“enter”. You may read Section 2-5 again to review the questions related to this process testing. Once the process characteristics are obtained and the controller tuned using the formulas of Chapter 3, the tuning can be tested by changing the set point or by intro- ducing a disturbance by starting or stopping a fan. Designing the Feedforward Controller. It is known that for this scrubber unit the input flow can vary much and very often. That is, it is common to have one fan working (e.g., fan 2 with a flow of 25 cfm, and suddenly the other two fans turn on, to have a total input flow of 100 cfm. When this occurs, the outlet HCl will increase until the feedback controller can take hold by adding more NaOH to bring the HCl back to set point. We must be sure that the HCl ppms do not violate the EPA reg- ulation. Thus, under normal operation the set point to the controller must be set low enough to ensure staying within regulation under this upset condition. Although the low set point guarantees not violating the regulation during any upset condi- tion, it costs extra money during normal operation because it requires extra NaOH flow. If we could provide a tighter control, less deviation from set point under upset conditions, we could raise the set point and thus save a portion of the extra NaOH. Feedforward control can provide this tighter control. The idea is to measure the flow entering the scrubber, and if this flow changes, manipulate the NaOH 210 PROCESSES FOR DESIGN PRACTICE Figure B-2 Scrubber. app_b.qxd 7/3/2003 8:02 PM Page 210 valve. That is, do not wait for a deviation in HCl before taking action. There is a flow sensor/transmitter with a range of 0 to 100 cfm measuring the input flow to the scrubber. Chapter 6 shows that a way to design a feedforward controller is to use a first- order-plus-dead time transfer function (K, t, and t 0 ) describing how the disturbance (feed to the scrubber in this case) affects the controlled variable (outlet HCl ppm in this case), and another first-order-plus-dead time transfer function describing how the manipulated variable affects the controlled variable. The former transfer func- tion is obtained by clicking on/off one of the fans to generate a change in input flow, recording (every 5 sec) the HCl ppm value, graphing the response curve, and using the two-point method described in Chapter 2. The latter transfer function was obtained to tune the feedback controller. Once both transfer functions are obtained, Eq. (7-2.5) is used to tune the feedforward controller. Once the feedforward controller is designed, it can be tested. We recommend the testing to proceed the following way. Under feedback control, one of the fans should be turned on or off and this control performance be used as a baseline to compare the feedforward performance. Then, under steady-state feedforward/feedback control, generate the same disturbance and compare the control obtained with that of feedback. Repeat, but this time add the lead/lag unit. Finally, do the same, adding the dead-time compensator if needed. Process 2: Catalyst Regenerator A catalyst is used in a hydrocarbon reaction. As the reaction proceeds, some car- bon deposits over the catalyst, poisoning the catalyst. After enough carbon has deposited, it poisons the catalyst completely. At this moment it is necessary to stop the reaction and regenerate the catalyst. This regeneration consists in blowing hot air over the catalyst so that the oxygen in the air reacts with the carbon to form carbon dioxide, and in so doing to burn the carbon. Figure B-3 shows the regener- ation process. Ambient air is first heated in a small furnace and then flows to the regenerator, which is full of catalyst. Manipulating the fuel flow controls the tem- perature in the catalyst bed. The set point is changed by either double clicking on the number and entering the new set point, or by clicking on the up/down arrows next to the numerical value; each click changes the set point by 1°F. The controller’s action is set by clicking on the switch indicating reverse (REV) or direct (DIR). The controller’s output is set, when in the manual mode, by either double clicking on the number and entering the output, or by clicking the up/down arrows next to the value; each click changes the output by 1%. The controller’s tuning terms—gain, reset, and rate—are set by either by double clicking on the number itself and enter- ing the value, or by clicking the up/down arrows. Tuning the Feedback Controller. To tune the feedback controller we must first find the process characteristics. Section 2-5 we explain that to obtain the process characteristics, a process reaction curve is necessary. To obtain this curve, we intro- duce a step change in the controller’s output and record the temperature in the regenerator. Unfortunately, there is no recorder to record this temperature. Thus you will have to generate a table of the temperature in the regenerator versus time PROCESSES FOR DESIGN PRACTICE 211 app_b.qxd 7/3/2003 8:02 PM Page 211 and graph these data. We recommend that the temperature be read every 5 sec. You should read the temperature until a steady state is achieved again. To generate the step change in the controller’s output, double-click on the number, type the new desired output, and press “enter.” You may reread Section 2-5 to review the ques- tions related to this process testing. Once the process characteristics are obtained and the controller tuned using the formulas of Chapter 3, the tuning can be tested by changing the set point or intro- ducing a disturbance. The temperature of the air entering the furnace can be changed to induce a disturbance. We recommend changing this inlet temperature, by 10°F and recording the largest deviation from the set point. Next you implement a cascade control scheme, and can then compare the control performance given by feedback and cascade. Tuning Cascade Controllers. In Chapter 4 we explained how to tune cascade controllers. Figure B-4 shows the cascade control implemented in the regeneration process. The first step is to obtain the process reaction curve for the secondary vari- able and the process curve for the primary variable. Both curves are generated by the same step change in the secondary controller’s output; this is the controller con- nected to the final control variable. This time you will have to generate two tables, the temperature in the regenerator (primary controlled variable) versus time, and the temperature leaving the furnace (secondary controlled variable) versus time. 212 PROCESSES FOR DESIGN PRACTICE Figure B-3 Catalyst regenerator—feedback control. app_b.qxd 7/3/2003 8:02 PM Page 212 Remember, in taking the data you should read the variables every 5 sec after chang- ing the controller’s output. From the temperature in the regenerator versus time graph, you obtain K 1 , t 1 , and t 0 1 , and from the temperature leaving the furnace versus time graph, you obtain K 2 , t 2 , and t 0 2 . Using the last set of terms the secondary con- troller is tuned as a simple feedback controller (tuning formulas presented in Chapter 3). Using all the terms and the tuning of the secondary, the primary con- troller is tuned using either Table 4-2.1 or 4-2.2. Once you have tuned both con- trollers, you should try the secondary first to make sure that it works fine by itself. Once this is done, you can set the secondary controller in cascade (remote set point) and the primary controller in automatic. A good test to perform is to change the inlet air temperature to the furnace and record the largest deviation from set point. You can then compare this deviation with the one you obtained under simple feed- back control. Process 3: Mixing Process Figure B-5 shows the schematic of a tank where cold water is mixed with hot water. The valve in the cold water pipe is manipulated to control the temperature of the PROCESSES FOR DESIGN PRACTICE 213 Figure B-4 Catalyst regenerator—cascade control. app_b.qxd 7/3/2003 8:02 PM Page 213 water leaving the exit pipe. You may assume that a level controller (not shown) maintains perfect level control. The hot water flow and temperature and the cold water temperature act as disturbances to the process. The set point is changed by either double clicking on the number and entering the new set point, or by clicking on the up/down arrows next to the numerical value; each click changes the set point by 1°F. The controller’s output is set, when in the manual mode, by either double clicking on the number and entering the output, or by clicking the up/down arrows next to the value; each click changes the output by 1%. The user also has the capa- bility of selecting the PV tracking option. The controller’s tuning terms—gain, reset, and rate—are set by either by double clicking on the number itself and entering the value, or by clicking the up/down arrows. Tuning the Feedback Controller. Tune the feedback controller by the method presented in Chapters 2 and 3, and used in the other processes. Note the units of the reset time. A very interesting disturbance is the flow of hot water. Once the tem- perature controller is tuned, start to decrease the hot flow by 25 lb m /min at a time and watch the control performance. 214 PROCESSES FOR DESIGN PRACTICE Figure B-5 Mixing tank. app_b.qxd 7/3/2003 8:02 PM Page 214 action, 3 analog, 5 block diagrams, 127 boiler control, 83 boiler level control single-element, 168 three-element, 169 two-element, 168 cascade control primary variable, 63 secondary variable, 64 cascade controllers, tuning, 65 combustion control, 83 computing algorithms, 74 control automatic, 2, 4 cascade, 61 closed-loop, 4 constraint, 88 cross-limiting, 86 feedback, 2, 6 feedforward, 8, 142 manual, 4 override, 88 ratio, 80 regulatory, 4 selective, 92 servo, 5 controller, 2, 38 action, 38 derivative time, 48 gain, 40 master, 63 offset, 41 primary, 63 proportional (P), 40 proportional band, 43 proportional-derivative (PD), 50 proportional-integral (PI), 44 proportional-integral-derivative (PID), 48 rate, 48 reset, 44 slave, 64 stability, 132 tuning, 53 cross-limiting control, 86 dead time, 21 dead time compensation, 151, 174 Dahlin’s controller, 176 Smith Predictor, 174 decision, 3 digital, 5 distributed control systems (DCS’s), 38, 74 disturbance, 4 external reset feedback, 90 feedforward control, 8, 142 dynamic, 153 steady-state, 153 final control element, 2 forcing function, 14 215 INDEX index.qxd 7/3/2003 8:04 PM Page 215 Automated Continuous Process Control. Carlos A. Smith Copyright ¶ 2002 John Wiley & Sons, Inc. ISBN: 0-471-21578-3 216 INDEX gain, 17 lead/lag, 151, 155 level average control, 59 tight control, 58 master controller, 63 multivariable process control, 180 decoupling, 194 pairing, 181 stability, 191 tuning, 192 measurement, 3 noise, 33 offset, 41 process, 11 characteristics, 11 dead time, 21 first-order, 24 first-order-plus-dead-time (FOPDT), 24 gain, 17 higher-order, 26 integrating, 14 multicapacitance, 24 nonlinearities, 23 nonself-regulating, 13 open loop unstable, 14 reaction curve, 29 self-regulating, 13 single capacitance, 14 time constant, 20 programming block oriented, 76 software oriented, 76 relative gain analysis, 184 reset feedback, 90 reset windup, 50 responding variable, 14 sensor, 2 set point, 4 local, 64 remote, 64 signals, 5 slave controller, 64 stability, 132 time constant, 20 tracking, 73 transducer, 5 transfer function, 24 transmitter, 2, 28 tuning cascade controller, 65 controller synthesis method, 55 flow loops, 56 lambda method, 55 level loops, 57 Ziegler-Nichols, 53, 55 two-point method, 29 ultimate gain, 54, 136 ultimate period, 54, 136 upset, 4 variable controlled, 3 manipulated, 4 index.qxd 7/3/2003 8:04 PM Page 216 . 90 feedforward control, 8, 142 dynamic, 153 steady-state, 153 final control element, 2 forcing function, 14 215 INDEX index.qxd 7/3/2003 8:04 PM Page 215 Automated Continuous Process Control. Carlos. 155 level average control, 59 tight control, 58 master controller, 63 multivariable process control, 180 decoupling, 194 pairing, 181 stability, 191 tuning, 192 measurement, 3 noise, 33 offset, 41 process, . the furnace (secondary controlled variable) versus time. 212 PROCESSES FOR DESIGN PRACTICE Figure B-3 Catalyst regenerator—feedback control. app_b.qxd 7/3/2003 8:02 PM Page 212 Remember, in taking