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.

Table CDP2.1 Typical Parameters for the Armature-Controlled DC Motor and the Capstan and Slide Ms Mass of slide M Mass of drive bar Jm Inertia of roller, shaft, motor and tachometer Roller radius 5.693 kg 6.96 kg 10.91.10-3 kg m 31.75.10-3 m 0.268 N ms/rad 0.8379 N m/amp 0.838 V s/rad r bm Motor damping Km Torque constant Kp Back emf constant Rm Motor resistance Lm Motor inductance 3.6 mH 1.36