Course: ENGR 3280L. Section: 001. Date: 9/6/2012. Instructor: Jim Henry. Chris Hawk 9/6/2012

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1 1 University of Tennessee at Chattanooga Steady State Operating Curve for Filter Wash Station ENGR 328L By: Red Team (Casey Villines, Brandon Rodgers) Course: ENGR 328L Section: 1 Date: 9/6/12 Instructor: Jim Henry 9/6/12

2 2 Introduction: The objective of this laboratory experiment is to use the flow rate output responses at given pump power inputs on a time scale to develop a steady state operating curve for a filter wash station. The input for the system is the power of the pump and the output of the system comes from a flow meter in the system. The experiment will be ran on a range of output values from 33 lb/min to lb/min by varying the pump power in 2% increments. An operating curve and average value will be developed at each pump power level used in the experiment. Finally all of the average values will be combined to create a steady state operating curve for a range of power levels that generate flow rates that lie inside the experimental range. The Background and Theory section of this report will go into basic control systems along with their steady state operating curves in more detail as well as covering the basic apparatus that is used in the experiment. The Procedure section will cover how the apparatus is used to perform the experiment as well as how the data is gathered from the experiment for analysis. The Results section of this report will cover what was found experimentally in the experiment. The data in the results section will be organized in tables and graphs to improve the understandability of the material. The Discussion section will explain the data collected from the experiment in more detail and discuss the significance of the experimental data to the background and theory of the experiment. The Conclusions and Recommendations section of this report will give a brief overview of what was covered in this report as well as make recommendations to anyone who will be performing this experiment in the future. 9/6/12

3 3 Background and Theory: A control system in the most basic form is a system that receives inputs and responds to the inputs by generating outputs. A basic control system diagram is shown below in Figure 1. Input m(t) System Output c(t) Figure 1: Diagram of a Basic Control System Every control system has inputs and outputs, the name for the basic input function is generally referred to as m(t) and the name for the basic output function is referred to as c(t). The functions are related by a common variable, time. If a time t is plugged into the input function, m(t), the resulting output can be generated by plugging time t into the output function, c(t). A steady state operating curve is a curve that compares the output values, on the vertical axis, with the controlled input values, on the horizontal axis. To accomplish this, a graph of the outputs at each input must be generated using time as the common variable. This graph is used to find the point in time when the system operates at a steady state. This graph has three different variables that are all related through the common variable, which is time. The left vertical axis represents the input, which will be constant, the right vertical axis represents the output, and the common horizontal axis represents time. The point when the system reaches steady state is when the output values have the smallest amount of variation over time. This can be observed in the operating curve simply by finding the range of time where the output line becomes somewhat level. An example of an operating curve is shown in Figure 2 and an example of a steady state operating curve is shown in Figure 3 on the next page. 9/6/12

4 4 Input m(t) Example Operating Curve Steady State Region Input m(t) Output c(t) Time Output c(t) Figure 2: Example of an Operating Curve Example Steady State Operating Curve y =.4666x Output c(t) Output c(t) Linear (Output c(t)) Input m(t) Figure 3: Example of a Steady State Operating Curve 9/6/12

5 5 The system in this experiment is a filter was station where the input for the system is the power level (%) of the pump via a variable frequency drive on the pump motor and the output comes from a flow meter in the system that gives flow rates in pounds per minute. The basic diagram of the system is show below in Figure 4. Input Pump Power (%) System Output Flow Rate (lb/min) Figure 4: Basic Control Diagram of Filter Wash System The components of the Filter Wash System that is used for this experiment are a pump that is connected to a variable frequency drive, which allows for power percentage adjustment, a set of nozzles, and two electronically controlled valves that each connect to a different filter was station. A schematic of the Filter Wash System that is used in this experiment is shown in Figure 5 below. Figure 5: Schematic of Filter Wash System As shown in Figure 3 above the wash water comes into the pump, it then travels through a flow meter where the flow rate is measured. The water lines then branch off to three different 9/6/12

6 6 paths. One path goes to a set of filter was nozzles, the other two paths each go through an electronic valve and then to separate filter wash stations. For this experiment both of the valves will be closed and the wash water will only go to the filter wash nozzles. The way that the raw data from the experiment will be analyzed starts first with determining a point where the flow rate output of the system shows steady state behavior. At this point and for the remaining points in time until the end of the experiment an average and a standard deviation will be calculated for the outputs from this time range. For each of the input points the true value of the function will be found using the Mean ± 2 X Standard Deviation, this calculation will yield a 95% confidence level for the true values of the function. 9/6/12

7 7 Procedure: This experiment will be performed remotely through an online interface that is connected to the filter was system. The inputs that are required to run the experiment are as follows: the input power level of the pump, the state of Valve 1 (Open or Closed) and the time interval for that state, the state of Valve 2 (Open or Closed) and the time interval for that state. For this experiment both valves will be closed for the duration of the experiment and the motor will be ran to achieve flow rates between 33 (lb/min) and (lb/min). Trial and error will be used to find the input power (%) that correlates to the starting point of roughly 33(lb/min) output. After this starting power (%) is found, the power will be increased from that point in 2% increments until either the maximum output is reached or the pump reaches 1% power. At each of the power increments the experiment will be ran for a total of 15 seconds to be certain to achieve steady state operation. As the experiment is running the control computer records the flow rates at a large number of points in time, this data is recorded in a file that can be saved locally and opened in excel. Excel will be used to generate the operating curve, average of the steady state output values, and standard deviation of the steady state output values for each power input used. After these values are calculated they will be combined to form a table with the true values for the function along with a steady state operating curve for the system at a range of power inputs. 9/6/12

8 8 Results: The starting power level for the experiment was found through trial and error and it was found to be 88% power to the pump motor. The maximum power used was 1% because the pump could not generate the targeted maximum flow rate of 44 (lb/min). The calculated values that correlate to each of the power inputs along with the standard deviation, the error and the true value are shown below in Table 1. Pump Power (%) Mean (lb/min) Standard Deviation (lb/min) Error (lb/min) True Value (lb/min) ± ± ± ± ± ± ± 1.62 Table 1: Reported values for mean of steady state operating outputs, standard deviation of steady state operating outputs, error in true value, along with actual true values for each pump power input. From the calculated values above, a steady state operating curve was generated using excel for the pump power interval of 88% to 1% which generated flow rates between roughly 33 (lb/min) and 39 (lb/min). This steady state operating curve is shown in Figure 6 on the next page, the curve also include a linear trend line for the data points and an equation for that trend line that can be used to fairly closely estimate the output flow rate at a given input within the range of this experimental data. 9/6/12

9 9 45 Output Flow Rate (lb/min) Linear () Output (lb/min) = (.4666)(Input %) Input Pump Power (%) Figure 6: Steady state operating curve for the Filter Wash System for pump input powers ranging from 88% to 1% 9/6/12

10 1 Discussion: At the starting point of 88% power to the pump, the system generated a flow rate output of 33. ± 1.66 (lb/min) and then at the other end of the experiment interval the pump maxed out at a power level of 1% and a flow rate of ± 1.62 (lb/min). The maximum target flow rate of the experiment, 44 (lb/min), could not be achieved due to limitations of the system. Between the operating range of 88% power to the pump and 1% power to the pump the error of the calculations maxed out at 1.66 (lb/min) and was a minimum at 1.48 (lb/min). Steady state operating at all of the input pump power levels was reached at an experimental duration of 6 seconds and the experiments continued up to a duration of 15 seconds. On the steady state operating curve shown in the Results section of this report an excel trend line was used to calculate a linear relationship between the data values in order to give a function as a tool for estimating outputs at inputs not recorded in this experiment. The function for the line is =(.4666)(Input(%))-7.795, this function shows that there is a linear correlation between the data points that were calculated in this experiment. The true values for the output flow rates in this experiment are shown in Table 1 in the Results section of this report. These true values show the mean flow rate with the error associated with the variation of the outputs during the time interval where the system reached a steady state. The true values for this experiment were calculated with a 95% confidence interval to ensure accuracy. 9/6/12

11 11 Conclusions and Recommendations: This experiment was performed in order to gather data from a Filter Wash Station at several power input percentages so that a steady state operating curve could be generated for the system. The experiment was successful in that the values for the experiment were recorded and corresponding calculated values were generated. Also a steady state operating curve was generated along with a linear correlation between the data points in the interval. A function was generated so that the data points not calculated in the experiment could be estimated by simply plugging in the input power of the pump. A better understanding of basic control systems was gained along with an better understanding of linear steady state operating curves and operating curves. A recommendation for any follow up experiments would be to increase the number of data points used in the experiment to increase the accuracy of the linear correlation and thus generating an even more accurate steady state operating curve. Another recommendation from a system design standpoint would be to increase the pump capacity so that the maximum target flow rate for the experiment could be achieved. 9/6/12

12 12 Appendices: Time(sec) Figure 7: Operating Curve for 88% Pump Power Input Time(sec) Figure 8: Operating Curve for 9% Pump Power Input 9/6/12

13 Time(sec) Figure 9: Operating Curve for 92% Pump Power Input Time(sec) Figure 1: Operating Curve for 94% Pump Power Input 9/6/12

14 Time(sec) Figure 11: Operating Curve for 96% Pump Power Input Time(sec) Figure 12: Operating Curve for 98% Pump Power Input 9/6/12

15 Time(sec) Figure 13: Operating Curve for 1% Pump Power Input 9/6/12