FIG 1: The mixing chest accepts a combination of flows of stock.
Simulation on the road to optimization |
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John Gerry, P.E., ExperTune Inc., Hubertus, WI 53033 USA |
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Michel Ruel, P.E., TOP Control Inc., Levis, QC G6V 6K9 Canada |
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Reprinted with permission of Control Solutions. This article appeared in the November 2002 issue of Control Solutions. |
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You've got an in integrated processing plant, but have you optimized your processes? One sure-fire way to fine tune your controller and get the most out of it is through simulation. While you may not have the same process as the paper manufacturer we'll cover below, you'll find plenty of ideas about how you can apply the same techniques to help you get the most out of your controller, eliminating waste and improving product quality.
At a large paper manufacturer, a paper machine was experiencing high variability in paper quality because of cycling in the stock preparation. The stock preparation in a paper mill is a combination of the flows of stock mixed together in a mixing chest (Fig. 1).
This mill has many grade changes in its paper, which means the speed of the machine and, hence, the demand for pulp can change often. Also, when operators change the grade, they try to reduce the level in the reservoir to make sure there is as small amount as possible of the older grade pulp in the chest.
The plant needed moderately aggressive tuning for regulation to handle the upsets from pulp demand. The process also needed good setpoint response with little overshoot to handle the change in the level just before and after grade changes.
Initially, plant personnel did not think it was possible to get good tuning for upsets and good setpoint response all at the same time. The plant controls its process with a Honeywell DCS that has a selection of algorithms available.
To understand the controller algorithms, consider the simplified PID equations when the controller has gain only. There are no integral or derivative terms, and the controller calculation or algorithm is fairly simple. With algorithm A and C, the gain in the controller works on the error signal:
Controller Output = gain*error + bias
error = SP - PV
Where:
SP = Setpoint
PV = Process Variable (or level measurement)
With algorithm C, the controller works on the process variable alone:
Controller Output = gain*PV + bias
Where PV = Process Variable
In both cases, the output at setpoint is adjusted by the bias. If the controller had integral action or reset action, the controller would automatically reset the bias signal based on the error.
Also, in both cases, with SP constant, the same PV change will cause the same change in controller output. For example, if the gain were 1.0 and the PV changed by 10%, the controller output would also change by 10% in both equations. In a process upset, only the PV changes, so both controllers have the same response to upsets.
However, they respond differently to setpoint changes. With algorithms A and C the controller output will move immediately with a setpoint change. Since the SP does not appear with the gain in algorithm C, the output will not move at all until the bias adjustment (or integral action) starts moving the output.
The mill had been using the A controller algorithm. When using this algorithm, plant operators had to choose between good setpoint response and good regulation. Perhaps by using C they could get both. Trying what-if simulations with both controller algorithms on their process should provide the answer.
Any simulation requires a model of the plant and controller. Simulating the controller is as easy as picking it off a list as "Honeywell TDC EC, BC, MC, AM, PM real, A" or "Honeywell TDC EC, BC, MC, AM, PM real, C." The second step in simulating the loop is to get a good model of the process.
To model the loop, the modeling software needs both the level and the controller output data from a change done to the loop. For example, data from the level loop, shown in Fig. 2, was collected by ExperTune software. This data is then analyzed by the software, which finds the best process model. The model found from this the data that's shown in Fig. 3.
Using this model with either the A or C controllers lets us simulate and try what-if analysis on this loop. Figure 4 shows simulated PV (level) and controller output response to a load upset. The blue line shows the response of the loop with the PI tuning as found in the controller. The green lines show the response using the tuning recommended by software. This tuning was backed off from the software's optimal settings by a safety factor of three.
This load response simulates a decrease in the demand of pulp by the paper machine. The decrease in demand occurs at time 0 in the simulation, but the level starts to go up 30 seconds later, after the process deadtime has passed. After this time, the level increases since less pulp is being removed from the mixing chest. The controllers take corrective action to bring the level back, giving the resulting response in PV or level.
The blue line or "as found" tuning was overly aggressive, causing the controller output—and hence—the entire paper machine to cycle. The new tuning responds almost as fast and provides a smooth non-oscillatory controller output.
The load response of both the A and the C algorithms is identical to that shown in Fig. 4 since A and C algorithms respond the same to process upsets. But, what about setpoint changes? The plant's operators want no overshoot on a setpoint change.
Figure 5 shows the simulated PV (level) and controller output response to a setpoint change. The setpoint change occurs at time 0 in the simulation. The setpoint is graphed as a dashed red line. The blue lines show the response using the as-is tuning with the A algorithm. We have already decided from the load simulation that we prefer the new tuning—at least for response to upsets. The new tuning using the A algorithm is shown in green.
Since the plant did not want overshoot on setpoint changes, we tried simulating the setpoint response using the new tuning and C algorithm. The PV response in red is using the C algorithm. For the responses represented by both the red and green lines, the tuning was identical. The only difference was the choice of PID algorithm.
The C algorithm has the gain operating on the PV only and not the setpoint. Hence, when the setpoint occurs, its controller output (shown in red in the lower graph in Fig. 5) does not initially move. It slowly starts to move as a result of integral action in the controller.
Using the C algorithm gives the setpoint response the plant personnel like while still providing good response to load upsets. The A algorithm has the same response to load upsets, but overshoots (green line) to setpoint changes more than they want. C algorithm wins in this case. In other situations, plant engineers might want the quicker response of the A algorithm and can tolerate the overshoot.
Some controller algorithms (Foxboro's new PID Tau, for example) let the user apply a certain percentage of the controller gain to act on the setpoint. This allows the user to tailor the setpoint response further. They may have been able to avoid overshoot and yet reach setpoint sooner.
Another technique for achieving smooth setpoint response would have been to filter the setpoint with a lead-lag algorithm while using the Honeywell A algorithm. Again, this would allow for a more specific definition of the shape of the setpoint response—the PV would get to setpoint faster than the C Algorithm, but without overshooting.
The shape of the setpoint response will vary for different processes. This process tends toward one end of the range where the difference in the shapes of the setpoint and load responses is greater when using algorithm A. If the process were mostly deadtime or had mostly deadtime with a small lag, there would be less difference between the shape of the setpoint response and the shape of the load response using the A algorithm. In these cases, the plant engineers may prefer the A algorithm because of its faster response.
Simulation can help you decide what controller algorithm and PID tuning to use in your plant. The what-if analysis allows you to try many different combinations, quickly, so you can find the optimal solution.
The analysis software used in this article was from ExperTune Inc, www.expertune.com. Figures reproduced with permission of ExperTune and TOP Control.
John Gerry, Registered Professional Engineer, holds a M.S. in chemical engineering from the University of Texas and B.S. chemical engineering from the University of Illinois. He has worked for Foxboro Company, Eastman Kodak, Eli Lilly, and S.C. Johnson. In 1986 he founded ExperTune Inc., and is its president. You can reach him at www.expertune.com.
Michel Ruel, P.E., from TOP Control Inc., St. Romuald, Quebec, has 25 years of plant experience at companies including Monsanto, Domtar Paper, Dow Corning, and Shell Oil. Author of several publications on instrumentation and control and frequent university lecturer, Ruel is experienced in solving unusual process control problems. He has presented process control lectures to more than 4000 engineers and technicians in four countries. His e-mail address is mruel@topcontrol.com Website: www.topcontrol.com
Control Solutions November, 2002
Authors: John Gerry, Michel Ruel