Week 4 Lab

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EET 220 Industrial Applications Professor D. Overbye Week 4 Lab 6 “Proportional and Proportional-Integral Control System” By: Deandre Wheelington ECPI University I pledge to support the Honor System of ECPI. I will refrain from any form of academic dishonesty or deception, such as cheating or plagiarism. I am aware that as a member of the academic community it is my responsibility to turn in all suspected violators of the honor code. I understand that any failure on my part to support the Honor System will be turned over to a Judicial Review Board for determination. I will report to a Judicial Review Board hearing if summoned. Name Deandre Wheelington Date: 03 Dec 23 1

Abstract: In this lab, we will be using an application known as LabView. Within this application we will be determining the difference between input gain and steady state error can make on a tank controlled by a setpoint value and an added slow leak. In a second portion, we will discuss the effect of a time integral on the steady state error. The variables used in this lab will help determine how imperative an inputted gain could be to the output of a system that would experience steady state error due to the fault of the system. Introduction: We will first discuss the process of proportional control. With proportional control, we will be covering how the tank level output follows the setpoint value given a small amount of gain with no added time integral. We will discuss oscillations of the steady state error as we add different values to the setpoint of the tank and different values of gain at the input of the controller. With both values at play, we will determine how it affects the steady state error. In the second part of the lab, we will discuss the process of proportional integral control. In this process, we will determine the effect of adding a time interval to the input of the controller has on the steady state error with a given gain amount. 2

Lab 6: Proportional and Proportional - Integral Control System I. Objectives : After completing this lab experiment you should be able to tune and understand the, 1. Behavior of Proportional (P) system. 2. Behavior of Proportional – Integral (PI) system. II. Procedures : 1. Download the LabVIEW file EET220_Lab_6_LabVIEW_file_Online.vi file from canvas. 2. On the front panel, there should be two tabs Introduction and Operations as seen in Figure 1 below. The introduction tab gives an overview of the simulator with a review of Piping and Instrumentation Diagrams (P&ID). The operation tab has the tank simulator. 3

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Figure 1: Introduction tab of VI 3. Select the operation tab in the LabVIEW VI it should look like Figure 2 below. 4 Tabs

Figure 2: Operation Tab of VI 4. Review the Figure 2 above to become familiar with your Setpoint and PID gains before getting started. 5. Run the LabVIEW VI, by clicking on the white Run button or using shortcut Ctrl + R. 6. Leave the VI in the RUN mode. Now tune the setpoint slider and observe the red plot which is the set point changes from 100 to 0. 7. On the graph, the blue plot is the current location of the process variable which is the feedback signal coming from the tank level sensor. 8. Now tune the setpoint Slider. Since the PID gains are set to zero, the controller output (Green Plot) should stay at 0, so the tank level will not change. 9. Going forward, we will tune the PID gains of this control system such that the blue plot (current level of the tank from the tank level sensor) should follow the red plot (set point) as quickly and as closely as possible. Part I: Proportional Control 10. Now, set the proportional gain (Kc) to 5 and integral time to 0. 5 Setpoint Slider PID Gains

11. Fill the following table by tuning the Setpoint Slider. Setpoint Slider Set point value Tank Level Sensor output Steady State Error (SSE) Oscillations (yes/no/small/large ) Setpoint @ 20 20.00 15.92 21.06 no Setpoint @ 100 100 86.66 68.89 no Table 3: Output and error reading when Kc = 5 12. Does the tank level output (blue plot) follow the set point (red plot) closely? Explain the reason below. Yes, the tank level output follows the set point closely because the controller is trying to match the setpoint and the proportional side of the house is trying to match that input. However, there is a slow leak in the tank, so the output will never quite reach the designated setpoint (input). The higher the set point value, the bigger the gap between output and setpoint 13. Put back the Setpoint slider to 100. Now, set the proportional gain (Kc) to 10 and integral time to 0. Write your observations below? There is a higher tank level output (closer to setpoint) and a controller output because you’re adding more gain to the input. The difference between controller output to setpoint is about the same amount of gap. 14. Fill the following table by tuning the setpoint slider. Setpoint Slider Setpoint Output Tank Level Sensor Output Steady State Error (SSE) Oscillations (yes/no/small/large ) Setpoint @ 100 100 92.94 72.67 small Setpoint @ 20 20 17.85 22.65 small Table 4: Output and error reading when Kc = 10 15. Compare the results from Table and with Table 4 with the Setpoint at 100, what happened to the steady state error (SSE)? The SSE relatively did not change too much even though we added gain, we just saw a higher tank level sensor output. 16. Now, change the value of Kc to 15 and integral time to 0. 6

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17. Now, now adjust the Setpoint slider to 50. Now the Tank level (blue plot) should begin to move towards the setpoint (red plot). The system begins to oscillate sometimes for a long time before reaching to the steady state. The steady state error (SSE) when compared to Kc = 10 is increased ( increased/decreased) 18. Now change the gain Kc to 20. Write your observations below. When the gain is changed to 20, there is a dramatic oscillation of steady state error, where the controller output can not reach a point of steady output. The gain added to the tank level is so high that the value of the output is increasing to its max and then decreasing to its minimum never able to reach that solid output. Its trying to compensate for itself almost as an infinite pendulum never reaching back to its flat steady output. 19. So, in a proportional control system, as the proportional gain (Kc) increases, the steady state error Increases. ( increases/decreases) and tendency for oscillations are Increased. ( increased/decreased) 20. Increase the Kc value in steps of 1 and move the Setpoint slider, observe the response of the system and from your testing choose proper Kc value required, so that the oscillations are minimum. The chosen kc value is __________ 50___. Part II: Proportional – Integral Control 21. Since proportional control alone cannot eliminate the steady state error, we will incorporate integral action into the control loop. When we add integral mode to the system, the controller continues to make the adjustments until the Tank level feedback voltages match with the setpoint voltage meaning until the SSE is zero . 22. Leave the Setpoint slider around 50% and adjust the Integral time to Ti = 0.01. 23. What happened to the system? It adds a 1 second integral to the steady state error when accounting for input gain. 24. Increase the value of Integral time (Ti) by considering all the following guidelines a. After setting Ti, move the setpoint slider from one value to the other and wait. The tank level should move gradually without developing large oscillations (It is recommended that Ti should be increased by 0.01 with each test). b. When you see the oscillations are large, increase the Ti. c. Also make sure the blue signal will not overshoot the red one. 7

d. Reach to the setpoint as quickly as possible without large oscillations and overshoot. 25. As you increase the Ti, what happened to the following? a. Oscillations decreased because it adds a delay in the controller output (SSE) b. Time to reach towards the set point 0.07 c. Steady state error 10.3 26. Amount of overshoot .10 below process variable (basically right on the dot) 27. Based on the above tuning process the Ti value you end up with is 0.07 Conclusion: To conclude this lab, we determined that with a given gain input at our controller, our steady state error increases on the output of our controller. The higher the gain no matter the setpoint, the more oscillations and higher steady state error you will receive. This is because once the steady state error becomes so large, it is essentially uncontrollable because of the constant compensation it is trying to make between both the highest point of oscillation and the lowest point of oscillation. With less gain added, the steady state error will decrease again. In the second portion of the lab, we determined that if we add a slight time integral (delay) in the input of the controller, it tends to delay the amount of gain thus smoothing out the oscillations of steady state error and providing for a cleaner output as close to the setpoint as possible (because of the slow leak). SOURCES: Bartelt, T. L. (2011). Industrial Automated Systems: Instrumentation and Motion Control. Cengage Limited. https://ecpi.vitalsource.com/books/9781305474277 8