Modeling and Control of DC Motors: Lab 8a & 10a, Study notes of Engineering

Download Modeling and Control of DC Motors: Lab 8a & 10a and more Study notes Engineering in PDF only on Docsity!

EGR 345

Dynamics System Modeling and Control

Lab 8a &10a – Modeling of DC Motor

Adam Heintzelman Andrew Edler November 9, 1999

Objective Lab 8a: To investigate a permanent magnet DC motor with the intention of determining a descriptive equation. Lab 10a: To position a DC motor using a proportional controller. Theory The motor is made up of coiled wires in a magnetic field and when a current is passed through those wires a force against the magnetic field will be created. The torque created by the motor shaft is proportional to the current. K T I T KI    where, K = constant; T = torque; I = current The power of the motor is:    V K P V I T KI m m      When a rotating mass is added the moments are summed the following equation is found:                  ^  dt d T J dt d M T J When the equations are manipulated, an equation relating voltage and angular velocity can be found:       ^       ^                      JR K V JR K dt d R V K K dt d J R V K K T R V V I s s s s m 2      Setup

A small disc was used in the second part of the experiment with the following parameters: Table 1: Parameters of inertial disc used. Radius 0.0508 m Mass 0.0363 kg Thickness 0.0015875 m Procedure Lab 8a:

1. Measure the resistance of the motor. Resistance 1.015 k
2. The motor, motor amplifier, power supply and tachometer were connected to a computer running the LabVIEW program shown in Fig. 1. The analog output was used to drive the motor amplifier. The analog input was used to measure the motor speed from the tachometer.
3. A hand-held strobe tachometer was then used to find the relationship between the tachometer voltage and the angular speed.
4. Two different ramps were found when the voltage output from LabVIEW was increased from 0 to 4 volts and from 2 to 4 volts. This step involved the LabVIEW program shown in Fig. 2. Lab 10a:
5. Wire the motor control servo amplifier. Connect the amplifier input to a potentiometer to test the motor driver circuit. After testing and debugging is complete, disconnect the potentiometer and connect the servo amplifier to the analog output of the computer. Test the connection using the DAQ Configure program.
6. Connect the large potentiometer to the analog inputs for the computer, and use the +/- 12V supply. Test the input range using LabVIEW. Connect the potentiometer and motor shafts together with a piece of hose. In this configuration the potentiometer voltage will be proportional to the angle of the motor shaft.
7. Enter a LabVIEW interface for a feedback controller that will read the position of a motor shaft using a potentiometer, and then position the motor with an analog output voltage. Results Lab 8a: Table 2 shows the relationship between the voltage that was output from the tachometer to the RPM that the tachometer was reading. Table 2: Tachometer voltage relation to shaft RPM.

LabVIEW Output Voltage to Amplifier (V) Tachometer Voltage (V) RPM of Motor Shaft 5 1.6 620 4.9 1.3 500 4.8 1.1 410 Then the small disc was placed on the shaft of the motor and the RPM and tachometer were was again observed. Table 3: Tachometer voltage relation to shaft RPM w/ inertial disc. LabVIEW Output Voltage to Amplifier (V) Tachometer Voltage (V) RPM of Motor Shaft 5 1.65 650 4.9 1.4 560 4.8 1.3 500 The second LabVIEW program was then run (see Fig. 2) and the ramps of two different functions were observed. Fig. 3 shows the output from the tachometer when the input voltages from the LabVIEW program to the amplifier were 0 to 4 volts. Fig. 4 shows the output from the tachometer when the input voltages from the LabVIEW program to the amplifier were 2 to 4 volts. The ramp function causes a exponential increase that settles to a constant angular velocity. No inertial mass was used in this step. Ramp From 0 to 2 Volts

Time (S) Voltage (V) Figure 3: Ramp fucntion from 0 to 2 volts from the tachomter.

For Fig. 4 the function was found to be: Vm = 2 - 1.5e-1/(1.5-1.25)t Therefore, Vm = 2 - 1.5e-(1/0.25)t

0 V (^) m2 ( t) 0 t 4 0 1 2 3 4 0 1 2 Tach Voltage vs. Time Time (sec) Voltage (v) Figure 6: Mathcad verification of experimental function. Converting both of these equations over in terms of angular velocity, the following functions were found:

  t

e^121

1



   Fig. 3

  t

e^97

1



   Fig 4

Since the inertial disc was not used in the second step (Fig. 3 and Fig. 4), a theoretical model is not available because some of the theoretical values were based on experiment. Lab 10a: There were no results for lab 10a. Conclusion Lab 8a: A DC motor can be modeled mathematically using the values of voltage observed from the tachometer. The mathematical model accurately portrayed the experimental plot.

Lab 10a: Lab 10a was not completed due to complications with the circuitry shown below in Figure 7. Therefore, no results were obtained and the performance of the proportional controller could not be determined. Figure 7: Lab 10a circuitry.