20 60 100 z/mm y/mm (d) Common control track PID control track End theory track 图 6    进给速率为 15000 mm·min−1 时不同控制下末端的平面圆形跟踪轨迹对比图. （a）三维图；（b）x−y 平面投影；（c）x−z 平面投影；（d）y−z 平面投影 Fig.6     Comparison  of  the  planar  circular  tracking  trajectories  at  ends  under  different  controls  when  the  feed  rate  is 15000 mm·min−1:  (a)  three￾dimensional figure; (b) x–y plane projection; (c) x–z plane projection; (d) y–z plane projection · 250 · 工程科学学报，第 44 卷，第 2 期