We want to accurately position a table for a machine as shown in Figure CDP2.1. A traction-drive motor with a capstan roller possesses several desirable characteristics compared to the more popular ball screw. The traction drive exhibits low friction and no backlash. However, it is susceptible to disturbances. Develop a model of the traction drive shown in Figure CDP2.1(a) for the parameters given in Table CDP2.1. The drive uses a DC armature-controlled motor with a capstan roller attached to the shaft. The drive bar moves the linear slide-table. The slide uses an air bearing, so its friction is negligible. We are considering the open-loop model, Figure CDP2.1(b), and its transfer function in this problem. Feedback will be introduced later.

Traction drive motor and capstan roller .c Drive bar Linear slide FIGURE CDP2.1 (a) Traction drive. capstan roller, and inear slide. (b) The block diagram model Table CDP2.1 Typical Parameters for the Armature-Controlled DC Motor and the Capstan and Slide M, Mass of slide M, Mass of drive bar 5.693 kg 6.96 kg 1091.10 3kg m Inertia of roller, shalt, motor and tachometer 31.75-1m 0.268 N ms/rad 0.8379 N m/amp 0.838 V s/tad 136 0 3.6 mH Roller radius Motor damping Torque constant K K, R Back emf constant Motor resistance Motor inductance