Motion equation and transfer function of mass on a conveyor

[alv13]

Homework Statement

A camera (mass = m) is mounted on a box (mass = M, position=x), that is placed on a horizontal conveyor.

The conveyor is moved using a DC engine (Input voltage = V , Moment coefficient = Kt , Induced EFM coefficient = Kb , Viscous friction in engine's axis = C , Resistance =R) attached to it's left wheel (radius = a).

Jm negligible.

Need to find system's motion equation and the transfer Function between V and x.

Relevant Equations

.

Denote wheel turning angle as theta--> Induced EFM (Em)=Kb*Theta_dot.
Voltages on the wheel: R*i= V - Em
Moments on engine's axis: Kt*i-C*a + a (m+M)*x_double_dot=0 (As Jm negligible).

From here I would find another equation to have x and theta expressing each other, but i think I'm missing something and I'm stuck...

 

[Valkarie]

A:It's not clear what you're trying to do; there are different ways to calculate the induced voltage in a DC motor, but regardless of which method you use, it is a function of both current and angular velocity.You can't just write down an equation for the induced voltage based on angular velocity (or angular position) alone.