# lab4 procedure

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```					    Grand Valley State University

Dynamic Systems Modeling and Control

Experiment 4

Permanent Magnet DC Motors

October 5, 2000

Joe Matecki
Brent Dyke
1.3.4.2 Laboratory Experiment 4- Permanent Magnet DC Motors

1- Grand Valley State University
EGR 345 Dynamic Systems Modeling and Control
Lab Exercise 4
Joe Matecki and Brent Dyke
10-5-00

2- Purpose
Investigate a permanent magnet DC motor and derive descriptive equations.

3- Equipment
      2- Power supplies #TW60975
      Permanent Magnet DC Electric Motor model #40791205
      Potentiometer (Small DC motor)
      DMM
4- Procedure
1. Measure resistance across the motor terminals using a DMM.
2. Assemble circuit below of figure 1.

Figure 1 Circuit consisting of 2 power supplies hooked up to a potentiometer and an electric
motor, interfaced with a computer to take data.

3. Combining the output from the above circuit recorded in
Labview and the solution to the following differential equation,
 d     K  V   K 
2
                s      
 dt       J R    J R    ( 1)

Which at steady state can be re-written as,
 K2 
 Vs 
K                           ( 2)
ss                  
 J R       J R 
so,
Vs
K
ss                ( 3)

4. At this point, Vs can be measured with a DMM, and  can be
graphically displayed in Labview.
5. Once K is known, J can be determined by graphically
determining the time constant t. Which is the time it takes the
motor to reach

ss1  e 1                   
.632ss
( 4)

The general solution to the differential equation in (1) can be
shown to be.
2
K
Vs           J R
t           Vs                         ( 5)
g            e               
K                                K

w hich can be re-w ritten as
t

g   ss  ss e                                                 ( 6)

w here
   t ime_constant

R                                                       ( 7)
   J
2
K
Figure 2 Voltage with respect to time.

Our analog device was interfaced in Labview and its output was
collected at a rate of 100 iterations of the output per second. This
was done by consecutively timing with a stopwatch how many
seconds it took Labview to iterate 1000 times, then taking an
average. Below are the results.
Trial 1        s
9.89
Trial 2        s
9.89
Trial 3        s
10.0
Trial 4         s
10.04
s
Av erage    9.96                     ~ 100 iterations / 1 s   ( 8)

1000iterat ions

This number can help us calculate the time the motor took to
complete it’s entire rotational cycle when fixed to the potentiometer.
It was found that the number of iterations to complete the cycle was
172.
During the 172 iterations the motor shaft rotated a total of 1.75
radians. It did this in a time of 1.72 seconds. Which allows us to find
the angular velocity.
1.75
ss                                                ( 9)
 48 1 
       
 100
ss  3.646          s

From equation (3) the value of K was found to be
12
K                                                  ( 10)
)
( 3.646

K  3.291 V s                                       ( 11)

From equation (11) the time constant can be derived.
It took 48 iterations of Labview to reach ss. So,

  48
1 
 1e  
1          ( 12)
100

  0.303 s                          )
( 12.1
From equation (9), J was found to be
With an R value of 20.2 

R  20.2

3.291
2

J  .303                           ( 13)
20

J  0.164                                )
( 13.1

Equation (5) can now be re-written as
2
 3.291
t
12       .164 20.2              12
g( t)           e                                                               ( 14)
3.291                            3.291

The equation is graphed below , indicating that the motor w ould reach it's steady state angular
velocity at 1.64 seconds.

5

 g ( t)

0
0                       5                   10
t
Figure 3 Shows the theoretical angular velocity motor response curve.

From figure 2 and equation (8) we can see that the actual response curve
indicates that the time it takes to reach steady state angular velocity is

1        iterat ions s           ( 15)
t  172
100       iterat ions
t  1.72
s                                          )
( 15.1

The percent error betw een theoretical and actual motor response curves is

1.72  1.64
s      s
Percent _Error                                100               ( 16)
s
1.72

)
( 16.1
Percent _Error 4.651

6-Conclusion:
Using Labview and a derived differential equation we were able to solve
for constants, which can be plugged into a solved differential equation. This
solved differential equation will allow the calculation of angular velocity for any
point in time.

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