Lab Report on Process of heat exchange

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Lab Report on Process of heat exchange

A feedforward/feedback controller was to be designed, implemented and tested to control the outlet water temperature of a heat exchanger. The control scheme was to be designed for water flow rates of 4-8gpm and outlet water temperatures of 120-160. The controller was to be tested by evaluating its response to step changes in outlet water flow rate and temperature set points.

First, the ability of the controller to maintain an average outlet water flow rate within +/- 0.2gpm of the set point as well as an average outlet water temperature within +/- 1 of the set point was assessed at steady state. Second, the controller’s ability to sustain the outlet water temperatures within 5 of the set points was assessed for step changes in water flow rate of 1gpm. Finally, for step changes in the outlet water temperature of 20, the peak overshoot ratios (PORs) in the controller’s temperature responses were calculated with the target set to be less than 25%.

Initially, a set of tuning parameters were predicted using the open-loop tuning method and adjusted by guessing their values and observing the changes in the control scheme’s authority. At steady state, this set of tuning parameters allowed the controller to maintain an average outlet water flow rate within +/- 0.2gpm, and an average outlet water temperature within +/- 1 of the flow rate and temperature set points. The controller also succeeded in sustaining the outlet water temperature within +/- 5 of the set point for 1gpm step changes in water flow rates between 4-8gpm conducted at a temperature of 120. However, the controller did not work as well for higher temperatures as the temperature deviated by more than 5 for step changes of 4-5gpm and 7-8gpm at a temperature of 140, and for a step change of 6-7gpm at a temperature of 160 For 20 step changes in the outlet water temperature for temperatures between 120-160, the PORs in the controller’s temperature response were above 25% for all of the flow rates between 4-8gpm except one; thus, the controller failed to respond to these disturbances rapidly nine out of ten times.Lab Report on Process of heat exchange

Due to the controller’s great many failures, especially in response to step changes in temperature, the time constant of the controller’s temperature feedback portion was adjusted. The controller was once again tested specifically for the tests that it had originally failed. The results improved slightly. For step changes in water flow rate, the controller maintained the temperature within the boundaries of +/- 5 for all step changes at 140, but had failed once again for a step change of 6-7gpm at a temperature of 160 Two trials were conducted for step changes in temperature using the new set of tuning parameters. In both trials, the POR was above 25% at flow rate of 4gpm for each of the step changes in temperature of 120 to 140 and 140 to 160. While the new set of tuning parameters allowed the controller to achieve the target POR better than it used to, such as achieving PORs of 5% and 4% at flow rates of 5gpm and 8gpm respectively, the controller failed to maintain a stable outlet water temperature in both cases and at other occasions as well; thus, failing numerous tests using the new set of tuning parameters.

The original set of tuning parameters failed 25% of the tests involving step changes in water flow rate, and 90% of the trials involving step changes in water temperature. The new set of tuning parameters had better results, where only 12.5% of the tests involving step changes in water flow rate and 50% of tests involving step changes in temperature failed.

Further tuning of the parameters is recommended, as the parameters used in this lab did not seem to work well. Conducting more trials for each set of parameters and observing the trends in the data would help in better tuning. In addition, conducting trials at a time when water and steam are not used by others in the pilot plant would prevent inconsistencies in the results.

Results and Discussion-Lab Report on Process of heat exchange

Prior to designing and implementing the feedforward/feedback control scheme, two feedback loops were created to control the outlet steam and water flow rates. These feedback loops adjusted the difference between the set points and the actual outlet flow rates by sending signals to the steam and water actuators. The actuators convert these signals into forces that act on the control valves, causing them to adjust the amount of water/steam allowed into the heat exchanger. The tuning parameters of these feedback loops were first predicted using the open-loop tuning method. However, due to the imprecision in the temperature probes and flowmeters, the parameters predicted did not work well and had to be adjusted. There was no good way to adjust these parameters other than guessing their values and observing how these changes affected the control scheme until the output was controlled well enough. Table 1 shows the tuning parameters that were used in this lab for each of the steam, water, and temperature feedback loops, where the latter was used in the combined feedforward/feedback controller.

Lab Report on Process of heat exchange

Table 1(3A): Original Kc and τi  Values for the Different Controllers.

  Kc τi (sec)
Water Flow Feedback 0.2 3
Steam Feedback 0.5 3
Temperature Feedback 0.05 17.278

 

When steam and water are allowed into the heat exchanger, heat is transferred from the steam to the water, as governed by the second law of thermodynamics. The equation that governs the temperature at which the water leaves the heat exchanger is described by Equation 1 below. This description of how the outlet water temperature is affected by different variables acting on the heat exchanger was the basis of the feedforward controller’s design. The heat capacity, cpw, was assumed to be constant. The volumetric flow rate of water was measured and multiplied by the density of water, which was also assumed to be constant, to give the mass flow rate of water mw. The outlet water temperature, Two, was the set point, and the inlet water temperature, Twi, was measured by temperature probes. The inlet and outlet enthalpies of steam, Hsi and Hso respectively, were defined as functions of temperature and multiplied by the measured mass of steam, ms. Finally, for this non-insulated heat exchanger, the heat loss had to be accounted for. The value for Qloss was guessed at the midpoint operating conditions of outlet water temperature of 140 and flow rate of 6gpm. The value was altered until the measured outlet water temperature agreed with the set point. The value of the heat loss obtained was validated by comparison with the change in enthalpy of steam. It was found that the heat loss value was almost 20% of the value of the change in enthalpy of steam, which is a reasonable estimate.

Lab Report on Process of heat exchange

Equation 1

After implementing the feedforward controller, a feedback temperature loop was added in parallel with it. This combined controller was tested using two different sets of tuning parameters. When the first set of tuning parameters failed to meet some of the design specifications, the time constant τi of the temperature feedback loop was adjusted to 100s while the rest of the tuning parameters were kept constant.

The first design specification that the controller had to meet was to maintain a stable water flow rate and temperature at the set point values. The controller’s ability to meet this specification was assessed after allowing the heat exchanger system to reach steady state. Boundaries for the average outlet water flow rates and temperatures were set as +/- 0.2gpm and +/- 1 of the set point values. The controller succeeded in maintaining a stable water flow rate at the set point values for either set of tuning parameters. Figures 1,2, and 3 show the response of the actual outlet water flow rate measured to 1gpm step changes of water flow rate set point at temperatures of 120, 140, and 160 respectively. Unfortunately, the controller failed to maintain temperatures within +/- 1 of the set point once for the original set of tuning parameters, and numerous times for the new set of tuning parameters during the various trials conducted in this lab.

 

 

Figure 1(A1): Response in water flow rate with a step change of 1gpm between 4gpm and 8gpm at constant temperature of T=120  with original Kc and Ti Values.

 

Figure 2(A13): Response in water flow rate with a step change of 1gpm between 4gpm and 8gpm at constant temperature of T=140  with new Kc and Ti Values.

 

Figure 3(A14): Response in water flow rate with a step change of 1gpm between 4gpm and 8gpm at constant temperature of T=160  with new Kc and Ti Values.

 

 

 

 

 

 

 

 

 

 

The second design specification of the combined controller was to prevent the outlet water temperature from deviating by +/- 5  of the set point for 1gpm step changes in the water flow rate. The step changes in the controller’s water flow rate set points were tested for flow rates between 4 -8 gpm at three temperatures: 120, 140, and 160. Using the original tuning parameters, the controller maintained the outlet water temperature within the boundaries of +/-5  of the set point for a temperature of 120, as illustrated by Figure 4. However, at a temperature of 140, the controller failed to maintain the temperature within the boundaries at step changes of 4-5 gpm and 7-8gpm. The controller also failed at temperature of 160 for a step change from 6-7 gpm, where the temperature deviated from the set point twice during the same trial. Table 2 displays the results of these trials. The tests for the second design specifications were repeated with the new set of tuning parameters. Due to time limitations, only trials that had failed to meet the specifications were repeated. Using the new set of tuning parameters improved the results slightly. Table 3 displays the results of the controller’s second design specifications’ trials conducted using the new set of tuning parameters. The controller maintained the outlet water temperature within the boundaries for all step changes of flow rate at temperature of 140, as illustrated by Figure5, and failed once at temperature of 160, which also happened to be for a step change of 6-7gpm.

Figure 4(A4): Temperature of Water Out, T=120 , for a 1gpm step change ranging from 4gpm to 8gpm with original Kc and Ti Values.

Table 2(A4): Step change in water flow rate with original Kc and Ti Values.

Set Point °F Initial Flow (gpm) Final Flow (gpm) Temp. Deviation °F Avg. Water Flow (gpm) Avg. Temp. °F
120 4 5 3.3 5.02 119.86
5 6 4.4 5.92 119.66
6 7 2.7 6.99 119.94
7 8 3.5 7.89 120.02
140 4 5 5.4 4.97 140.01
5 6 3.6 5.93 139.93
6 7 4.4 7.00 139.81
7 8 5.2 7.97 139.70
160 4 5 4.9 5.01 159.64
5 6 4.8 5.98 160.05
6 7 5.8 6.99 160.01
7 8 3.8 7.97 159.55

 

Table 3(A7): Step change in water flow rate with new Kc and Ti Values.

Set Point °F Initial Flow (gpm) Final Flow (gpm) Temp. Deviation °F Avg. Water Flow (gpm) Avg. Temp. °F
140 4 5 2.6 4.93 140.37
5 6 4.3 6.03 139.32
6 7 3.7 6.97 140.16
7 8 2.5 8.01 140.33
160 4 5 4.6 5.00 160.76
5 6 4.1 5.96 160.23
6 7 6.4 6.99 160.15
7 8 3.5 8.00 159.97

 

 

Figure 5(A15): Temperature of Water Out, T=140 , for a 1gpm step change ranging from 4gpm to 8gpm with new Kc and Ti Values.

Lab Report on Process of heat exchange

The third and final design specification for the combined controller was to have peak overshoot ratios (PORs) of less than 25% for 20step changes in the temperature set point. The controller was tested for step changes of 20 of outlet water temperature for temperatures between 120 to 160 at flow rates between 4-8gpm. Thus, for each of the five flow rates, two step changes in temperature were conducted. Using the original set of parameters, the controller’s temperature response had PORs more than 25% nine out of ten times. Table 4 shows the peak overshoot ratio of the controller’s temperature response for each step change at each of the five flow rates. For the new set of tuning parameters, two trials were conducted. For a flow rate of 4gpm, the POR was above 25% for both step changes of 120 to 140 and 140 to 160 during both trials. Flow rates of 5gpm and 8gpm were the only ones that had PORs less than 25% for both step changes. During the second trial, PORs of less than 25% were only achieved for both step changes at flow rates of 7gpm and 8gpm. However, while the new set of tuning parameters seemed to bring us closer to our POR target, it failed to maintain a stable outlet water temperature. For instance, PORs of 4% and 5% were achieved using the new set of tuning parameters, illustrated by Figures 6 and 7. However, in both cases, the average outlet water temperature was not within +/- 1 of the set point and thus ultimately the controller failed to meet the objective. The results of both trials, including the peak overshoot ratios and the average water flow rats and temperatures, are shown in Table 5.

 

Table 4(A5): Step change in temperature with original Kc and Ti Values.

Fixed Flow Rate

(gpm)

Initial Temp. °F Final Temp. °F  

Max Temp. °F

POR Avg. Water Flow (gpm) Avg. Temp. °F
4 120 140 147.4 37.0% 4.01 138.68
140 160 167.9 39.5% 4.00 159.77
5 120 140 147.7 38.5% 5.00 139.81
140 160 166.1 30.5% 4.99 159.70
6 120 140 147.3 36.5% 6.00 139.79
140 160 165.4 27.0% 5.98 159.23
7 120 140 146.4 32% 6.98 139.70
140 160 166.5 32.5% 7.02 160.18
8 120 140 144.9 24.5% 7.98 139.46
140 160 165 25.0% 7.97 159.65

 

 

 

 

 

 

Lab Report on Process of heat exchange

Figure 6(A18): Temperature of Water Out at 5gpm for a 20 step change ranging from a 120 to a 160 with new Kc and Ti Values for two trials.

Figure 7(A21): Temperature of Water Out at 8gpm for a 20 step change ranging from a 120 to a 160 with new Kc and Ti Values for two trials.

 

Table 5(A8): Two trials of step changes in temperature with new Kc and Ti Values.

Fixed Flow Rate

(gpm)

Initial Temp. °F Final Temp. °F Max Temp. °F POR Avg. Water Flow (gpm) Avg. Temp. °F
4 120 140 147.3 36.5% 3.94 140.99
147.3 36.5% 4.04 139.51
140 160 165.1 25.5% 3.95 161.18
166 30.0% 3.97 160.63
5 120 140 144.6 23.0% 5.04 140.39
141 5.0% 4.97 138.56
140 160 164.1 20.5% 5.04 160.15
165.8 29.0% 4.95 160.25
6 120 140 143.1 15.5% 5.99 139.59
142.5 12.5% 6.04 139.5
140 160 166.4 32.0% 6.02 160.93
165.3 26.5% 6.04 161.46
7 120 140 142.3 11.5% 6.99 139.73
142.9 14.5% 6.99 140.25
140 160 166.8 34.0% 7.01 160.71
163.2 16.0% 6.99 160.72
8 120 140 142.9 14.5% 7.99 140.21
140.8 4% 8.01 138.71
140 160 162.3 11.5% 7.99 160.56
163.1 15.5% 7.99 159.99

 

 

All in all, using the original set of tuning parameters, the controller failed 25% of the tests involving step changes in water flow rate set points. In addition, the controller failed 90% of the tests involving step changes in outlet water temperature set points. On the other hand, using the new set of tuning parameters, the controller failed only 12.5% of the tests involving step changes in water flow rate set points. Combing the two trials conducted for step changes in the outlet water temperature set points, the controller failed 50% of the tests, whether it was a failure in achieving the target POR or failure in maintaining a stable outlet water temperature.

The combined feedforward/feedback controller’s design can work to control the outlet water temperature of the heat exchanger at any temperature outside the range that these experiments were operated at. However, the tuning parameters and the heat loss term would have to be adjusted accordingly. Repeating the tests conducted in this lab with the same parameters, constants, and conditions would not necessarily give the same results, since not enough trials were conducted in this lab to confirm the repeatability of the results. In addition, no trends were observed in the data. This is largely due to insufficient data sets, which makes it very difficult to draw any conclusions from.

 

 

 

 

 

 

 

 

Lab Report on Process of heat exchange

 

 

Lab Report on Process of heat exchange

A feedforward/feedback controller was to be designed, implemented and tested to control the outlet water temperature of a heat exchanger. The control scheme was to be designed for water flow rates of 4-8gpm and outlet water temperatures of 120-160. The controller was to be tested by evaluating its response to step changes in outlet water flow rate and temperature set points.

First, the ability of the controller to maintain an average outlet water flow rate within +/- 0.2gpm of the set point as well as an average outlet water temperature within +/- 1 of the set point was assessed at steady state. Second, the controller’s ability to sustain the outlet water temperatures within 5 of the set points was assessed for step changes in water flow rate of 1gpm. Finally, for step changes in the outlet water temperature of 20, the peak overshoot ratios (PORs) in the controller’s temperature responses were calculated with the target set to be less than 25%.

Initially, a set of tuning parameters were predicted using the open-loop tuning method and adjusted by guessing their values and observing the changes in the control scheme’s authority. At steady state, this set of tuning parameters allowed the controller to maintain an average outlet water flow rate within +/- 0.2gpm, and an average outlet water temperature within +/- 1 of the flow rate and temperature set points. The controller also succeeded in sustaining the outlet water temperature within +/- 5 of the set point for 1gpm step changes in water flow rates between 4-8gpm conducted at a temperature of 120. However, the controller did not work as well for higher temperatures as the temperature deviated by more than 5 for step changes of 4-5gpm and 7-8gpm at a temperature of 140, and for a step change of 6-7gpm at a temperature of 160 For 20 step changes in the outlet water temperature for temperatures between 120-160, the PORs in the controller’s temperature response were above 25% for all of the flow rates between 4-8gpm except one; thus, the controller failed to respond to these disturbances rapidly nine out of ten times.

Due to the controller’s great many failures, especially in response to step changes in temperature, the time constant of the controller’s temperature feedback portion was adjusted. The controller was once again tested specifically for the tests that it had originally failed. The results improved slightly. For step changes in water flow rate, the controller maintained the temperature within the boundaries of +/- 5 for all step changes at 140, but had failed once again for a step change of 6-7gpm at a temperature of 160 Two trials were conducted for step changes in temperature using the new set of tuning parameters. In both trials, the POR was above 25% at flow rate of 4gpm for each of the step changes in temperature of 120 to 140 and 140 to 160. While the new set of tuning parameters allowed the controller to achieve the target POR better than it used to, such as achieving PORs of 5% and 4% at flow rates of 5gpm and 8gpm respectively, the controller failed to maintain a stable outlet water temperature in both cases and at other occasions as well; thus, failing numerous tests using the new set of tuning parameters.

The original set of tuning parameters failed 25% of the tests involving step changes in water flow rate, and 90% of the trials involving step changes in water temperature. The new set of tuning parameters had better results, where only 12.5% of the tests involving step changes in water flow rate and 50% of tests involving step changes in temperature failed.

Further tuning of the parameters is recommended, as the parameters used in this lab did not seem to work well. Conducting more trials for each set of parameters and observing the trends in the data would help in better tuning. In addition, conducting trials at a time when water and steam are not used by others in the pilot plant would prevent inconsistencies in the results.

Results and Discussion Lab Report on Process of heat exchange

Prior to designing and implementing the feedforward/feedback control scheme, two feedback loops were created to control the outlet steam and water flow rates. These feedback loops adjusted the difference between the set points and the actual outlet flow rates by sending signals to the steam and water actuators. The actuators convert these signals into forces that act on the control valves, causing them to adjust the amount of water/steam allowed into the heat exchanger. The tuning parameters of these feedback loops were first predicted using the open-loop tuning method. However, due to the imprecision in the temperature probes and flowmeters, the parameters predicted did not work well and had to be adjusted. There was no good way to adjust these parameters other than guessing their values and observing how these changes affected the control scheme until the output was controlled well enough. Table 1 shows the tuning parameters that were used in this lab for each of the steam, water, and temperature feedback loops, where the latter was used in the combined feedforward/feedback controller.

 

Table 1(3A): Original Kc and τi  Values for the Different Controllers.

  Kc τi (sec)
Water Flow Feedback 0.2 3
Steam Feedback 0.5 3
Temperature Feedback 0.05 17.278

 

When steam and water are allowed into the heat exchanger, heat is transferred from the steam to the water, as governed by the second law of thermodynamics. The equation that governs the temperature at which the water leaves the heat exchanger is described by Equation 1 below. This description of how the outlet water temperature is affected by different variables acting on the heat exchanger was the basis of the feedforward controller’s design. The heat capacity, cpw, was assumed to be constant. The volumetric flow rate of water was measured and multiplied by the density of water, which was also assumed to be constant, to give the mass flow rate of water mw. The outlet water temperature, Two, was the set point, and the inlet water temperature, Twi, was measured by temperature probes. The inlet and outlet enthalpies of steam, Hsi and Hso respectively, were defined as functions of temperature and multiplied by the measured mass of steam, ms. Finally, for this non-insulated heat exchanger, the heat loss had to be accounted for. The value for Qloss was guessed at the midpoint operating conditions of outlet water temperature of 140 and flow rate of 6gpm. The value was altered until the measured outlet water temperature agreed with the set point. The value of the heat loss obtained was validated by comparison with the change in enthalpy of steam. It was found that the heat loss value was almost 20% of the value of the change in enthalpy of steam, which is a reasonable estimate.

Lab Report on Process of heat exchange

Equation 1

After implementing the feedforward controller, a feedback temperature loop was added in parallel with it. This combined controller was tested using two different sets of tuning parameters. When the first set of tuning parameters failed to meet some of the design specifications, the time constant τi of the temperature feedback loop was adjusted to 100s while the rest of the tuning parameters were kept constant.

The first design specification that the controller had to meet was to maintain a stable water flow rate and temperature at the set point values. The controller’s ability to meet this specification was assessed after allowing the heat exchanger system to reach steady state. Boundaries for the average outlet water flow rates and temperatures were set as +/- 0.2gpm and +/- 1 of the set point values. The controller succeeded in maintaining a stable water flow rate at the set point values for either set of tuning parameters. Figures 1,2, and 3 show the response of the actual outlet water flow rate measured to 1gpm step changes of water flow rate set point at temperatures of 120, 140, and 160 respectively. Unfortunately, the controller failed to maintain temperatures within +/- 1 of the set point once for the original set of tuning parameters, and numerous times for the new set of tuning parameters during the various trials conducted in this lab.

 

 

Figure 1(A1): Response in water flow rate with a step change of 1gpm between 4gpm and 8gpm at constant temperature of T=120  with original Kc and Ti Values.

 

Figure 2(A13): Response in water flow rate with a step change of 1gpm between 4gpm and 8gpm at constant temperature of T=140  with new Kc and Ti Values.

 

Figure 3(A14): Response in water flow rate with a step change of 1gpm between 4gpm and 8gpm at constant temperature of T=160  with new Kc and Ti Values.

 

 

 

 

 

 

 

 

 

 

The second design specification of the combined controller was to prevent the outlet water temperature from deviating by +/- 5  of the set point for 1gpm step changes in the water flow rate. The step changes in the controller’s water flow rate set points were tested for flow rates between 4 -8 gpm at three temperatures: 120, 140, and 160. Using the original tuning parameters, the controller maintained the outlet water temperature within the boundaries of +/-5  of the set point for a temperature of 120, as illustrated by Figure 4. However, at a temperature of 140, the controller failed to maintain the temperature within the boundaries at step changes of 4-5 gpm and 7-8gpm. The controller also failed at temperature of 160 for a step change from 6-7 gpm, where the temperature deviated from the set point twice during the same trial. Table 2 displays the results of these trials. The tests for the second design specifications were repeated with the new set of tuning parameters. Due to time limitations, only trials that had failed to meet the specifications were repeated. Using the new set of tuning parameters improved the results slightly. Table 3 displays the results of the controller’s second design specifications’ trials conducted using the new set of tuning parameters. The controller maintained the outlet water temperature within the boundaries for all step changes of flow rate at temperature of 140, as illustrated by Figure5, and failed once at temperature of 160, which also happened to be for a step change of 6-7gpm.

Figure 4(A4): Temperature of Water Out, T=120 , for a 1gpm step change ranging from 4gpm to 8gpm with original Kc and Ti Values.

Table 2(A4): Step change in water flow rate with original Kc and Ti Values.

Set Point °F Initial Flow (gpm) Final Flow (gpm) Temp. Deviation °F Avg. Water Flow (gpm) Avg. Temp. °F
120 4 5 3.3 5.02 119.86
5 6 4.4 5.92 119.66
6 7 2.7 6.99 119.94
7 8 3.5 7.89 120.02
140 4 5 5.4 4.97 140.01
5 6 3.6 5.93 139.93
6 7 4.4 7.00 139.81
7 8 5.2 7.97 139.70
160 4 5 4.9 5.01 159.64
5 6 4.8 5.98 160.05
6 7 5.8 6.99 160.01
7 8 3.8 7.97 159.55

 

Table 3(A7): Step change in water flow rate with new Kc and Ti Values.

Set Point °F Initial Flow (gpm) Final Flow (gpm) Temp. Deviation °F Avg. Water Flow (gpm) Avg. Temp. °F
140 4 5 2.6 4.93 140.37
5 6 4.3 6.03 139.32
6 7 3.7 6.97 140.16
7 8 2.5 8.01 140.33
160 4 5 4.6 5.00 160.76
5 6 4.1 5.96 160.23
6 7 6.4 6.99 160.15
7 8 3.5 8.00 159.97

 

 

Figure 5(A15): Temperature of Water Out, T=140 , for a 1gpm step change ranging from 4gpm to 8gpm with new Kc and Ti Values.

Lab Report on Process of heat exchange

The third and final design specification for the combined controller was to have peak overshoot ratios (PORs) of less than 25% for 20step changes in the temperature set point. The controller was tested for step changes of 20 of outlet water temperature for temperatures between 120 to 160 at flow rates between 4-8gpm. Thus, for each of the five flow rates, two step changes in temperature were conducted. Using the original set of parameters, the controller’s temperature response had PORs more than 25% nine out of ten times. Table 4 shows the peak overshoot ratio of the controller’s temperature response for each step change at each of the five flow rates. For the new set of tuning parameters, two trials were conducted. For a flow rate of 4gpm, the POR was above 25% for both step changes of 120 to 140 and 140 to 160 during both trials. Flow rates of 5gpm and 8gpm were the only ones that had PORs less than 25% for both step changes. During the second trial, PORs of less than 25% were only achieved for both step changes at flow rates of 7gpm and 8gpm. However, while the new set of tuning parameters seemed to bring us closer to our POR target, it failed to maintain a stable outlet water temperature. For instance, PORs of 4% and 5% were achieved using the new set of tuning parameters, illustrated by Figures 6 and 7. However, in both cases, the average outlet water temperature was not within +/- 1 of the set point and thus ultimately the controller failed to meet the objective. The results of both trials, including the peak overshoot ratios and the average water flow rats and temperatures, are shown in Table 5.

 

Table 4(A5): Step change in temperature with original Kc and Ti Values.

Fixed Flow Rate

(gpm)

Initial Temp. °F Final Temp. °F  

Max Temp. °F

POR Avg. Water Flow (gpm) Avg. Temp. °F
4 120 140 147.4 37.0% 4.01 138.68
140 160 167.9 39.5% 4.00 159.77
5 120 140 147.7 38.5% 5.00 139.81
140 160 166.1 30.5% 4.99 159.70
6 120 140 147.3 36.5% 6.00 139.79
140 160 165.4 27.0% 5.98 159.23
7 120 140 146.4 32% 6.98 139.70
140 160 166.5 32.5% 7.02 160.18
8 120 140 144.9 24.5% 7.98 139.46
140 160 165 25.0% 7.97 159.65

 

 

 

 

 

 

Lab Report on Process of heat exchange

Figure 6(A18): Temperature of Water Out at 5gpm for a 20 step change ranging from a 120 to a 160 with new Kc and Ti Values for two trials.

Figure 7(A21): Temperature of Water Out at 8gpm for a 20 step change ranging from a 120 to a 160 with new Kc and Ti Values for two trials.

 

Table 5(A8): Two trials of step changes in temperature with new Kc and Ti Values.

Fixed Flow Rate

(gpm)

Initial Temp. °F Final Temp. °F Max Temp. °F POR Avg. Water Flow (gpm) Avg. Temp. °F
4 120 140 147.3 36.5% 3.94 140.99
147.3 36.5% 4.04 139.51
140 160 165.1 25.5% 3.95 161.18
166 30.0% 3.97 160.63
5 120 140 144.6 23.0% 5.04 140.39
141 5.0% 4.97 138.56
140 160 164.1 20.5% 5.04 160.15
165.8 29.0% 4.95 160.25
6 120 140 143.1 15.5% 5.99 139.59
142.5 12.5% 6.04 139.5
140 160 166.4 32.0% 6.02 160.93
165.3 26.5% 6.04 161.46
7 120 140 142.3 11.5% 6.99 139.73
142.9 14.5% 6.99 140.25
140 160 166.8 34.0% 7.01 160.71
163.2 16.0% 6.99 160.72
8 120 140 142.9 14.5% 7.99 140.21
140.8 4% 8.01 138.71
140 160 162.3 11.5% 7.99 160.56
163.1 15.5% 7.99 159.99

Lab Report on Process of heat exchange

 

All in all, using the original set of tuning parameters, the controller failed 25% of the tests involving step changes in water flow rate set points. In addition, the controller failed 90% of the tests involving step changes in outlet water temperature set points. On the other hand, using the new set of tuning parameters, the controller failed only 12.5% of the tests involving step changes in water flow rate set points. Combing the two trials conducted for step changes in the outlet water temperature set points, the controller failed 50% of the tests, whether it was a failure in achieving the target POR or failure in maintaining a stable outlet water temperature.

The combined feedforward/feedback controller’s design can work to control the outlet water temperature of the heat exchanger at any temperature outside the range that these experiments were operated at. However, the tuning parameters and the heat loss term would have to be adjusted accordingly. Repeating the tests conducted in this lab with the same parameters, constants, and conditions would not necessarily give the same results, since not enough trials were conducted in this lab to confirm the repeatability of the results. In addition, no trends were observed in the data. This is largely due to insufficient data sets, which makes it very difficult to draw any conclusions from.