Understanding Liquid Level Control Using PID: Experimental Study

Discuss about the BUS303 International Business Project.

The focus in this particular laboratory work was on the controlling level of the liquid. The laboratory work has helped in the understanding of the ways to control the level of the liquid that was found within the tank and its subsequent analysis. It was found that the same principle can find its application in the areas that include control of the flow of the liquids and determination of the temperature. The water level in the tank was regulated using a system of the sensors through tuning of the PID control parameters. The behaviour of the system was carefully observed. In the later hours, there was determination of the values of different variables while using the controller of PID.In this particular case, Edibon water level apparatus was used.

The core aim of the experimental work was to comprehend the primary principles that are used in the process of controlling the level of liquid in the container. This was done while using different variables. The volume of water was brought to the desired point through adjustment of the control output. The adjustment was achieved through using the PID combination. The similar combinations can be applied in the control of the temperatures, pressures and other parameters of different control systems in the industries.

This was also known as the proportional control loop. In this section of the experiment, the liquid level within the container was regulated while using a system of  sensors. The sensor was configured using a controller connected to the output. This was meant to control the actuating system of the requirements. The type of the configuration was meant to make it easier in the study of the dynamics of the system. This was then followed by the application of the response to the applied actions. The set point for the controller was at a point of 120mm when the output was regulated using the proportional output. The initial point for setting was found to be at approximately 20%.After reaching the initial set point, an increment of 10mm was introduced to the initial set point and proportional controller () value was set to 0.5. The reaction of system was observed carefully, and the results obtained were recorded. The study was repeated for two different values of Kc = 0.25 and 0.75 trying to achieve different control response. The reactions of the system for the 3 different values of Kc are shown in Figure 2.

Results and Analysis

The results that were extracted from the system were as indicated in the above graph. From the graph, it is very visible that the level of the water in the tank was at 114mm after the increment of 6mm was made. The system tried to shift to the point that had been set and that was 120mm which was based on the water level rising above the set point.  There was a time delay of approximately 60 seconds (for kc=0.5) and 80 seconds (for kc=0.25 and 0.75) before the system acted to bring the water level to new set point. This particular reason can be related to the dead time. The dead time is normally considered as the delay that exists between the period when a process of the changes in the variable are noticed and when the changes impacts are observed. Also there is an obvious observation of the deviation of the new set point from the graph with values being undershoot or overshoot.

The level of the liquid within the container under study was monitored using a system of the controllers and sensors in this particular section of the experiment. The setting of the proportional value was at 0.5 while the integral values changed from 0.1 to 10.There were observation of the system under the influence of the combination that had been stated before. The results that were obtained were indicated in the figure 3.There was also an observation on the experimental work regarding the approximation of the lagging time. The time was found to be between 3-4 seconds for the apparatus of the sensor and the actuator.

From the above graph, it can be observed that through use of the integral controller alongside the proportional, the overall system got batter. The variance from new set point (135ml) is less when proportional and integral controller is set at 0.1 and 10 respectively. Also the response of the system was very fast as opposed to the previous results. In contrary to the other results, when proportional control value was set at 0.5 while integral control value is set at 5, the response of the system was sluggish and the deviation from set point was high. It is important to note that the system even took more time to response through stabalization.This is very evident from the graph.

It is also known as the PD control. In this specific part of the experiment, the control of the water level within the tank was done while using a system of the sensors and the controllers. The control output was configured using actuating system. The response of the set up was put into consideration while using different combinations. In this particular section the effect was very evident as the system quickly shifted to the new point that had been set as the deviation was introduced.

Observations

As can be seen in the  graph, the values of the derivative controller are greatly increased from the initial set point that was approximately 135ml.There was a general deviation of positive or negative 3.It is important to note that the system response was faster as compared to the previously obtained results.

The component of the proportional is dependent on the variation that exists between the set point and the variable in the process. This variation is referred to as the error. The integral component adds the error over time. The variation of even a very small error will cause a variation of the component to slowly increase. There will be a continuous increase overtime of the error unless the error reduces to zero. This will possibly give a steady state.

From the graph it is very evident that when the value of proportional controller was 0.5, the integral value was 0.1 and the derivative value was 0.5, the system reacts little slower as compared to the cases when proportional controller is set at 0.25, =0.5 and = 0.25.This could be translated to be  the case for other similar results. The response from the system was very quick when the changes were introduced.

It involved the use of the control curve to determine optimum values of proportional, derivative and integral controller. This is normally an open loop method that consists of the opening control valve. This includes introduction of very small changes in the system. The obtained results from this system was used to calculate the optimum values of the variables.The entire process involved  drawing of a tangent line in the inflection point of sigmoid and the values of R and L are measured. L is the retard time of the process while R is the slope of the tangent in the inflection point of the curve. The time of retardation was the defined as the period between the instant changes of the setup. The percentage of the position was determined at these particular points and was later used in the control of the valve. This was the DP percentage and its process was as shown.

In order to obtain the maximum PID controller, a step response was introduced which allowed the level of water in the tank to rise. This was used to obtain the period or the duration of the rise, since the rise of the water level was allowed to raise slowly, the smooth reaction curve was obtained as indicated in the figure below. The optimum values of the PID controller was then determined. It is very possible to use the curve reaction method to obtain the maximum values of the PID controller.

The optimum values of the PID controller were as illustrated below

According to the above values the analysis of the results using the PID control system could be presented using a graph that has been shown below.

From the graph it is quite obvious that the optimum values of the PID controller were calculated from the curve of the reaction method. The system was so quick to recognize the changes and tried to adjust to the new point that had just been set. The new point was at 120ml.The deviation from this particular new point was very little. The system adjusted to the new point after a period of 40seconds.After this period of time, the system remained in a stable condition with little variations being observed at the respective intervals. This shows that the values of the approximation that were obtained from the curve correction methods were relatively correct. Although the curve was obtained using the reaction curve method, the values that were obtained were higher and the stability of the system was much better.

Conclusion

There was analysis of the response of the system for different configuration to produce the output. The initial set point of water was at 250mm.This was followed by an increment of 5mm.Observation was made in regard to the response of the system before comprehensive analysis could be effected. From the analysis, it was found that the system response to the changes or increments was very much better in the combination. The end curve method assisted in the obtaining of the optimum values that were used in the analysis. The analysis done indicated that the system response was quick with very little deviation from the set point. The experiment was found to be very useful and its principles can be applied to other industrial processes of controlling pressure and temperature.