Question

If anyone is feeling a challenge? I'm hoping you could help with at least free body diagrams, and possibly elemental equations. Anything helps thank you

A vertical crane is used to quickly place loads at a given distance from the ground. A simplified representation of the vertical crane (VC) is shown in Figure 1. Positioning control is a common control problem in industry. The drive pulley is driven by torque produced by a DC motor. There is a flexible belt between the drive pulley and transfer pulley that exhibits stiffness and damping as shown. The belt between the transfer pulley and load pulley is considered to be a rigid inextensible) belt. Finally the connection between the load mass and load pulley also has stiffness and damping. The objective of the VC control system is to move the load as fast as possible to the desired position with little overshoot to avoid possible load damage and time spent waiting for it to settle to its final position. Load Transfer Pulley Pulley Hb, Drive Pulley M Figure 1. Vertical crane system. Additional Details • The drive pulley experiences rotational damping of Bo (N.m.s) • The transfer and load pulleys have rotational damping of By and B. (N.ms) respectively • The drive pulley is driven by torque produced by the electric motor Nomenclature • 1, and are the drive pulley's inertia and radius, respectively. To includes the rotational inertia of the electric motor. • Iand are the transfer pulley's inertia and radiuses, respectively. • I and are the load pulley's inertia and radiuses, respectively. • is the mass of the load. • kp and bo are the belt's stiffness and damping ratio, respectively. • ky and b, are stiffness and damping, respectively, of the connection between the load pulley and load. • K, is the torque constant of the motor. • K, is the electric constant of the motor • Rand L are the motor circuit resistance and inductance, respectively. • is the voltage applied to the motor circuit. • is the motor circuit current. Assumptions • The position of the load is measured from static equilibrium. • The inertias of the transfer pulley and load pulley are negligible and can be ignored. • The torque T generated by the motor equals Ki and is in the direction of positive • No belts slip. The belt between the transfer and load pulleys is rigid (inextensible) • The model for the motor circuit that relates voltage to current is + Ri+K0, Lº+Ri+K0, -e

Answer 1

The free body diagram for this system will be

We 3 will pants divide for 3 the free pulleys. body diagrams in x 7 x 7 x . 16 Drive Let's assume pulleys Where, x =r. O To(x4-2, 26 Transfer pulleyr T Ta - Tensions in Belt. Tq tto (2-3) s Load palleyr K.XL 1999