1 Steady State Operating Curve University of Tennessee at Chattanooga Engineering 3280L Instructor: Dr. Jim Henry By: Fuchsia Team: Jonathan Brewster, Jonathan Wooten Date: February 1, 2013
2 Introduction The basis of this experiment is to start with an input-output mechanism to achieve a steady state curve in a system. The start is with an input which we use though the computer that runs a power generator within the lab. This provides an output which is a graph given in cm- H2O. From the results, the data is provided with the input at a certain percentage while the output was in cm-h2o with time. The true objective of the work is to develop a steady state curve where we form a graph that plots input vs. output at different power percentages. Background and Theory: This experiment explains an input-output relationship with a single function going into the overall system. The means of acquiring data is though the computer which requires an input percentage and provides the output in cm-h2o. However, there will be some uncertainty in the experiment which will be calculated later on. The basis of this experiment starts with the computer which transmits a signal to the power motor which is the input. Afterwards, the power motor generates pressure which is measured as cm-h2o through the system. Data is given out though a graph and can be downloaded as a text file or using Excel for further analysis. Figure 1: -
3 m time. This variable goes into the system and provides the end of the system known as the c( m(t) is known as the manipulated variable whereas the c(t) is known as the controlled variable. Within the experiment, Figure 1 shows that the input is power in percentages going into a motor generator. This provides the ending output of cm-h2o which is the measured pressure within the lab. Eq. 1 the population, m is the mean of the values, and N is the sample size of the range used. The
4 Procedure: The start of the experiment begins with the internet which we use LabVIEW (Laboratory Virtual Instrument Engineering Workstation) to gather data [1]. There are given inputs for the specific input power percentage and the length of time for the experiment. As the experiment runs, we have to refresh the browser or wait till it refreshes itself to show a plot of the data that is obtained. The percentage inputs were done at different ranges depending on the range desired. The data obtained was allowed to be transferred into Excel where it was analyzed. The standard deviation is then calculated over a certain range. Using this information, the data will be used to form a steady state curve. Figure 2 below shows a diagram of procedure. Computer LabVIEW Output Repeat process Calculate data from selected range Data used to form a chart Data transfer to Excel
5 Result: The data obtained was used to create graphs that plotted cm-h2o output verses time with the input percentage in Excel. The figure below is a sample graph generated by Excel. 80 From Figure 3, the data is in a plotted graph version where the x axis is the time in seconds. The primary y axis (left) is the output in cm-h2o which matches the red line. The secondary y axis (right) is given the input in percentages which matches the blue line. The mean value is shown below the brackets which also include the error margin. Because the system is in a steady state condition, the way to read the numbers below the graph is the average output was 45.86 ± 1.6 cm-h2o between 1 to 30 seconds at an input of 80%. A few other graphs are included in the Appendices. From the results gathered by the graphs of the experimental runs, the data is used to make a table of values that can be used to graph a steady state operating curve. The table below shows the range of input that we used.
6 Power Input Percent % Output (cm-h2o) Standard Deviation Uncertainty 0.0 0.0 0.0 0.0 10.0 0.0 0.0 0.0 20.0 0.9 0.6 1.2 30.0 4.9 0.6 1.2 40.0 10.4 0.7 1.5 50.0 17.1 0.7 1.4 60.0 25.3 1.1 2.1 70.0 35.0 1.3 2.5 75.0 40.3 1.3 2.6 80.0 45.9 1.5 3.1 90.0 51.7 1.7 3.4 100.0 51.3 1.7 3.4
7 From Figure 4 above, the plotting on the vertical y axis is the cm-h2o output of the system where the horizontal x axis is the percentage input. Based on Figure 4, the data shows that the range is somewhat linear between 20% and 90%. Doing an analysis of the data, the range has a slope of 0.7 cm-h2o per percent.
8 Discussion: From the Steady State Operating Curve diagram, the system is at a consistent line. Due to the linearity, it is possible to describe with a first order differential equation since the slope of the line is 0.7 cm-h2o per percent for the overall system. Graphing of the selected individual reports is shown in the Appendices section that shows the data reported with the error. However, the main assumption of this experiment was assuming the system was at steady state conditions. Ending the experiment, the error percentage at most was 1.7% at the 90% mark. Conclusions and Recommendation: Considering the experiments done to gather and analyze data, the steady state operating curve was formed. As the results go, the steady state curve was linear from the range of 20% to 90%. Regarding all the graphs that will be in the Appendices, the input-output graphs all had a transient state where the system required a certain amount of time before reaching its steady state form. Using LabVIEW and Excel, we were able to analyze the data and graph the points to find the standard deviation and determine its importance. The importance of the experiment is the ability design a system that operates within the linearity of the steady state operating curve.
9 Appendices: A. Cm-H2O Vs. Time Graphs B. References
10 A. 12 10 8 6 4 2 0 Input Value(%) Output (cm H2O) Sample Graph of Experimental Data at 10% Input 35 30 25 20 15 10 5 0 Input Value(%) Output (cm H2O) Figure 6 Sample Graph of Experimental Data at 30% Input
11 60 50 40 30 20 10 0 Input Value(%) Output (cm H2O) Figure 7 Sample Graph of Experimental Data at 50% Input 80 70 60 50 40 30 20 10 0 Input Value(%) Output (cm H2O) Figure 8 Sample Graph of Experimental Data at 70% Input
12 100 90 80 70 60 50 40 30 20 10 0 Input Value(%) Output (cm H2O) Figure 9 Sample Graph of Experimental Data at 90% Input
13 References: [1] http://chem.engr.utc.edu/3280l/ [2] Carlos A. Smith and Armanso Corripio, Principles and Practice of Automatic Process Control., John Wiley & Sons Inc., 3rd edition, 2006