Develop a open-loop model of the traction drive shown in

Question

The goal of this 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 1. 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 1. The drive uses a DC armature-controlled minor with a capstan roller attached to the shaft. The drive bar moves the linear slide-table. The slide uses an air bearing, an its friction is negligible.

Figure 1. (a) Traction drive. capston roller and linear slide. (b) The block diagram of the model

Table 1. Typical Parameters for the Annum Controlled DC Motor and the Capstan 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 -10-3 m
Km	Torque constant	0.8379
Kb	Back emf constant	0.8379
vd	Voltage source	60V
vm	Magnitude of the PWM sawtooth wave	5V
Rm	Motor resistance	1.36 Ω
Lm	Motor inductance	3.6 mH

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 45^o, 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 41^o 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 45⁰, 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.