Modeling of Electromechanical Systems, Transfer functions, System Modeling Diagrams, Effect of Pole Locations, Time Domain Specifications, PD Control)
engineering
Description
Question 1 (40 pts): (Related Topics: Modeling of Electromechanical Systems, Transfer functions, System Modeling Diagrams, Effect of Pole Locations, Time Domain Specifications, PD Control)
Consider the electrical and mechanical dynamics of a DC motor coupled by a
gearbox. The gearbox is loaded by a pulley with radius l that stretches a linear
spring with stiffness coefficient (k). The reduction ratio of the gearbox is given as
1/n. The pulley is supported between bearings, thus the load is affected by friction
coefficient of bearings (bm). The effect of inductance (L) is neglected from the
electrical model of the DC motor. Symbols Ke and Kt are electric constant and
torque constant, respectively. The overall representation of the geared DC motor is
shown in Figure 1.
Fig1. Schematic representation of a geared DC motor under the load
The voltage source applied to the motor’s armature is represented by V, the output
of the DC motor is the rotational speed of the shaft . The viscous friction model
of the DC motor is obtained by means of motor viscous friction constant (bm). As
the motor shaft coupled with a gearbox, the speed of the pulley (
) is affected by
the gear ratio (reduction ratio). (Hint: )
