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Introduction:

The purpose of this lab is to obtain mathematical model for the motor by

determining the parameters K, J, and Ra. Using the experimental data to obtain the

motor armature resistance and moment of inertia (J). We used the motor model

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equation to derive the experimental design, open loop equation, which is the

experimental model equation for the behavior of the motor.

The equipment was used: motor- GM8X12, NIS Elvis Board, LabVIEW program, Amp

Meter, pliers.

Discussion:

Block Diagram: We added 3 frames, before after and the middle one. Outside the

first frame we added a variable power supply to initialize (it is important to be

outside the loop), 1 inside the first frame with a constant voltage of 5[V], 1 to finish

in the last frame of the flat sequence. Time Sequence: In the first frame of the flat

sequence we have a tick count, and as before we have one in the first frame of the

flat sequence and one inside the while loop to give us the time in ms. We have 2-

initialize arrays, one to take data from good rpm one to take data from time. Now we

have a time constant, of a 1000, which is linked to a stop sequence, in other words

we had run for 1 s. We have 2 build array inside the middle flat sequence inside the

while loop, 2 build array wired to itself as before, one to take data from time, one to

take data from good rpm. Finally in the last frame of the flat sequence we used

another build array and wired the two outputs (one from time array, one from rpm

array) and we send that signal to write to spreadsheet (2D data, 2 arrays), and to a

graph.

Resistance Measurements:

We obtained Ra1, Ra2 (resistance of the motor)in two ways.

First by measuring the resistance across the two terminals of the motor. The big

resistance is the armature resistance but there is some error in that measurement.

The motor does have other components inside the motor that have resistance andthat would cause higher resistance reading. We measured the resistance to be

Ra1 = 6.5[Measured resistance).

Second Resistance Ra2 we obtained by measuring the current through the Elvis

board with an Amp meter and applying enough torque so that the armature that it

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does not rotate, therefore the w=0, due to no rotation and this allowed us to

calculate the current through the motor, and we know the constant voltage of 5[V],

Using Ohms Law we calculated the Resistance Ra2. Current I= 1.025 [A], V=IRa2,

Ra2= 4.878[Calculated Resistance)

Derivation for the open loop equation:

dw

dt+K2

JRaw =

K

JRaea +

Tapplied

J,there is no applied torque so equation becomes:

dw

dt+K2

JRaw =

K

JRaea ,

w = wc +wp(1),

where wc = complete (complementary homogeneous) solution, and

wp = particular (forced) solution.

dw

dt+Kw = 0, w = Aekt,

dw

dt= -

K2

JRaw k= -

K2

JRa

wc = Ae

- K2

JRat

(2),

wp =C (3),

Now substituting equation (2) and (3) into equation (1), we get:

w = Ae

- K2

JRa+C,

K2

JRaC=

K

JRaea C=

ea

K,

w = Ae

- K2

JRa ,using initial condition of w (0)=0 we get:

0 = A +ea

K A = -

ea

K; Now plugging the constants back in we get:

w(t) = ea

Ke

- K2

JRa+ ea

K w(t) = ea

K(1 - e

- K2

JRa ),

where

t = JRaK2

, w(t) =ea

K(1 - e

- t

t ).

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t = JRaK2

, from here we can solve for J (Moment of Inertia of the Motor), using from

the excel spreadsheet that we created of the motor step response, of reaching the

steady state.

Using

w(t) =ea

K(1 - e

- tt ). setting t we get:

w(t) =1 - e-1

t = 0.632121w.Using the Excel spreadsheet graph that we created and the 63% of the steady state

value, we obtained the corresponding time = 106.5 [ms].

Correlation Linear Regression

Steady State

RPM Tau RPM Tau Time

0.595792707 1.253848324 2936.962515 1856.454006 106.5 [ms]

Calculating J:

t = JRaK2

, solving for J, using K=1.43 [Volts/kRPM] = 13.7e-3 [Nm/A] and

R=4.878[], .1065 [s]

J= 4.0977829[Kg*m2].

Comparison:

Obtained Experimentally Manufacturers Specifications

Resistance [] R= 4.878 R= 4.38Voltage [V] V=5.0(constant) V=12(reference)

Motor Constant K [V/kRPM] K=1.433 K=1.43

Current [A] I=1.025(w/ applied torque) I=0.22(no load)

Torque constant [Nm/A] KT=13.7e-3 KT=13.7e-3

Moment of Inertia [kg*m2] J= 4.0977829 J=9.18e-7

Conclusion: In conclusion we used the motor model equation to derive the

experimental design, open loop equation, which is the experimental model equation

for the behavior of the motor. We obtained the resistance in 2 ways; one was more

accurate than the other. We derived the open loop equation and an excel plot that

was used that to calculate J.

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Block Diagram:

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Good Rpm:

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Graph from LabVIEW (white line is time and the axis in number of samples, in excel

we make a plot of rpm vs. time where we make the time to be the x-axis):

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