Page 705 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 691
= 0.00407 N ⋅ m∕rpm (8.332)

The ratio of the slope change in the torque-speed curve is
slope
i 4.27 1
= = (8.333)
slope v 89.7 21
For a given unit speed change, the torque variation under the current controlled amplifier
operation is 21 times less than that under the voltage controlled amplifier.

8.9 PROBLEMS

1. Consider the solenoid shown in Figure 8.17. Assume that the permeability of the iron core is
much larger that the permeability of the air gap (x). Hence, let us neglect the reluctance of the path
in the iron core.
(a) Draw the equivalent electromagnetic circuit diagram.
(b) Derive the relationship for the inductance as a function of the air gap distance x which is variable.
2
Let the air gap cross-sectional area A = 100 cm , number of turns of the coil N = 250. Plot the
g
inductance as a function of the air gap x for 0.0mm ≥ x ≥ 10.0 mm.
2. Consider the linear motion mechanism shown in Figure 3.3. Draw a block diagram of the closed
loop position control system components for this motion control system. Discuss the advantages
and disadvantages of using a (i) DC motor, (ii) stepper motor, (iii) vector controlled AC induction
motor as the actuator to provide the mechanical power to the ball-screw mechanism. Assume that the
necessary power level is under 1.0kW.

3. Consider a DC motor (or equivalent) motion control system. Assume that the DC bus voltage
available is V = 90 V DC. The back EMF constant of the motor is K = 20 V∕krpm. The nominal
s
e
terminal resistance of the motor stator windings is R = 10 Ω.
(a) Determine the maximum no-load speed and the maximum torque capacity at stall (zero speed)
of the motor in steady-state. Discuss the factors that detemine the peak torque and RMS torque
capacity of the motor and predict peak and RMS torque capacity of the motor.
(b) Assume that the DC motor is controlled by the velocity mode amplifier and speed sensor feedback
(i.e., tachometer). The amplifier sends a voltage command to the motor proportional to the speed
error. Input speed is commanded with a 0–10 V DC voltage source. Determine the sensor gain
and amplifier gain so that the closed loop system has good closed loop response and that a
0–10 V DC command signal results in proportional output speed in the speed range of the motor.
4. Consider a hybrid PM stepper motor.
(a) What is the difference between the half step and full step mode. What is the main advantage and
disadvantage of the half stepping mode?
(b) Discuss how microstepping is accomplished and its advantages/disadvantages.
(c) Discuss the major performance differences between step motors and brushless DC motors.

5. Consider a stepper motor with two phases (Figure 8.67). Phase 1 is wound with two identical
coils. Phase 2 is also wound with two identical coils. Therefore, there are eight wires that come out
from the stator winding, four for each phase.
(a) Connect the phase terminal wires in such a way that the motor can be used as a unipolar wound
motor and draw a schematics for the amplifier circuit of the motor windings.
(b) Connect the phase terminal wires in such a way that the motor can be used as a bipolar wound
motor with series connected windings (two identical windings for each phase are connected in
series). Draw the amplifier circuit and its connections to motor windings.