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Steady State Operating Curve

By Lanze Berry

University of Tennessee at Chattanooga

Engineering 3280L

Blue Team (Khanh Nguyen, Justin Cartwright)

Course: ENGR 3280L

Section: 001

Date: September 4, 2012

Instructor: Dr. Jim Henry

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Introduction

This laboratory was used to understand a single-input, single-output system and to

observe the relationship between the two in a steady state condition. A motor generator is used

by a single input to provide constant power and the single output is current that was also

generated by the motor generator. The input and output are measured as functions of time by a

computer program and further analyzed. The results obtained will be used to observe the steady

state performance of the system. The main objective of this laboratory is to develop and

interpret a steady state curve of the system and how it will respond to varying power input.

The background and theory of the experiment is discussed. Following the background

and theory is the procedure of the experiment. The results are then presented and followed by

the discussion of the results. The last two sections will include the conclusions and

recommendations and the appendices, which will be at the end of the report containing all the

raw data.

Initially, the “Background and Theory” section will present the physical and

mathematical models used to represent and analyze the data. The “Procedure” section will then

describe how the laboratory was conducted and the method in which it was performed. The

“Results” section will include graphs and tables to explain how the experimental data relates to

the initial objective of the laboratory. The “Discussion” will contain the significance of the

results. The “Conclusions and Recommendations” section will describe the principles that were

demonstrated by the results and the discussion. The “Appendices” will be the last section

containing all the remaining data and graphs involved with the results.

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Background and Theory:

This laboratory shows the relationship between a single-input and single-output of a

control system in steady state conditions. A steady state operating curve is developed by using

the data acquired by sensors and a computer. This operating curve will help show when steady

state is reached. Then the average values of the output will be analyzed using statistics to find

uncertainties in the measurements.

The materials used in this lab are a computer, motor, generator, controller, transmitters

and light bulbs. A computer program called LabVIEW is used to graph the readings of the

experiment. The computer is used to send a constant input power signal to the motor. The motor

will then cause the generator to produce amps. A signal will then be sent back to the computer

as an output. Once the signal is received by the computer, LabVIEW will then graph the input

and output readings. Once this has been done, the data can be read by EXCEL, which will help

in the analysis of the data. Figure 1 shows the schematic of the motor-generated system.

Figure 1: Schematic of the Motor- Generated System

Computer

Motor Generator

Light Bulbs

JT 101

JRC 101

ERT 101

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Figure 1 demonstrates in schematic form the procedure of sending an input and receiving the

output. The computer sends a signal to the power transmitter (JT 101) which in turn relays it to

the power-recording controller (JRC 101). Once the signal is received, it is sent to the motor

where the percentage power is the input. The motor begins to turn and the mechanical energy is

converted to electrical energy. The generator uses electromagnetic induction to convert the

energy. The new electrical energy is then used to create current to the light bulbs. The generator

then sends an amps output signal back to the (ERT) and relays the signal to the computer where

it is interpreted in LabVIEW as a graph. The block diagram is shown in Figure 2.

Figure 2: Block Diagram of the Motor-Generated System

Figure 2 shows the input to the system on the left hand side of the block. The input is the time

allotted (in seconds) for the experiment and the motor power (in a percentage from 0 to 100).

The output response from the system is shown on the right side of the block. The output C(t)

demonstrates that it is a function of time. The output also contains the generated amps. The

system responds by giving a different amp output to each different input containing the time and

motor power percentage used.

Motor-

Generator

System

Input M(t)

Motor Power (%)

Output C(t)

Generated Voltage (V) Generated Amps (A)

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Procedure

The experiment begins with using a computer. A program called LabVIEW is used as

system control and it collects data throughout the duration of the experiment. This program was

accessible through the internet and the Control Systems class website. Once the Current

Information Systems group was selected, a choice appeared to begin collected data for the

Constant input function. Once this was selected, a screen appeared with credentials to fill out

(name, email, etc…). Also, a space was provided to enter the how many seconds the experiment

was to last and there was also a space to enter at what percentage the power should be. Once the

criterion was complete, the program would conduct the experiment according to the time and

percentage entered. The program then records and plots the data into a data base. The

experiment was conducted five times at various percentages to provide an output between three

to four amps. The data was then translated into excel to plot a steady state operating curve and to

statistically analyze the data. Figure 3 shows the flow of information in LabVIEW.

Figure 3: Flow of Information to and from LabVIEW

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Results

The experimental data was collected using LabVIEW. LabVIEW measured the current

in amps of the input percentage. Once it was collected, it was compiled into graphs using excel.

These graphs represented the power input percentages from 72.5% - 74%. The target output was

3 to 4 amps. Figure 4 is a sample graph that was created using a power input percentage of

72.5%.

Figure 4: Time(s) vs. Input(%) vs. Output(Amps) for 72.5% Power

Figure 4 shows that the system reached steady state around 39 to 40 seconds. Therefore, any

data collected previous to that can be neglected. From 0 seconds to 39 seconds, the data was not

included to find the average or the standard deviation. The average came out to be about 3.6

amps and the standard deviation was calculated to be about 0.007 amps. At 72.5% input power,

the system took about 39 seconds to reach a consistent level thus reaching steady state. Graphs

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were created for power input percentages of 72.5% - 74% in 0.5% intervals and can be found in

the appendix. The results of the experiments can be represented in Table 1.

Table 1

Input Percentage (%) Output (Amps) Uncertainty (Amps)

72.5 3.6 0.006

73 3.7 0.005

73.5 3.8 0.005

74 3.9 0.006

The average amps and standard deviations in Table 1 were used to create a graph. This graph is

a representation of the steady state operating curve (SSOC). Figure 5 is the graph of the SSOC

for the current system from 72.5% - 74% power inputs at 0.5% intervals.

Figure 5: SSOC

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Figure 5 shows that the system is stable between 72.5% and 74%. The system output current

through the steady state operating range is 3.6-3.9 amps. The graph shows a linear line with a

constant slope having the equation Amps = 0.2input% - 10.9. This validates the linearity and

constant slope.

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Discussion

After obtaining the results, this experiment indicates that at a constant steady state is

obtained in the current system with varying input percentages. The steady state operating curves

are linear within the 72.5% - 74% range. This is the primary point of interest of this experiment.

The maximum standard deviation within the steady state operating curve was 0.06 amps. This

shows that the data and the mean of the data had a very close relationship and validates that the

output reached a constant or steady state.

The steady state operating curve provides confidence to the numbers that were obtained

in the experiment. It is proven that the motor in the system can be forced to operate within a

desired region of performance. The motor is able to generate the desired current. Since the

motor level determines the output amps, it was necessary that the motor could produce 3 to 4

amps and make it steady state. The motor was able to do this for all the tested percentages

between 72.5% and 74%. When working with a system, it is important that the system can

operate within a steady state region.

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Conclusions and Recommendations

Initially, this experiment was to determine the output in volts using a power input

percentage. After some complications, the experiment changed to measuring current. After this

change was made, data was collected on a system by a power input percentage that gave an

output in amps. The results that were obtained in the experiment clearly showed what was

necessary for a steady state operational curve for the system. The experiment validated that a

current system with a constant input has an operating range where steady state can be attained.

The main objective of the lab was to determine a steady state operating curve for a

current system with an input power percentage and an output in amps. To do this, a computer

was used to generate the motor and produce a current. The results obtained clearly present the

necessity for a system to operate within the steady state region of the curve.

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Appendix

Figure 6: Amps vs. Time for 73% Input Power

Figure 7: Amps vs. Time for 73.5% Input Power

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Figure 8: Amps vs. Time at 74% Input Power

References:

1) http://chem.engr.utc.edu/329/

2) Carlos A. Smith and Armanso Corripio, Principles and Practice of Automatic

Process Control., John Wiley & Sons Inc., 3rd

Edition, 2006 (Appendix A)