MIT2_017JF09_p32 - 32 MOTOR SERVO WITH BACKLASH 32 114...

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32 MOTOR SERVO WITH BACKLASH 114 32 Motor Servo with Backlash Consider the following: a motor is attached to a load through a gearbox, and the gearbox has a backlash behavior. Physically, backlash is a decoupling of gear teeth (due to imprecise meshing), so that the motor-side and the load-side teeth are not always in contact. Contacts are characterized by the condition | θ m θ l | >h , where the θ ’s are the motor and load angles respectively, and h is the half-width of the backlash. During contact, a small deflection material occurs according to a linear spring model. In the forward direction, that is, when θ m leads θ l by a positive amount, τ t = k ( θ m θ l h )when θ m θ l >h , where τ t is the torque transmitted from the motor side to the load. A similar condition holds in the reverse direction. Conversely, whenever θ m is within h of the angle θ l , the teeth are out of contact and no torque is passed between the motor and the load. h T m T l 2h (motor side gear) (load side gear) The rotary mass on the motor side is J m ; on the load side, we have rotary mass J l as well as a rotary damping b . It is desired to position the load via a servo, so a simple feedback controller is implemented of the form τ m = l ,where τ m is the motor torque. We assume that we can control the torque in the motor directly through a current amplifier. All the physical properties in a particular system built by Company XYZ are well understood, except for the load-side damping b . This varies slowly over time because the bearings break in and then age, and because the load side is connected to an unpredictable environment.
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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MIT2_017JF09_p32 - 32 MOTOR SERVO WITH BACKLASH 32 114...

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