Steady State Operating Curve Voltage Control System

Size: px

Start display at page:

Download "Steady State Operating Curve Voltage Control System"

Damian Malone
5 years ago
Views:

1 UTC Engineering 39 Steady State Operating Curve Voltage Control System Michael Edge Partners: Michael Woolery Nathan Holland September 5, 7

2 Introduction A steady state operating curve was created to show the relationship between the input percentage and the output voltage. The curve was created so that the output voltage could be estimated for any input percentage. The objective of this lab was to create a steady state operating curve for the voltage control system. The output voltage was recorded with respect to time for twenty different inputs in five percent increments. The data was then put into excel, and the average voltage and standard deviation was calculated. These calculated values were then used to plot the steady state operating curve, which shows the output voltage with respect to the percentage of the input. This Report contains six sections. The background and theory section which provides needed information about the system. The procedure section provides the steps that were taken to complete the experiment. The following three sections display and discuss the results, as well as provide the conclusions that have been drawn. An appendix has been added on to the end to display the remaining data recorded. Background and Theory To start off the experiment you pull up the lab view front panel. Lab view asks you for two inputs. It asks you for the length in seconds that the experiment will be run and the percent of input. Edge 9/5/7

3 The experiment is run using a generator that is being powered by an electric motor though a direct drive unit. The input that you put into lab view is a percentage. So if the motor has an operational range from to 36 rpm, % would be rpm and % would be 36 rpm. In this particular experiment the motor speed is held constant to achieve a constant output voltage. The time that is entered into lab view is the time in seconds that the experiment will run. The time in the experiment should be long enough for the system to reach steady state conditions. Once the experiment is finished lab view presents the output voltage in volts as a function of time in seconds. A diagram that shows the inputoutput relation is in Figure. m(t), Input Motor power (%) Generator c(t), Output Voltage (V) Figure. Block diagram of Voltage Control System Procedure The output voltage is measured at steady state condition for a specific percentage of input. The input is measured in five percent increments from zero percent to one hundred percent. The length of each experiment was to be as long as needed to reach steady state conditions. The collected data was then put into an excel spreadsheet. A graph was then created with the independent axis being the time of the experiment and the dependant axis being the output voltage. The steady state portion of the graph was then found. The Edge 9/5/7 3

4 average output voltage was then found for the steady state portion of the data using the following equation. x = n n i = x i The standard deviation of the steady state portion of the data was also found using the following equation. n ( x x) i= i s = n A table was then formed in excel containing the input percentage, the output voltage, standard deviation, and two times the standard deviation. The values from the excel table were then used to form a steady state operating curve with input percentage on the independent axis and the average output voltage on the dependant axis. Dependant axis error bars were then formed using two times the standard deviation. Results At sixty percent input, it takes the output voltage about 5 seconds to reach a steady state output of 7.68 volts (Figure, pg 5). The standard deviation is calculated using the output voltage from 5 sec. to the last data point. The standard deviation of this steady state is.3. Edge 9/5/7 4

5 Output Voltage vs Time - 6% Ouptut Voltage (V) Figure. Output Voltage vs. Time at 6% Input At eighty percent input, it takes the output voltage about 6 seconds to reach a steady state output of 88. volts (Figure 3, pg 5). The standard deviation is calculated to be.338 for this steady state time interval. Output Voltage vs. Time - 8% Output (volts) Figure 3. Output Voltage vs. Time at 8% Input Edge 9/5/7 5

6 At one hundred percent input, it takes 7 seconds to reach a steady state output voltage of 39. volts (Figure 4, pg 6) The standard deviation is calculated to be.84 for this steady state time interval. Ouput Voltage vs. Time - % Ouput Voltage (V) Figure 4. Output Voltage vs. Time at % Input The graphs for the rest of the inputs have been placed in Appendix A. Table, (Table, pg.6), shows the average output voltage, the standard deviation, and two times the standard deviation for all of the inputs tested. Table. Steady State Operating Values Input Motor Speed (%) Output Voltage (V) Standard Deviation * Std- Dev.. ±. 5.. ±..3.4 ± ± ± ±.3 Edge 9/5/7 6

7 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±.69 The steady state operating curve, (Figure 5, pg 8), shows the data in Table, (Table, pg 6), in graphical form. The Dependant axis error bars were formed by using two times the standard deviation. Edge 9/5/7 7

8 Steady State Operating Curve - Voltage System c, m, Input Motor Speed (%) Figure 5. Steady State Operating Curve for the Voltage System Discussion As expected with and input percentage of zero percent the output was zero. The output stayed around zero until the input percentage reached around forty-five percent. Once reaching 5 percent the output then started increasing at a higher rate. Between seventy and seventy-five percent the output voltage jumped from 6.6 volts to 7.3 volts. From seventy-five to one hundred percent the output voltage steadily increased from 7.3 volts to 39. volts. Now looking at the graphs of output voltage verses time for each input percentage, it takes the system a few seconds to reach steady state. A maximum time of about forty Edge 9/5/7 8

9 seconds to reach steady state, looking at the 75% input. The standard deviation stayed fairly low with a maximum of.3, excluding the.88 at seventy-five percent input. Conclusions and Recommendations A steady state operating curve has been formed for the voltage control system. After evaluating the steady state operating curve for the voltage control system, some things have been brought to my attention when considering designing a voltage control system. One must take into account the time that it takes for the system to reach steady state. One must also take into account the error involved between the output voltages and input percentages. Now having run the experiments, a person looking to design a control system can look at the data collected in this experiment and account for the time it takes for the system to reach steady state, as well as look at the steady state operating curve and predict the input required for a certain output voltage. The data found in this experiment can be used with 95% confidence. Meaning the system will function without problems 95% of the time. Edge 9/5/7 9

10 Appendices Output Voltage vs. Time - % Figure A. Output Voltage vs. Time at % Input Output Voltage vs. Time - 5% Figure A. Output Voltage vs. Time at 5% Input Output Voltage vs. Time - 5% Figure A3. Output Voltage vs. Time at % Input Edge 9/5/7

11 Output Voltage vs. Time - 5% Figure A4. Output Voltage vs. time at 5% Input Output Voltage vs. Time - % Figure A5. Output Voltage vs. Time at % Input Output Voltage vs. Time - 5% Figure A6. Output Voltage vs. Time for 5% Input Edge 9/5/7

12 Output Voltage vs. Time - 3% Figure A7. Output Voltage vs. Time for 3% Input Output Voltage vs. Time - 35% Figure A8. Output Voltage vs. Time for 35% Output Voltage vs. Time - 4%.5 Output voltage (V) Figure A9. Output Voltage vs. Time for 4% Input Edge 9/5/7

13 Ouput Voltage vs. Time - 45% Figure A9. Output Voltage vs. Time for 45% Input Output Voltage vs. Time - 5% Figure A. Output Voltage vs. Time for 5% Input Ouput Voltage vs. Time - 55% Figure A. Output vs. Time for 55% Input Edge 9/5/7 3

14 Output Voltage vs. Time - 65% Output (volts) Figure A. Output Voltage vs. Time for 65% Input Output Voltage vs. Time - 7% Output (volts) Figure A3. Output Voltage vs. Time for 7% Input Output Voltage vs. Time - 75% Output (volts) Figure A4. Output Voltage vs. Time for 75% Input Edge 9/5/7 4

15 Output Voltage vs. Time - 85% Output (volts) Figure A5. Output Voltage vs. Time for 85% Input Output Voltage vs. Time - 9% Output (volts) Figure A6. Output Voltage vs. Time for 9% Input Output Voltage vs. Time - 95% Output (volts) Figure A7. Output Voltage vs. Time for 95% Input Edge 9/5/7 5

University of Tennessee at. Chattanooga

University of Tennessee at. Chattanooga University of Tennessee at Chattanooga Step Response Engineering 329 By Gold Team: Jason Price Jered Swartz Simon Ionashku 2-3- 2 INTRODUCTION: The purpose of the experiments was to investigate and understand