Exercise 2-2. Second-Order Interacting Processes EXERCISE OBJECTIVE DISCUSSION OUTLINE. The actual setup DISCUSSION

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1 Exercise 2-2 Second-Order Interacting Processes EXERCISE OBJECTIVE Familiarize yourself with second-order interacting processes and experiment with the finer points of controller tuning to gain a deeper understanding of interacting processes. DISCUSSION OUTLINE The Discussion of this exercise covers the following point: The actual setup DISCUSSION The actual setup In this exercise, you will set up and control a second-order interacting level process similar to the one described in Figure 2-4, except that an additional drain line will be connected to the first tank, as shown in Figure This introduces a new flow rate,, and an additional resistance,, in the process. This causes the overall transfer function of the process to become: (2-27) Vent tube Figure The interacting second-order system. Festo Didactic

2 Outline The final height of liquid in the second column can be found using the final-value theorem. The calculations assume the incoming flow to be constant during the experiment so that. (2-28) The resistance,, which controls the output flow,, will be adjusted with a hand valve and will be taken in a first time to be so large as to make. Equation (2-27) reduces to the previously obtained equation in such a case and we obtain: (2-29) and (2-30) PROCEDURE OUTLINE The Procedure is divided into the following sections: Setup and connections Adjusting the differential-pressure transmitter Adjusting and characterizing the system Controlling the process PROCEDURE Setup and connections 1. Connect the equipment according to the piping and instrumentation diagram (P&ID) shown in Figure 2-12 and use Figure 2-13 to position the equipment correctly on the frame of the training system. Table 2-3. Material to add to the basic setup for this exercise. Name Model Identification Column (small diameter) Differential-pressure transmitter (low-pressure range) LIT 1 Color paperless recorder UR Controller * LIC 1 70 Festo Didactic

3 Vent tube Open to the atmosphere Figure P&ID - Second-order interacting process. Festo Didactic

4 Air from the pneumatic unit (140 kpa (20 psi)) Figure Setup - Second-order interacting process. 2. Connect the control valve to the pneumatic unit. 3. Connect the pneumatic unit to a dry-air source with an output pressure of at least 700 kpa (100 psi). 4. Wire the emergency push-button so that you can cut power in case of emergency. 5. Do not power up the instrumentation workstation yet. You should not turn the electrical panel on before your instructor has validated your setup that is not before step Festo Didactic

5 6. Connect the controller to the control valve and to the differential-pressure transmitter. You must also include the recorder in your connections. On channel 1 of the recorder, plot the output signal from the controller, on channel 2, plot the signal from the transmitter. Be sure to use the analog input of your controller to connect the differential-pressure transmitter. 7. Figure 2-14 shows how to connect the different devices together. Analog input Analog output In1 Out1 Ch1 Ch2 24 V Figure Connecting the equipment to the recorder. 8. Before proceeding further, complete the following checklist to make sure you have set up the system properly. The points on this checklist are crucial elements to the proper completion of this exercise. This checklist is not exhaustive, so be sure to follow the instructions in the Familiarization with the Training System manual as well. f All unused ports of the two tanks are closed with a cap. The hand valves are in the positions shown in the P&ID. The control valve is fully open. The pneumatic connections are correct. The controller is properly connected to the differential-pressure transmitter and to the control valve. The paperless recorder is connected correctly to plot the appropriate signals on channel 1 and channel Ask your instructor to check and approve your setup. Festo Didactic

6 10. Power up the electrical unit, this starts all electrical devices as well as the pneumatic unit. Activate the control valve of the pneumatic unit to power the devices requiring compressed air. 11. With the controller in manual mode, set the output of the controller to 0%. The control valve should be fully open. If it is not, revise the electrical and pneumatic connections and be sure the calibration of the I/P converter is appropriate. 12. Test your system for leaks. Use the drive to make the pump run at low speed to produce a small flow rate. Gradually increase the flow rate, up to 50% of the maximum flow rate that the pumping unit can deliver (i.e., set the drive speed to 30 Hz). Repair any leaks and stop the pump. Adjusting the differential-pressure transmitter 13. Connect the impulse line leading to the high-pressure port of the differentialpressure transmitter to the pressure port at the base of the column. Leave the low-pressure port open to atmospheric pressure. Bleed the impulse lines and configure the transmitter for level measurement. Adjust the zero of the differential-pressure transmitter. Set the transmitter parameters so that a 4 ma signal is sent for a level of 5 cm (2 inches) and a 20 ma signal for a level of 50 cm (20 inches). Adjusting and characterizing the system The adjustment of the different parameters is delicate and requires some trial and error over a few minutes. The following steps will guide you through the process of adjusting the resistance at the output of the small-diameter column. 14. With the controller in manual mode (or with a calibrator), send a signal of about 40% (about 10 ma) to the control valve. The control valve should be partly closed. Start the drive at a speed of 25 Hz. Valve HV4 should be fully open and valve HV5 should be fully closed. The flow, as measured by the rotameter, should be close to 12 L/min (3.2 gal/min). Adjust the opening of the control valve to match this value. Write down the control signal used to obtain the required flow rate: Control signal: % (or ma) 15. The resistance,, must now be adjusted in order to obtain an appropriate level in the small-diameter column when the system reaches equilibrium. Turn valve HV4 about halfway through its full course to increase the resistance and let the level of water increase in both columns. 74 Festo Didactic

7 16. Adjust valve HV4 to obtain, at equilibrium, a level of about 43 cm (17 inches) in the small-diameter column. Aim for the specified level within a ± 3 cm (± 1 inch) range. This step takes time, but is crucial to the proper completion of the exercise. Once valve HV4 is properly adjusted, do not modify its opening for the remainder of the exercise. Record the measured levels below: Level measured in the small column: Level measured in the large column: 17. The system is to be characterized in this step. Configure the trend recorder correctly to record the step change in the controller output. Perform a step change by increasing the output of the controller by 5.0% (or increasing the output current of the calibrator by 0.8 ma). Wait until the level in the small column stabilizes (about 10 minutes), transfer the data to a computer, and note the following information: Flow rate: Control output: % or ma Level in the small-diameter column: Level in the large-diameter column: 18. Assuming you can approximate the resultant process as a first-order process, analyze your results and write down the process parameters obtained: Use these parameters to calculate : 19. From the process characteristics you just obtained, you can now calculate the PID coefficients prescribed by the open-loop Ziegler-Nichols method. Write your results in Table 2-4. Table 2-4. Calculated control parameters for the Ziegler-Nichols method. Mode Proportional Gain Integral Time Derivative Time PI PID a Be on the lookout with units. Your controller might use units different from those you used in Table 2-4. Festo Didactic

8 Ex. 2-2 Second-Order Interacting Processes Conclusion Controlling the process 20. Set the controller to operate in PID mode with the parameters you just calculated. Optimize your parameters if possible. 21. Create a 40-60% step change in set point and observe the evolution of the system. Record and transfer the data to a computer. Plot a graph of your results. 22. Stop the system, turn off the power, and store the equipment. CONCLUSION This experiment allowed you to work with a second-order system where two tanks were interacting. Approximating the system to a first-order process made it possible to obtain process characteristics, which were used to calculate PID parameters with the Ziegler-Nichols method. Finally, control was exerted upon the process. REVIEW QUESTIONS 1. What is the difference between a second-order non-interacting process and a second-order interacting process? 2. Is the mathematical representation of a second-order non-interacting process simpler if two identical tanks are used? Why? 76 Festo Didactic