Determining the Dynamic Characteristics of a Process

Transcription

1 Exercise 1-1 Determining the Dynamic Characteristics of a Process EXERCISE OBJECTIVE Familiarize yourself with three methods to determine the dynamic characteristics of a process. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: Open-loop method How to obtain an open-loop response curve Setting the recorder. Steps to obtain the response curve. Preliminary analysis of the open-loop response curve Determine the process order. Determine the process gain. Prepare the response curve for analysis. Analyzing the response curve Graphical method. 2% 63.2% method. 28.3% 63.2% method. DISCUSSION Open-loop method Ultimately, the purpose of determining the dynamic characteristics of a process is to obtain enough information on the process to be able to tune the controller for efficient process control. There are two different approaches for tuning a controller. The closed-loop approach uses the automatic mode of the controller, while the open-loop approach uses the manual mode of the controller. Throughout this manual, you will use open-loop approaches to tune your controller. This type of approach provides a quick estimate of the controller tuning settings. The method that this section presents will result in an open-loop response curve. In this method, the controller is set to manual mode and is only used to create the step change in the input variable that will trigger a process response. This method requires a self-regulating process. For non-self-regulating processes, a different method must be used to tune the controller. An analysis of the open-loop response curve enables the determination of the following process characteristics: Dead time, constant, Process gain, Order of response (first order or n th order) Festo Didactic

2 Ex. 1-1 Determining the Dynamic Characteristics of a Process Discussion How to obtain an open-loop response curve To obtain the open-loop response curve of a process, you must have a system comprising a: primary/secondary element that is properly installed and configured recorder with at least two channels controller calibrator final control element Setting the recorder To record both the response curve and the step change with the recorder, both the calibrator and the output of the secondary element must be connected to a channel of the recorder. Figure 1-18 shows a typical setup that allows for the recording of both the response curve and the step change. In this setup, there are two current loops. In the first loop, the calibrator that will produce the step change is the input for channel 1 of the recorder and channel 1 is the input for the final control element. The current loop is closed by connecting the negative connector of the final control element to the negative connector of the calibrator. In the second loop, the output of the secondary element is connected to channel 2 of the recorder, which is then connected to the controller. Ch1 Ch2 Calibrator Ch1 Ch2 In1 Out1 24 V Analog input 24 V Figure Typical response curve recording setup. 16 Festo Didactic

3 Ex. 1-1 Determining the Dynamic Characteristics of a Process Discussion If available, a digital recorder allowing export of the recorded data to spreadsheet software should be used. Using spreadsheet software to analyze the response curve gives more precise results than a graphical analysis alone. Both channels of the recorder should be plotted in units of 0% to 100% of the measured variable range. The calculation to determine the tuning parameters of the controller will be easier if you set the units for the horizontal axis to minutes or fractions of minutes. This can be done directly on the recorder or afterward in the spreadsheet software. Steps to obtain the response curve Below are the general steps to obtain the response curve: 1. Make sure your controller is in manual mode. 2. Start your system and set the calibrator output to a given value (e.g. 60%). 3. Wait for the system to stabilize and start recording the calibrator output and the measured variable on the recorder. 4. Create a step change in the manipulated variable by suddenly changing the calibrator output. 5. Wait for the system to be at steady state. 6. Stop your system and prepare your data for analysis. Preliminary analysis of the open-loop response curve Determine the process order Remember that the analysis of the response curve should provide four essential characteristics of the process. One of these characteristics is the order of the process. Before selecting the method for analyzing the response curve, you can determine if your process is a single-capacitance process (first-order) or a multiple capacitance process (n th order) just by looking at the shape of the response curve. Figure 1-19 shows the difference between the response curve of a single-capacitance process and a multiple-capacitance process. This figure also shows the tangent to the curve at the point where the slope is maximum. The latter has a response curve with an exaggerated S shape. On this curve, the point at which the slope is maximum is in the S instead of at the beginning of the curve. This point is the inflection point of the curve, which is the point where the curvature changes sign. Festo Didactic

4 Ex. 1-1 Determining the Dynamic Characteristics of a Process Discussion Output variable Output variable Tangent Tangent Maximum slope Maximum slope (a) Single-capacitance process. (b) Multiple-capacitance process. Figure Determination of the process order. Once you have determined if your process is a single-capacitance process or a multiple capacitance process and you have calculated the process gain, you must prepare the response curve for further analysis using one of the three suggested methods. This will allow you to determine the dead time and the time constant of the process. Determine the process gain You can easily determine the process gain by dividing the percentage of change in the process variable after the step change () by the height of the step change in percent (). Figure 1-20 shows how you can determine the process gain using the response curve. The gain of the process with the response curve that Figure 1-20 shows is: % Figure Calculating the process gain. Prepare the response curve for analysis A little bit of preparation is required before you can analyze the response curve using one of the methods below. Figure 1-21 shows a typical response curve before preparation for analysis. On this graph, the response curve starts before the step change and it does not occupy the vertical scale from 0% to 100%. 18 Festo Didactic

5 Ex. 1-1 Determining the Dynamic Characteristics of a Process Discussion % 100 The curve occupies only a fraction of the vertical scale Figure Response curve before preparation for analysis. To allow an easier analysis, it is convenient to plot the data on a new graph with the horizontal time scale starting at the moment the step change was created. You must also set the vertical scale so that the curve starts at 0% and reaches 100% when it is at steady state. This way, the curve occupies 100% of the vertical scale of the graph. % The curve does not start at The curve is at 100% at steady state 100 At the curve is at 0% The curve starts at Figure Response curve ready for analysis. Analyzing the response curve The approach for determining the gain and the process order from the open loop response curve is straightforward and does not vary from one method to another. However, there are different methods for determining the time constant and the dead time of a process from the open-loop response curve. This section provides three methods for analyzing the response curve. Although these methods give slightly different results, they are all acceptable and suitable for most processes. The first one is a graphical method suggested by Ziegler and Nichols as part of their well known method for tuning PID controllers. This graphical method requires a fine and careful analysis of the graph and may give only middling results. The two other methods give more consistent results since they rely on the analysis of the data rather than the graph. Graphical method This method of analysis requires a paper copy of the response curve ready for analysis. On the response curve you must determine the point where the curve is the steepest. For a first-order response curve, this point is right where the curve starts to rise as Figure 1-23a shows. For an n th order response curve the maximum slope is at the inflection point, where the curvature of the response curve changes from concave to convex as Figure 1-23b shows. Once you have Festo Didactic

6 Ex. 1-1 Determining the Dynamic Characteristics of a Process Discussion determined the point where the slope is at its maximum, draw a tangent line passing through this point. On the graph, the point where the line intercepts the abscissa is the dead time. For a first-order curve, the dead time is the time elapsed before the process variable starts to rise. For an n th order curve, the process variable begins to change before the dead time ends. The time constant of the process is the time it takes for the process variable to reach 63.2% of its maximum value. For a firstorder process, the time constant also corresponds to the point where the line you have drawn intercepts the 100% asymptote. Output variable Output variable 100% 100% 63.2% 63.2% (a) First-order response curve. (b) N th -order response curve. Figure Graphical method. 2% 63.2% method For n th order response curves, it is sometimes difficult to determine the position of the inflection point. To eliminate error due to the interpretation of the curve, you can use this second method. With this method, the dead time corresponds to the time it takes for the process variable to reach 2% of the total change. The time constant is the time it takes for the process variable to increase from 2% to 63.2%. Figure 1-24 illustrates this method. Output variable 100% 63.2% 2% Figure % 63.2% method. 20 Festo Didactic

7 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure Outline 28.3% 63.2% method The third method consists of evaluating the time it takes for the process variable to reach 28.3% and 63.2% of the 100% span. Once you have these two values, use Equation (1-2) to calculate the time constant and Equation (1-3) to calculate the dead time. Figure 1-25 illustrates this method. (1-2) (1-3) Output variable 100% 63.2% 28.3% Figure % 63.2% method. PROCEDURE OUTLINE The Procedure is divided into the following sections: Setup and connections Obtaining the characteristics of a temperature process PROCEDURE Before undertaking this exercise, you should have successfully completed all the exercises in the Measurement manual. Setup and connections 1. Verify that the emergency push button is wired so as to be able to cut the power in case of emergency. The Familiarization with the Training System manual covers the security issues related to the use of electricity with the system as well as the wiring of the emergency push button. 2. Make sure the 3531 system is properly set up to use the Heating/Cooling unit. The system should also be in its basic setup configuration. 3. Connect the equipment according to the piping and instrumentation diagram (PID) shown in Figure 1-26 and use Figure 1-27 to position the Festo Didactic

8 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure equipment correctly on the frame of the training system. To set up your system for this exercise, start with the basic setup presented in the Familiarization with the Training System manual and add the equipment listed in Table 1-2. The drives and pumps 3 and 4 must be connected to the setup as explained in the Familiarization with the Training System manual even though they are not shown explicitly in Figure Note how a T-shaped connector is used to split the flow of water from HV2B between the heat exchanger and the three-way control valve. This setup allows stopping the flow of cold water in the heat exchanger using the control valve. Table 1-2. Material to add to the basic setup for this exercise. Name Model Identification Brazed plate heat exchanger J-type thermocouple TE1B Platinum RTD TE1A Temperature transmitter TIT Paperless recorder Controller ---- TIC Calibrator Festo Didactic

9 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure Calibrator (4-20 ma) Figure PID Process characteristics. Festo Didactic

10 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure Air from the pneumatic unit (170 kpa (25 psi)) Figure Setup Process characteristics. 4. Connect the pneumatic unit to a dry-air source with an output pressure of at least 700 kpa (100 psi). 5. Connect the I/P converter of the three-way control valve to the pneumatic unit. Use the low-pressure port to do so. 6. Do not power up the instrumentation workstation yet. Do not turn on the electrical panel or the heating/cooling unit before your instructor has validated your setup that is not before step Festo Didactic

11 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure 7. To determine the dynamic characteristics of your process, you must connect your calibrator to the control valve and the temperature transmitter to the input of the controller. You must include the recorder in your connection. On channel 1 of the recorder, plot the signal from the calibrator and on channel 2, plot the signal from the transmitter. Be sure to use the analog input of your controller to connect the temperature transmitter. Refer to the manual of your controller for details on how to connect it to other devices. 8. Figure 1-28 shows how to connect the paperless recorder to your system to plot the calibrator signal on channel 1 and the controller input on channel 2. Calibrator Analog input In1 Out1 Ch1 Ch2 24 V Figure Connecting the equipment to the recorder. 9. 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 for 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 Every piece of equipment used is secured to the station with the appropriate bolt-and-nut mechanism. The heat exchanger is properly installed on the station. The hand valves are in the positions shown in the PID: Open valves: HV1A, HV1B, HV2A, HV2B, HV5A, and HV5B. Closed valves: HV3A, HV3B, HV4A, and HV4B. The hand valves under the drip trays are in the positions specified in the Familiarization with the Training System manual: Open valves: HV1A, HV1B, HV8A, and HV8B. Closed valves: HV6A, HV6B, and HV7. Festo Didactic

12 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure The L port of the three-way control valve is fully open. The pneumatic connections are correct. The controller is properly connected to the temperature transmitter. The calibrator is properly connected to the three-way control valve. The paperless recorder is connected correctly to plot the calibrator signal on channel 1 and the temperature transmitter output on channel Ask your instructor to check and approve your setup. 11. Power up the electrical unit, this starts all electrical devices as well as the pneumatic devices. Adjust the pressure at the low-pressure port so 170 kpa (25 psi) is sent to the I/P converter of the control valve. 12. Start the drives 3 and 4 (pumps P3 and P4). These pumps make the water of the two tanks flow in the Heating/Cooling unit. Ensure the process fluid from each tank is circulating correctly, then power up the heating/cooling unit. Make sure valve HV7 is closed. Continue with the next steps while the water in each tank is respectively heating and cooling toward their temperature set points. 13. Test your system for leaks. Use drives 1 and 2 to make pumps P1 and P2 run at low speed to produce a small flow rate. Progressively increase the frequency output of drives 1 and 2 up to 30 Hz. Repair any leaks. 14. The temperature in the two tanks should be stable and at their respective set points by now. If it is not the case, identify the problem or wait until the temperatures of the tanks stabilize. 15. Test the three-way control valve with your calibrator and make sure it is fully open on L for a 4 ma signal and fully-open on U for a 20 ma signal. 16. Keep sending a 20 ma signal to the control valve so that cold water circulates in the heat exchanger (i.e., U is open). 17. Use the temperature transmitter to display the temperature measured by the RTD (TE1A), which should be installed at the output of the heat exchanger, where the cooled water exits. 18. Configure the paperless recorder so it displays and records the control signal to the three-way control valve on channel 1 and the process temperature on channel Festo Didactic

13 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure a The sampling rate of the paperless recorder should be set to 1 s. To do so, go in the Main Menu Setup Application Signal Group Group X (where X is the number of your active group, typically set to 1) Save Cycle 1 s. Obtaining the characteristics of a temperature process 19. The temperature transmitter is preset to give temperature readings in degrees Celsius in a range from 15 C to 35 C. Hence, the temperature transmitter sends a 4 ma signal if the temperature is 15 C and a 20 ma signal if the temperature is 35 C. 20. To create a step change in the manipulated variable of the process, set the value of the calibrator signal to 12 ma and wait for the process temperature to stabilize. 21. Once the temperature is stable, unplug the RTD from the temperature transmitter. After a few seconds, the transmitter should display the temperature measured by the thermocouple (TE1B). Record the temperature of the cold water output with a 50% input signal to the control valve (i.e., 12 ma) below: Cold water temperature (control valve signal = 50%): 22. Plug the RTD back in place and be sure the paperless recorder displays the warm water flow temperature. 23. Set the calibrator signal to 8 ma to reduce the cold water flow and create a step change. 24. On the paperless recorder, watch the change in the value of the process variable when the calibrator output changes from 50% to about 25%. 25. Wait for the value of the process variable to stabilize. 26. Once the system is at steady state, you have all the information to determine the dynamic characteristics of the process. 27. Unplug the RTD from the temperature transmitter. After a few seconds, the transmitter should display the temperature measured by the thermocouple. Record the temperature of the cold water output with a 25% input signal to the control valve (i.e., 8mA) below: Cold water temperature (control valve signal = 25%): Festo Didactic

14 Ex. 1-1 Determining the Dynamic Characteristics of a Process Procedure 28. Plug the RTD back in place and be sure the paperless recorder displays the warm water flow temperature. 29. Compare the cold water output temperature recorded at step 21 and step 27. Explain the difference, if any. 30. Make a step change from 25% to 50% and wait for the process to stabilize. 31. Stop the system. 32. Follow the procedure in the Familiarization with the Training System manual to transfer the data from the paperless recorder to a computer. 33. Plot the data using a spreadsheet software. 28 Festo Didactic

15 Ex. 1-1 Determining the Dynamic Characteristics of a Process Conclusion 34. Analyze the data of the 50% to 25% step change using the three methods presented in this exercise and fill in Table 1-3 with the results. Table 1-3.Characteristics of the process for a 50% to 25% step change. Graphical Method 2% 63.2% Method 28.3% 63.2% Method (s) (s) (s) 35. Repeat the analysis for the data of the 25% to 50% step change using the three methods presented in this exercise and fill in Table 1-4 with the results. Table 1-4.Characteristics of the process for a 25% to 50% step change. Graphical Method 2% 63.2% Method 28.3% 63.2% Method (s) (s) (s) 36. Compare the characteristics of the two step changes. CONCLUSION In this exercise, you learned three methods for determining the dynamic characteristics of a process. You used these methods to determine the dynamic characteristics of a temperature process. REVIEW QUESTIONS 1. What is the order of the temperature process you analyzed in this exercise? How did you deduce that? Festo Didactic

16 Ex. 1-1 Determining the Dynamic Characteristics of a Process Review Questions 2. How does a process with a large gain react to a step change? 3. Describe the inflection point for the response curve of an n th order process. 4. Which of the three methods for analyzing a response curve is most subject to interpretation? 5. Which process characteristics does a careful analysis of the open-loop response curve allow you to determine? 30 Festo Didactic