The Discussion of this exercise covers the following points:

Exercise 6-2 Flow Process Control EXERCISE OBJECTIVE In this exercise, you will perform PID control of a flow process. You will use the ultimate cy...
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Exercise

6-2

Flow Process Control EXERCISE OBJECTIVE

In this exercise, you will perform PID control of a flow process. You will use the ultimate cycle tuning method to tune the controller.

DISCUSSION OUTLINE

The Discussion of this exercise covers the following points:

ƒ ƒ ƒ DISCUSSION

Brief review of new control modes Tuning with the ultimate cycle method Limits of the ultimate-cycle method

Brief review of new control modes This exercise introduces PID control schemes in the context of a flow process loop. The tuning of the controller is performed using the method of the ultimate cycle (sometimes simply called ultimate method). A controller in proportional, integral, and derivative mode (PID mode) incorporates the three control actions into a single polyvalent and powerful control scheme. The addition of derivative action to the PI mode covered in the previous exercise results in the capacity to attenuate overshoots to some extent; but it adds the risk of instability if the process is noisy. Tuning a controller in PID mode requires careful adjustment of the proportional gain (‫ܭ‬௖ ), the integral time (ܶ௜ ), and the derivative time (ܶௗ ) to properly address the control requirements of the process. In some circumstances, the controller output must not be zero when the error is null. In these cases a bias (ܾ), also known as manual reset, must be set. The PD mode is also introduced in this experiment. It is similar to the P mode; but it adds the derivative action just described for the PID mode. It is not a widely used mode; but it is interesting from a pedagogical perspective. Tuning a controller in PD mode implies adjusting the proportional gain (‫ܭ‬௖ ) and the derivative time (ܶௗ ).

Tuning with the ultimate cycle method The ultimate cycle tuning method is one of the first heuristic methods suggested by Ziegler and Nichols for tuning PID controllers (the method is consequently sometimes called the closed-loop Ziegler-Nichols method). The ultimate-cycle tuning method is designed to produce quarter-amplitude decay in the controlled variable after a given step change in the set point. This method enables the operator to calculate the P, I, and D tuning constants required for P, PI, PD, or PID control of a process using two parameters of the process: the ultimate gain (‫ܭ‬௨ ) and the ultimate period (ܶ௨ ). © Festo Didactic 87996-00

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Ex. 6-2 – Flow Process Control  Discussion

The ultimate proportional band ܲ‫ܤ‬௨ can be used instead of ‫ܭ‬௨ . It is then defined as the smallest value of ܲ‫ ܤ‬for which the process is stable. ܲ‫ܤ‬Ψ ൌ 

ଵ଴଴Ψ ௄೎

Controlled Variable

The ultimate gain ‫ܭ‬௨ is the largest value of ‫ܭ‬௖ in P-only control mode such that the process is still somewhat stable, i.e., the system is in a continuous, sustained oscillation. The ultimate period ܶ௨ is the period of the response when the gain is set to the ultimate gain.

Time

Controlled Variable

(a) Decreasing oscillation.

Time

Controlled Variable

(b) Increasing oscillation.

ܶ௨

Time

(c) Sustained oscillation. Figure 6-28. Types of oscillations and determination of the ultimate period.

The ultimate cycle tuning method follows this procedure: 1. With the controller in manual mode, turn off the integral and derivative actions so as to use only P mode. 2. Set the proportional gain ‫ܭ‬௖ at an arbitrary but somewhat small value, such as 1. 3. Place the controller in automatic (closed-loop) mode.

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Ex. 6-2 – Flow Process Control  Discussion 4. If the process starts to oscillate by itself, go to step 7. Otherwise, create a step change in the set point. The set point change should be typical of the expected use of the system. 5. If the process does not oscillate, increase the gain by a factor of 2. 6. Repeat steps 4 and 5 until the response becomes oscillatory. 7. Determine whether the oscillation is sustained, i.e., if it continues at the same amplitude without increasing or decreasing as in Figure 6-28c. If not, make small changes in the proportional gain until a sustained oscillation is achieved.

a

Note: It is often necessary to wait for the completion of several oscillations before it can be determined if the oscillation is sustained.

The proportional gain at which the sustained oscillation begins, without causing saturation of the controller output, is the ultimate proportional gain, ‫ܭ‬௨ . Note this value. Then note the period of the oscillation of the process, as shown in Figure 6-28c. This is the ultimate period, ܶ௨ .

8. Using the ultimate proportional gain and ultimate period, calculate the tuning constants of the controller as follows:

Table 6-2. Control parameters for the ultimate cycle tuning method (non-interacting ideal controller).

Mode P PI PD PID

Controller Gain ࡷࢉ

Integral Time ࢀ࢏

Derivative Time ࢀࢊ

-

-

‫ܭ‬௖ ൌ ͲǤͶͷ‫ܭ‬௨ ሺܲ‫ ܤ‬ൌ ʹǤʹʹܲ‫ܤ‬௨ ሻ

ܶ௜ ൌ ܶ௨ ΤͳǤʹ

-

‫ܭ‬௖ ൌ ͲǤ͸‫ܭ‬௨ ሺܲ‫ ܤ‬ൌ ͳǤ͸ͷܲ‫ܤ‬௨ ሻ

ܶ௜ ൌ ܶ௨ ΤʹǤͲ

‫ܭ‬௖ ൌ ͲǤͷ‫ܭ‬௨ ሺܲ‫ ܤ‬ൌ ʹܲ‫ܤ‬௨ ሻ

‫ܭ‬௖ ൌ ͲǤ͸‫ܭ‬௨ ሺܲ‫ ܤ‬ൌ ͳǤ͸ͷܲ‫ܤ‬௨ ሻ

-

ܶௗ ൌ ܶ௨ Τͺ ܶௗ ൌ ܶ௨ Τͺ

Once the tuning constants of the controller are adjusted to the calculated values and the controller is returned in the automatic (closed-loop) mode, changes in the set point should produce a quarter-amplitude decay response. Optimization of the controller settings may require further finetuning.

Quarter-amplitude decay ratio John G. Ziegler and Nathaniel B. Nichols, who were pioneers in control engineering, established a criterion to determine if a controller is appropriately tuned. This criterion is the quarter-amplitude decay ratio. It states that, for two successive oscillations, the amplitude of the second oscillation should be one fourth of the amplitude of the first oscillation.

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Ex. 6-2 – Flow Process Control  Discussion Controlled variable

‫ܣ‬ଵ

‫ܣ‬ଶ ൌ

‫ܣ‬ଵ Ͷ

‫ܣ‬ଷ ൌ

‫ܣ‬ଶ Ͷ Time

Set point

Figure 6-29. Quarter-amplitude decay ratio.

The quarter-amplitude decay response is a rough approximation for the optimal tuning of PID controllers. A controller is generally considered to be reasonably tuned when it satisfies this criterion; but fine tuning may be required to adapt the controller response to a specific process control application. The quarter-amplitude decay response is a compromise between an underdamped and an overdamped response. The process response is overdamped when the controlled variable slowly returns to the set point after the step change without overshooting it. The response is underdamped when the controlled variable quickly returns to the set point with one or more overshoots before stabilizing. An underdamped response often means that the controller reacts too aggressively to correct the error, thereby overdoing it.

Limits of the ultimate-cycle method It is important to note that the formulas given above apply only for non-interacting ideal controllers. Other formulas must be used for series or non-interacting parallel controllers. It is also important to stress that using the ultimate-cycle tuning method may be out of the question in processes where bringing the system into continuous oscillation could be dangerous or might cause damage. Instead, another method of tuning, such as the trial-and-error method or the open-loop step response method, should be used. The open-loop step response method is also known as the open-loop Ziegler-Nichols method (this is covered in the next exercise).

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Ex. 6-2 – Flow Process Control  Procedure Outline

PROCEDURE OUTLINE

The Procedure is divided into the following sections:

ƒ ƒ ƒ ƒ PROCEDURE

Set up and connections Transmitter calibration PID control of the flow process End of the exercise

Set up and connections 1. Set up the flow process shown in Figure 6-30. x

x x

x

x

Mount the rotameter and the column on the expanding work surface. Connect the DP transmitter to the pressure taps of the venturi tube, not to the inlet and outlet pressure ports. Make sure to connect the pump outlet to the column port with a pipe that extends down into the column. Block the unused hose ports of the column using the provided plugs. Firmly tighten the top cap.

SP

Figure 6-30. PID control of a flow process.

2. Power up the DP transmitter.

3. Make sure the reservoir of the pumping unit is filled with about 12 liters (3.2 gallons) of water. Make sure the baffle plate is properly installed at the bottom of the reservoir.

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Ex. 6-2 – Flow Process Control  Procedure 4. On the pumping unit, adjust valves HV1 to HV3 as follows: x x x

Open HV1 completely. Close HV2 completely. Set HV3 for directing the full reservoir flow to the pump inlet.

5. Turn on the pumping unit.

Transmitter calibration In steps 6 through 11, you will be adjusting the ZERO and SPAN adjustments of the DP transmitter so that its output current varies between 4 mA and 20 mA when the pump speed is varied between 0% and 100%. 6. Connect a multimeter to the 4-20 mA output of the DP transmitter.

7. Make the following settings on the DP transmitter: x

x

x

ZERO adjustment knob: MAX. SPAN adjustment knob: MAX. LOW PASS FILTER switch: I (ON)

8. With the pump speed at 0%, turn the ZERO adjustment knob of the DP transmitter counterclockwise and stop turning it as soon as the multimeter reads 4.00 mA.

9. Make the pump rotate at maximum speed.

10. Wait until the water level has stabilized in the column. Adjust the SPAN knob of the DP transmitter until the multimeter reads 20.0 mA.

11. Due to interaction between the ZERO and SPAN adjustments, repeat steps 8 through 10 until the DP transmitter output actually varies between 4.00 mA and 20.0 mA when the controller output is varied between 0% and 100%.

PID control of the flow process 12. Have the following signals plotted on a trend recorder: x

x

292

Set point, (‫)ݎ‬ Controlled variable, ܿሺ‫ݐ‬ሻ, the DP transmitter output

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Ex. 6-2 – Flow Process Control  Procedure

LVProSim From the Settings menu, change the sampling interval to 200 ms. Refer to Appendix B for details on how to use LVProSim.

13. Activate the square-root extracting function at the controller feedback input. Also, make the necessary controller settings to place a 0.5-second filter at the feedback input of the controller.

a

If you are using LVProSim, you can extract the square root using the set functions window (refer to Appendix B). However, if you are using the industrial DP transmitter, Model 46929, you can set the field device to calculate the flow instead of the controller. Refer to Appendix I for details.

14. Adjust the controller gain and disable the integral and derivative actions. For LVProSim, this translates into the following values: x x x

Controller gain (‫ܭ‬௖ ): 1 Integral time: OFF Derivative time: OFF

15. Place the controller in the automatic (closed-loop) mode.

16. Adjust the controller set point to 70% and let the controlled variable stabilize on the trend recorder.

17. Create a sudden change in set point from 70% to 40% and observe the controlled variable response. Does it oscillate continuously or does it stabilize after a certain time?

a

Because of the pressurized air attempting to push the water contained in the column through the Venturi tube, the process is more likely to enter into oscillation following a sudden decrease—rather than a sudden increase—in set point. This is why you will find the ultimate proportional gain by creating 7040% step changes in set point.

18. Adjust the controller set point to 70% and let the controlled variable stabilize.

19. Increase the controller gain by a factor of 2, then make another 70% to 40% step change in set point. Does the controlled variable oscillate after the set point change?

‰ Yes

© Festo Didactic 87996-00

‰ No

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Ex. 6-2 – Flow Process Control  Procedure If not, repeat steps 18 through 19 until the response becomes oscillatory.

20. Fine-tune the controller gain until a sustained constant amplitude oscillation is achieved. Refer to Figure 6-28c, if necessary. Note the value (ܲ‫ܤ‬௨ ‫ܭݎ݋‬௨ ) for which the sustained oscillation just starts. Then, note the period of the oscillation, ܶ௨ .

a

It is necessary to wait for the completion of several oscillations before it can be determined if the amplitude of the oscillation actually remains constant.

PI control 21. Using the ultimate controller gain and the ultimate period, calculate the controller tuning constants for PI control of the flow process.

22. Adjust the controller tuning constants for PI control of the flow process according to the values calculated above.

23. Create a 70-40% step change in set point and observe the controlled variable response. Does it have a quarter amplitude decay? Explain.

24. Try fine-tuning the P and I constants in order to reduce the stabilization time and overshooting of the controlled variable following a 70-40% step change in set point. Record your observations and your results.

PID control 25. Using the ultimate controller gain and the ultimate period, calculate the controller tuning constants for PID control of the flow process.

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Ex. 6-2 – Flow Process Control  Procedure 26. Adjust the controller tuning constants according to the values calculated above for PID control of the flow process.

27. Create a 70-40% step change in set point and observe the controlled variable response. Does it have a quarter amplitude decay? Explain.

28. Fine-tune the P, I, and D constants in order to reduce the stabilization time and overshooting of the controlled variable following a 70-40% step change in set point. Record your observations and your results.

29. Try different set point values by increasing or decreasing the set point through 20% step changes. Determine whether the controller tuning remains acceptable over a broad range of set points. Record your observations and fine-tune if you can.

30. When the system is well tuned, adjust the controller set point to 50%.

31. Rapidly open valve HV2 to create a sudden change in process load. Is the controller able to rapidly correct for the load change without oscillation of the controlled variable? Explain.

32. Close valve HV2 and allow the controlled variable to stabilize.

33. Close valve HV1 partially to create a change in process load. Record your observations.

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Ex. 6-2 – Flow Process Control  Conclusion

End of the exercise 34. Stop the pump and turn off the pumping unit.

35. Disconnect the circuit. Return the components and hoses to their storage location.

36. Wipe off any water from the floor and the training system.

CONCLUSION

In this exercise, you performed PID control of a flow process. You used the ultimate cycle tuning method as a starting point for controller tuning, then you fine-tuned the controller to reduce the stabilization time and overshooting. You observed that the main disadvantage of the ultimate cycle tuning method is that many values of controller gain must be tried before the ultimate proportional gain is found. To make a test, especially at values of controller gain near the ultimate one, it is often necessary to wait for the completion of several oscillations before it can be determined if the tried value is the desired one. Also, this method cannot be used in industrial processes where bringing the system into continuous oscillation could be dangerous or might cause damage.

REVIEW QUESTIONS

1. What are the required parameters for the ultimate cycle method?

2. How do you find the value of those parameters?

3. What does “sustained oscillation” mean?

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Ex. 6-2 – Flow Process Control  Review Questions 4. When would it be unsuitable to tune a process via the ultimate cycle method?

5. What happens if you increase ܶௗ too much in PID control mode?

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