A mass m is attached at the end of a cantilever beam. The bean has a stiffness k

Question

A mass m is attached at the end of a cantilever beam. The bean has a stiffness k_b in the vertical direction. Therefore, if a force, F pushes the beam down, it deflects by the amount of delta y = k__bF. In Oder to reduce the deflation of the beam, a servo-motor rotates a pulley with a radius of R and pulls the beam using a wire to keep it horizontal. Assume that the servo-motor has very small inertia, no friction and therefore applies the torque Tm instantly to the pully. The motor torque is controlled using a proportional feedback controller. The controller measures beam deflection delta Y and the motor to applies torque (Tm) by a proportional control law, k_p middot delta y to pull the beam back as shown in the figure below. Kp is p-controller gain. Draw a block diagram for this system. Based on the above information what is the overall stiffness (k=F/x) of the beam with the motor helping?

Explanation / Answer

a) a upward vertical force on beam due to motor . And vertical donward force due to self weight.
b)
Kef x = kb x - kp x
Kef = kb -kp

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