Innovative Solutions from the Process Control Professionals

Control Station Innovative Solutions from the Process Control Professionals Software For Process Control Analysis, Tuning & Training Control Station Software For Process Control Analysis, Tuning & Training Hands-on Workshop Series SOLUTION GUIDE A Companion to Fundamentals of Instrumentation and Process Control 1

Practical Process Control Fundamentals of Instrumentation and Process Control All rights reserved. No portion of this book may be reproduced in any form or by any means except with the explicit, prior, written permission of Control Station, Inc. 2

Process Dynamics Objective: To generate step test data and describe the dynamic process response with a first order plus dead time (FOPDT) model. Also, to learn about the nonlinear nature of processes. 1) Click LOOP-PRO s Case Studies icon on the main screen and select Gravity Drained Tanks. 2) Make sure the CO is at 70% and that the PV (liquid level) is steady. Perform a step test by clicking the controller output (CO) box on the tanks graphic and entering 80%. When the liquid level (PV) reaches a new steady value, click the Pause icon (II) on the tool bar. The strip charts now show dynamic process data from a step test (a kind of bump test). 3) Click the Plot icon on the tool bar to view a fixed plot of your step (bump) test dynamic data. 4) Use a graphical analysis to fit a first order plus dead time (FOPDT) model to the CO to PV step test dynamic behavior. The worksheet at the end of this workshop may be useful. Record the first order plus dead time (FOPDT) model parameters with units (e.g. m/% or minutes) Process gain, Kp = 0.13 m/% Time constant, p = 2.2 min Dead time, p = 0.5 min 5) Repeat tasks 2-4 above for a bump test where the CO is stepped from 50% up to 60%. Be sure the PV is moved from one steady state to another. Fit a FOPDT model to the plot data. Process gain, Kp = 0.09 m / % Time constant, p = 1.8 min Dead time, p = 0.3 min 6) The two steps in the CO (70 80% and 50 60%) are the same size. Are the FOPDT model parameters the same for these two steps? How/why are they different? The two sets of FOPDT model parameters are different. All three parameters are larger at the higher operating level. (it is not necessary that the parameters grow or shrink together as operating level changes. It is just as likely on a process for one model parameter to get larger while another gets smaller.) The important observation is that the dynamic process behavior can change as operating level changes. Since FOPDT model parameters are used in the design and tuning of a controller, the first step in our controller design recipe is to determine the Design Level of Operation. That is, where we expect the set point to be and the major disturbances to be during normal operation. 3

C o n t r o l l e r O u t p u t P r o c e s s V a r i a b l e / S e tp o i n C o n t r o l l e r O u t p u t P r o c e s s V a r i a b l e / S e tp o i n Step Control Output from 70% 80% for Gravity Drained Tanks 7 0 % ---> 8 0 % P r oces s : Gr avity Dr ained T ank C ont.: M anual M ode 5.0 4.5 y = (5.3-4.0) m 4.0 80.0 77.5 75.0 72.5 u = (80-70) % 70.0 10 11 12 13 14 15 16 17 18 19 20 Time (mins) P r oces s : Gr avity Dr ained T ank 5.0 y 63.2 =4.87 m 7 0 % ---> 8 0 % C ont.: M anual M ode 4.5 y = 1.3 m 4.0 80.0 77.5 75.0 P = 2.2 minutes 72.5 70.0 10 11 12 13 14 15 16 17 18 19 20 Time (mins) t Ystart t 63.2 4

C o n t r o l l e r O u t p u t P r o c e s s V a r i a b l e / S e tp o i n C o n t r o l l e r O u t p u t P r o c e s s V a r i a b l e / S e tp o i n C o n t r o l l e r O u t p u t P r o c e s s V a r i a b l e / S e tp o i n P r oces s : Gr avity Dr ained T ank 7 0 % ---> 8 0 % C ont.: M anual M ode 5.0 4.5 4.0 80.0 77.5 75.0 72.5 70.0 10 11 12 13 14 15 16 17 18 19 20 Time (mins) t Ustep t Ystart P = 0.5 minutes Step Control Output from 50% 60% for Gravity Drained Tanks 5 0 % ---> 6 0 % P r oces s : Gr avity Dr ained T ank C ont.: M anual M ode 3.0 2.5 2.0 y = (2.87 1.95) m 60 55 u = (60-50) % 50 45 46 47 48 49 50 51 52 53 54 Time (mins) P r oces s : Gr avity Dr ained T ank 3.0 y 63.2 =2.53 m 5 0 % ---> 6 0 % C ont.: M anual M ode 2.5 2.0 y = 0.92 m 60 55 P = 1.8 minutes 50 45 46 47 48 49 50 51 52 53 54 Time (mins) t Ystart t 63.2 5

C o n t r o l l e r O u t p u t P r o c e s s V a r i a b l e / S e tp o i n P r oces s : Gr avity Dr ained T ank 3.0 5 0 % ---> 6 0 % C ont.: M anual M ode 2.5 2.0 60 55 50 P = 0.3 minutes 45 46 47 48 49 50 51 52 53 54 Time (mins) t Ustep t Ystart 6

Workshop 1: Dynamics of the Gravity Drained Tanks Worksheet Compute FOPDT model parameters based on CO (controller output) to PV (process variable) step test data CO step from 70% 80% CO step from 50% 60% Compute process gain, Kp when CO 1 = 70%, then PV 1 = 4.0 m when CO 2 = 80%, then PV 2 = 5.3 m PV = PV 2 PV 1 = 1.3 m Compute process gain, Kp when CO 1 = 50%, then PV 1 = 1.95 m when CO 2 = 60%, then PV 2 = 2.87 m PV = PV 2 PV 1 = 0.92 m CO = CO 2 CO 1 = 10 % CO = CO 2 CO 1 = 10 % Kp is the how far variable Kp is the how far variable Kp = PV/ CO = 1.3/10 = 0.13 m / % Kp = PV/ CO = 0.92/10 = 0.092 m / % units units Compute process time constant, p t PVstart = time PV response starts = 12 min Compute process time constant, p t PVstart = time PV response starts = 46.3 min PV 63.2 = PV 1 + 0.632( PV) = 4.0 + 0.632(1.3m) PV 63.2 = PV 1 + 0.632( PV) = 1.95 + 0.632(0.92 m) = 4.82 m = 2.58 m t 63.2 = time PV 63.2 reached = 14.2 min t 63.2 = time PV 63.2 reached = 48.1 min p is the how fast variable p is the how fast variable p = t 63.2 t PVstart = 14.2 12 min = 2.2 min p = t 63.2 t PVstart = 48.1 46.3 = 1.8 min units units Compute process dead time, p t COstep = time CO stepped = 11.5 min p is the how much delay variable Compute process dead time, p t COstep = time CO stepped = 46 min p is the how much delay variable p = t PVstart t COstep = 12 11.5 = 0.5 min p = t PVstart t COstep = 46.3 46.0 = 0.3 min units units 7

7) Set the CO to 20% and let the measured PV steady out (as an aside, note that the PV enters a low alarm condition). Step the CO from 20% up to 40%, then up to 60%, then 80%. Let the PV (liquid level) steady between each step. View a plot of the entire test. Is the gravity drained tanks a linear or nonlinear process? Explain your conclusion. different PV responses as operating level changes Identical CO s The Gravity Drained Tanks is clearly nonlinear because the dynamic process response changes as operating level changes. This was evident from the work sheet results of Task 4 and 5. 8

Basic Process Terminology Figure 1-1 1. From Figure 1-7, answer the following with regards to heating process: a) What is process input? a) 8 ma b) 93 F c) Cold Water (the raw material ) d) Hot Water b) What is the process output? a) 8 ma b) 93 F c) Cold Water d) Hot Water (the finished product ) 9

c) What is the resource? a) 50 PSI b) 55 F c) Cold Water d) Steam d) What is the value of the PV? a) 55 F b) 95 F c) 93 F d) 11 PSI e) What is the value of the MV? a) 25% b) 8 ma c) 6 PSI d) 11 PSI f) What is the value of the SP? a) 55 F b) 95 F c) 93 F d) 11 PSI g) What is the tag number of the final control element? a) PP-100 b) TC-102 c) TV-102 d) HP-101 10

2. With the proper controller and controller settings any process can be controlled. a) True b) False 3. Dynamic behavior is: a) An uncontrolled response to a change in conditions. b) A change in response with respect to position. c) A change in response with respect to time. 4. The dynamic behavior of sensors and final control elements has no effect on process control, only the dynamic behavior of the process itself is important. a) True b) False 11

Basic Process Control 1. Error is equal to: a) SP MV b) PV CO c) SP PV d) Deadband 2. In closed loop control the controller output is a function of: a) Time b) The Final Control Element c) The Operator d) Error 3. Which mode of control has a required deadband? a) Time Proportion b) On-Off c) Open Loop d) PID 4. Decreasing a controller deadband will a) Increase Output Oscillations b) Decrease Output Oscillations c) Change the Set Point d) Do Nothing 5. Which controller automatically modulates its output? a) Manual Control b) PID Control c) On-Off Control d) Open Loop Control 12

6. If I have a time proportion controller with a 30 second duty cycle and the controller output is 30%, what is the amount of time the controller output is on within each cycle? a) 30 Seconds b) 21 Seconds c) 9 Seconds d) 0 Seconds 13

Process Linearity Lab In this exercise we will determine whether a process is linear or nonlinear. 1. Launch Loop Pro Trainer. Select Case Studies Heat Exchanger. 2. Ensure that the controller is in manual mode 3. Set the controller output to 20%. Let the process stabilize. 4. Increase the controller output by 10%. Let the process Stabilize. 5. Repeat Step 4 until you reach 90% on the controller output. 6. Pause the process. Examine your reaction curve by clicking on the plot icon. If the displayed curve does not show all of your controller steps expand the plot by clicking on the history icon. 7. From your reaction curve: a. Is this a linear or nonlinear process? b. If it is normal for this process to have its Set Point varied from 120 C to 140 C, at what Set Point would you perform your tuning? a) 120 C b) 130 C c) 140 C d) Doesn t Matter 14

Integrating Process Lab Objective: To understand the dynamic character of integrating processes and to explore the tuning issues associated with their control 1) The Pumped Tank process follows a non-self regulating (integrating) dynamic behavior. That is, the process does not steady out to a constant liquid level after the controller output or disturbance variables are changed when the controller is in manual mode. To explore the behavior and control of this process, start the Pumped Tank simulation by selecting it from the Case Studies list on Control Station s main screen. Study the graphic and observe that unlike the gravity drained tanks simulation, where the outlet flow rate adjusts according to changes in the liquid level, the flow rate out of the pumped tank is set by the throttling valve at the discharge of a constant pressure pump. If the feed and disturbance streams total a different flow rate into the tank than the fixed value leaving the tank, the liquid level will continue to fall or rise until the tank empties or overfills. To verify this, change the disturbance flow rate from 2.5 L/min up to 3.5 L/min and observe the results. Change it once more to 1.5 L/min and again observe the liquid level behavior. 2) Restart the process using the program default values (select this from the Run menu on the Pumped Tank screen), which are set to be a tank liquid level of 4 m and a disturbance flow rate of 2.5 L/min. We will now collect dynamic process data for controller tuning. Begin saving data to a file and step the controller output from 70% down to 65%. Wait for the liquid level to rise above 5 m and then step the controller output up to 75%. When the tank level has fallen past 3.5 m, stop saving data and pause the simulation. Notice that when you return the controller to its original output of 70%, the process does not return to its initial steady state, at which the tank liquid level was 4 m; instead, the level steadies at a new value. 3) Your data should now have a segment where the process variable (liquid level) is rising steadily and another where it is falling steadily. We want to compute the slope of each individual segment. Click the Plot button on the Pumped Tank screen to view a fixed plot of the data; use Plot Options to adjust the plot so you can see both step changes and the process variable response. The equation to compute a slope is: end start slope = dy t y y dt tend tstart where y start and t start are the start points and y end and t end are the end points of each slope segment. 15

First focus on the upward sloping segment and compute the slope: y 1 start = y 1 end = t 1 start = t 1 end = 1 end 1 start slope 1 = dy t y y dt t t 1 end 1 start controller output 1, CO 1 = Repeat the calculation for the downward sloping segment: y 2 start = y 2 end = t 2 start = t 2 end = 2 end 2 start slope 2 = dy t y y dt t t 2 end 2 start controller output 2, CO 2 = 4) Use this expression to calculate the integrator gain, Kp * : slope slope * 2 1 K P CO2 CO1 Remember, integrator gain is a ratio of the process gain to the process time constant; therefore, the units for this process are m/(% min). 5) Estimate the process dead time, θp, from the plot using the same graphical method discussed in Chapter 3. P 16

Input Aliasing I Lab This exercise is to demonstrate the effects of sampling intervals on the reconstruction of a signal. 1. Open the Signal Aliasing worksheet on the Desktop in the Process Control Folder 2. Try different waveform frequencies and sample intervals. 3. Did the suggested sample interval always reconstruct your waveform? No 4. Try doubling the suggested sample interval (1/10 th of the waveform period). Did you get good results? Yes, not perfect 5. Try quadrupling the suggested sample interval (1/5 th of the waveform period). Do you still get good results? No 17

Determining the Correct Sampling Interval While it s nice to know there is guidance on how to set the sample interval for a waveform based on its frequency, how does one know what the frequency of a process variable is? When it comes to instrumentation, it s not the frequency that s important, it s the time constant. Figure 3-6 is a graph of the response of an instrument with a 5 second time constant (25 second rise time). The signal from the instrument was sampled at 1 second intervals. Figure 3-6 One rule of thumb would be to set the sample interval for an instrument at 1/10 th to 1/20 th of the rise time (1/2 to 1/4 th of the time constant). Another rule of thumb would be to set the sample interval to 1/10 th to 1/20 th of the process time constant. Temperature instrumentation (RTDs and thermocouples in thermowells) typically have time constants of several seconds or more. For these processes sampling intervals of 1 second are usually sufficient. Pressure and flow instrumentation typically have time constants of ½ to 1 second. For these processes sampling intervals of 0.1 second are usually sufficient. 18

Input Aliasing II Lab This exercise is to demonstrate the relation of sampling intervals to instrument time constants. 1. Open the Aliasing & Time Constants worksheet located My Documents\Process Control. 2. Try different instrument time constants and sample intervals. 3. Did the sample interval of ½ to ¼ of the instrument time constant always give you good results? No. 19

Noise Filtering Lab This exercise is to demonstrate the effects of filtering on a process variable. 1. Open the Filter worksheet located My Documents\Process Control. 2. This filter is specified by its value. You may see the effects of the filter on a step response by entering a value of 0 for the signal frequency. You may see the effects of the filter on a waveform by entering a value 3. Enter a signal frequency of 0.02 (approximate response of an RTD) and a noise amplitude of 10%. 4. Enter a filter value of 0. Has any noise been filtered out of the signal? No 5. Enter a filter value of 1. Has any signal passed through the filter? No 6. Change the filter value until you are satisfied with the filtering effect you have achieved. Record your value for. 7. Enter a signal frequency of 0 to display your filters step response. What is the time constant of your filter? 8. What is the cut-off frequency of your filter? Cut - Off Frequency 1 5 Time Constants 9. Change the signal frequency to 0.2 (approximate response of a flow meter). Would this same filter configuration work for this process? 10. Change the filter value until you are satisfied with the filtering effect you have achieved. Record your value for. 11. Enter a signal frequency of 0 to display your filters step response. What is the time constant of your filter? 12. What is the cut-off frequency of your filter? Cut - Off Frequency 1 5 Time Constants 20

Temperature 1. Extension grade thermocouple wiring is used to: a) Compensate for lead wire resistance. b) Eliminate the self-heating effect. c) Remove errors caused by temperature differences between the controller and the thermocouple. d) Provide noise immunity. 2. Why do we use three wire RTDs? a) Compensate for lead wire resistance. b) Eliminate the self-heating effect. c) Remove errors caused by temperature differences between the controller and the thermocouple. d) Provide noise immunity. 3. Which temperature measurement device has a self-heating effect? a) Infrared b) RTDs c) Thermocouples d) Infrared and Thermocouples 4. Why is it important to match the thermocouple type to the controller configuration? a) A mismatch will harm the controller s circuitry. b) A mismatch will harm the thermocouple. c) It is not important at all. d) A mismatch will introduce errors in the controller s calculated value of the process variable. 5. Why is it important to match the alpha value of an RTD to the controller configuration? a) A mismatch will harm the controller s circuitry. b) A mismatch will harm the RTD. c) It is not important at all. d) A mismatch will introduce errors in the controller s calculated value of the process variable. 21

Pressure 1. In the figure to the right, label the pressure reading according to their reference a) Point A is i) Absolute ii) Gauge iii) Differential b) Point B is i) Absolute ii) Gauge iii) Differential c) Point C is i) Absolute ii) Gauge iii) Differential 22

Level 1. Which of the following affect the calibration of a pressure sensor for hydrostatic level measurement? a) The height of the tank. b) The density of the tank contents. c) The dielectric constant of the tank contents. d) Both A and B. 2. Which level sensor is affected by the dielectric constant of the contents of a tank? a) Ultrasonic b) Radar & Guided Wave Radar c) RF/Capacitance d) Both B and C. 3. Which level instruments are affected by the temperature and/or vapors in the tank air space? a) Radar b) RF/Capacitance c) Ultrasonic d) Both A and C 4. A sealed 10 foot high tank can contain 9 feet of product. Nine feet of product exerts 3 psi on the bottom of the tank. The bottom of the tank is 50 square feet in area and the product will be blanketed with nitrogen at 3 psi. Which hydrostatic pressure sensor is best for this application? a) 10 psi pressure sensor b) 150 psi pressure sensor c) 5 psi differential Pressure sensor d) 10 psi differential Pressure sensor 5. The relationship between fluid level in a tank and the psi exerted on the tank bottom is dependent on: a) The diameter of the tank b) The density of the fluid c) The shape of the tank d) The dielectric constant of the fluid 23

Flow 1. Which flow meter requires a conductive fluid? a) Coriolis b) Positive Displacement c) Magnetic d) All of the above 2. The Reynolds number is used to determine what flow characteristic? a) Viscosity b) Density c) Laminar or turbulent flow d) Velocity 3. A positive displacement meter s measurement? a) % b) lbs/min c) kg/sec d) gal/min 4. True or False: Viscosity is constant for all fluids. False 5. True or False: Flow irregularities do not affect flow meter accuracy. False 6. True or False: Viscosity changes with temperature. True 7. A mass flow meter has the following accuracy specification: Turndown 500:1 100:1 20:1 10:1 1:1 Accuracy (±%) 1.25 0.25 0.10 0.10 0.10 If this flow meter has an operating range of 500 kg/hr, what is the lowest flow value that it can measure with an accuracy of ± 0.10%? a) 500 kg/hr b) 50 kg/hr c) 25 kg/hr d) 5 kg/hr 24

Valves 1. Answer the following as True (T) of False (F) a) F Positioner tuning has no effect on loop performance. b) F Valve deadband has no effect on loop performance. c) F Valve stiction has no effect on loop performance. d) F Valve characterization has no effect on loop performance. e) F A valve s inherent characteristic will be a good indicator of its installed characteristic. 2. An oversized valve is replaced with one that is more suited for the process. The C v of the new valve is ½ the C v of the old valve. What would you do to the gain of the controller upon installation of the new valve? a) Nothing, the tuning will work just fine. b) Double the controller gain and tune from there. c) Halve the controller gain and tune from there. d) Quarter the controller gain and tune from there. 25

Pumps 1. A centrifugal pump is rated with a maximum head of 60 feet. a) Water has a specific gravity of 1.0 How high will it pump water? 60 b) Glycerin has a specific gravity of 1.21 How high will it pump glycerin? 49 c) Almond oil has a specific gravity of 0.92. How high will it pump almond oil? 65 2. For the pump in question one, will the pressure at the pump be the same as for the three fluids? No. 3. For the pump in question one, will the required horsepower be the same for the three fluids? No. 4. A pump curve relates what to what? a) Pump Horsepower to Pump Speed b) System Head to Pump Capacity c) System Head to Operating Point d) Pump Head to Pump Horsepower 5. A centrifugal pump will operate: a) At its maximum efficiency b) At its maximum head c) The intersection of its pump curve and the system curve d) No way to tell 6. Answer the following as True (T) or False (F) a) T The capacity of a centrifugal pump can be controlled by a VFD. b) T The capacity of a centrifugal pump can be controlled by a throttling valve. c) T The capacity of a PD pump can be controlled by a VFD. d) F The capacity of a PD pump can be controlled by a throttling valve. e) F The speed of a pump can be changed without affecting required horsepower. f) F A centrifugal pump has a linear capacity to speed relationship. g) F A PD pump has a nonlinear capacity to speed relationship. 26