The goal of project is to model a system and to design a controller for the system so that the closed-loop system performs satisfactorily.
We want to accurately position a table for a machine as shown in Figure. A Traction drive motor with a capstan roller possesses several desirable characteristics compared to the more popular ball screw.
The traction drive exhibits low friction and no backlash. However, it is susceptible to disturbances. The parameters are given in Table.
The drive uses a DC armature-controlled motor with a capstan roller attached to the shaft.
The drive bar moves the linear slide-table.
The slide uses an air bearing, so its friction is negligible.
Table 1. Typical Parameters for the Armature Controlled DC Motor and the Ca stan Slide
|
Ms
|
Mass of slide
|
5.693 kg
|
|
Mb
|
Mass of drive bar
|
6.96 kg
|
|
Jm
|
Inertia of roller, shaft, motor and tachometer
|
10.91.10'3 kg.m2
|
|
r
|
Roller radius
|
31.75.10 m
|
|
Km
|
Torque constant
|
0.8379
|
|
Kb
|
Back cuff constant
|
0.8379
|
|
Vd
|
Voltage source
|
60V
|
|
Tin
|
Magnitude of the PWM sawtooth wave
|
5V
|
|
Riff
|
Motor resistance
|
1.3651
|
|
Lm
|
Motor inductance
|
3.6rnH
|
1) Develop a open-loop model of the traction drive shown in Figure 1(a). And please derive its transfer function.
2) Design a switch mode PWM DC-DC converter for the speed regulation of the DC motor.
3) Design the current loop controller so that phase margin of the loop transfer function should be over 45o, and the crossover frequency is no larger than 5kHz.
4) Design the speed loop controller so that phase margin of the loop transfer function should be over 45o, and the crossover frequency is no larger than 5kHz.
5) Design the position loop controller so that phase margin of the loop transfer function should be over 45o, and the crossover frequency is no larger than 5kHz.
6) Using Matlab/Simulink, simulate the designed circuit with controller in (3), (4), and (5). Test the controller performance through designing disturbances in input and step change of the position. (Disturbances could be step change of the position reference, or the step change of the load torque TL).
Write a report that documents and describes your results and observations from parts. Make sure all plots are well labeled and that explanations contain solid analytical foundations.