Modeling and Control

Is this the time for process and automation system designs to minimize dead time and interactions? Is this the time for university graduates to understand controller modes and parameters and the power of the DCS environment? Is it possible for these graduates to know how to tune a controller with non perfect mixing, measurements, and valves? Is this the time for users to know how to improve control system performance? Is this the time for new engineers to have a virtual mentor? Is this the time for suppliers to be able to demo the value of better measurements, valves, tuning, and advanced control?

This could be the time if modeling is embedded in the DCS and becomes a common tool in universities and industry. It started to happen about 5 years ago. Terry Tolliver and Robert Heider at Washington University use an industrial DCS as a virtual plant and in a computer control lab to teach process modeling and control as part of their chemical and system engineering programs. Atanas Serbezov at Rose-Hulman Institute of Technology uses a DCS in a lab to teach process control to Chemical Engineers. A DCS system has just been installed at Purdue University as part of the Engineering Research Center with Rutgers and the New Jersey Institute of Technology. If you doubt the value, talk to the students. In industry, Broadley-James, Lilly, Lubrizol, Monsanto, and Solutia have started using embedded modeling in a DCS for process design and control.

Modeling was such an integral part of my career, it is difficult for me to imagine how I would have learned and accomplished anywhere near as much without it. Modeling was a key part of my job even in the old days when you had to key punch cards for the IBM Continuous Simulation Modeling Program (CSMP) and submit them for an overnight run in a room full of main frame computers. When I got terminal server access to a computer with the Advanced Continuous Simulation Language Program (ACSL), I thought I was in heaven even though ACSL was designed for the aerospace industry. When graphical flow sheet simulators on a PC came along that we could interface to a DCS, I was blown away even though the interface was slow and cumbersome and the model speedup was rather minimal and inconsistent. I gave this all up to retire in 2002 and set up the virtual plant at Washington University. This wasn’t quite enough so I ended up in Austin in the fall of 2004 to see if I could help the future of modeling by making it more accessible. While only 50% of my 75% part time venture is actually doing modeling, I am at a juncture to see how well it can be used.

Eventually the automation world will evolve to where modeling is an integral tool for learning and 4D processes (development, design, deployment, and diagnostics). While my physics and process modeling background leads me to focus on models based on first principles, data driven models such as neural networks, linear dynamic estimators (e.g. MPC models), and multivariate statistical process control such as projection to latent structures (PLS) have great relevance because they have make no assumptions and detect the inevitable unknowns. I envision a future of hybrid models embedded in the DCS that use the best that each of these modeling technologies offers. Is this the time?

I remember my very first time …. for simulation ….. for processes .… for chemical not biological. I was working as lead instrument and electrical engineer on what was then the largest acrylonitrile and hydrogen cyanide plant in the world and I decided maybe the huge compressor that provided the air for reaction with propylene and ammonia was worth a closer look. If the compressor tripped a whole day’s production was lost plus startup was the most dangerous mode of operation. Then there were the consequences of surge. The amount of energy from flow reversals was enormous. Surge cycles reduced the compressor efficiency and could damage the rotor from excessive vibration. Even though it wasn’t in my job description, I decided as an extracurricular activity to write a dynamic model of the compressor. I learned that surge can occur in seconds after crossing the surge set point and that once the compressor got into surge you could not rely upon feedback control could not get it out. The nearly full scale flow reversals every couple of seconds was just too much for a flow controller. I learned the importance of a feed forward signal from reactor feed valve position and an open loop backup. After a year in field construction for installation and startup, I was invited either to do an encore for the next plant in England or based on my simulation program venture take a job in engineering technology. Even though the overseas assignment was tempting, the chance to work with some of the brightest minds in process modeling and control (Henry Chien, Larry McCune, Bob Otto, Terry Tolliver, and Vernon Trevathan plus the legacy of Joel Hougen and Ted Williams) was too much to pass up. Dynamic simulation became the most important tool for me for more than 30 years.

I have used models of compressors many times in some pretty exciting situations. No other disturbance is faster. The precipitous drop in flow that precedes surge occurs in 0.05 seconds. To simulate these dynamics you need a momentum balance besides a material and energy balance as shown in the ACSL program on page 121 of the E-book: http://www.easydeltav.com/controlinsights/compressorcontrolstudent/. The phenomenon was worse than falling off a cliff with a bungee cord with a perpetual rebound.

For a summary of some my compressor startup experiences check out “Compressor Surge Control – Traveling in the Fast Lane” on page 19 of the E-book:
http://www.easydeltav.com/controlinsights/FunnyThing/default.asp

The process of creating a model is in itself a knowledge building activity because it makes you think through first principal and dynamic relationships. Often insight into the problem is gained before the model is completed but then again there are the surprises from the test runs of the models due to the interactions and multivariable nature of most processes. Last week I gave my first model as an example. Here I jump forward 30 years to my most recent model, which explores glucose control of a mammalian cell culture.

Even if you are not into bioreactors, you might want to read on because there are insights here for concentration control of batch reactors in general. Just substitute your favorite reactant for glucose and reaction rate for consumption rate.

Most bioreactors to date have a glucose feed rate scheduled as part of batch sequence. The feed rate changes are usually developed during research and development and fixed for the commercial process for the industrial plant. The chances that the glucose feed rate exactly matches the glucose consumption rate is next to none.

The advent of analyzers to measure glucose at-line and NIR probes to measure glucose online opens the opportunity for glucose concentration control and consequently finding and maintaining the optimum glucose concentration for cell growth and product formation as discussed in the article titled “Unlocking the Secret Profiles of Batch Reactors” http://www.controlglobal.com/articles/2008/230.html

For a step change in glucose feed rate, there should be an integrating process response. However, test results from a bioreactor model show that for step increases in glucose feed rate the response started to ramp but then leveled off and decreased for steps on day 2 and flat lined for a +5% step and accelerated upscale for a +10% step on day 8. This odd behavior is the result of a glucose consumption rate that parallels the exponential, stationary, and death phases of the batch. These phases can be seen in the dissolved oxygen controller output. In Glucose Test Results, slide 1 shows a batch with automatic glucose control and slides 2 and 3 show batches with the glucose controller in manual with steps at day 2 and 8 of +5% and +10%, respectively in the controller output. Not shown is the ramp down and eventual depletion of glucose for decreases in feed via steps of -5% and -10%. In each case, the glucose feed and consumption rate were in balance because the controller was in automatic prior to the first step. This may not be the case for new or improperly tuned controllers.

Slide 4 shows the glucose control test results described in the aforementioned article for an online probe (no delay) and an at-line analyzer (11 hr sample delay). These test results show that determining the integrator gain and arrest time is essential and that the use of a feedforward signal can provide remarkable improvement especially for at-line analyzers.

Obviously the size and duration of the steps and their time in the batch determines whether you see a self-regulating, integrating, or runaway response and even an eventual reversal of the process gain. So how does one tune such an animal? The short cut method as described on pages 53-57 of the Good Tuning: A Pocket Guide 2005 second edition published by ISA, which uses the initial change in the ramp rates, may be your best bet. The method identifies a “pseudo integrator” (“near integrator”) gain and does not require the controller be in auto or the process be lined out at the start of the tests. The referenced pages are in the book excerpt Good Tuning Short Cut Method.

The relay oscillation auto tuner can provide successful results if the step size is large enough to overcome the changes in the consumption rate. However, for at-line analyzers, the ultimate period and consequently the test time may be too long. For the default setting of 3 cycles and assuming an average period of 4 deadtimes, the auto tuner would typically take 12 deadtimes. The user may find it adequate to use the results available after just one cycle (4 deadtimes). The short cut method can provide an estimate of the tuning settings in about 4 dead times assuming you make 2 steps and wait at least 2 deadtimes to see the change in ramp rate. Regardless of method, the tests for an at-line analyzer with a 4 hour or longer sample time will cover several shifts. New adaptive online tuning tools such as DeltaV Insight offer the opportunity to non-intrusively find better tuning settings from the initial response of the loop at the start of the batch and the response to normal set point changes during the course of the batch. However, the auto tuner and the short cut method might be still be useful for getting a new loop in the ball park to enable basic closed loop control from the get go.

The glucose consumption rate depends upon cell growth and to a lesser extent on product formation rates. The oxygen uptake rate can be estimated from the dissolved oxygen controller output (more specifically the secondary loop flows for air and/or oxygen sparge). If this inferred oxygen uptake rate is then corrected for maintenance and yield factors, it is a good candidate for a feedforward signal if the dissolved oxygen control is fast and tight so that changes in process are rapidly transferred to the controller output and the mass balance of dissolved oxygen in the broth is maintained.

This week I completed a model with the help of Roger Reedy that allowed me to confirm some concepts besides detail how the design of the control system can cut a project cost almost in half by the use of 10,000 gallon instead of 40,000 gallon neutralization tanks. It wasn’t an easy pH control application but not many of them are. The titration curve slope and the hence process gain changed by a factor of 1,000:1 from the extremes of the pH scale range to the neutral point. The influent pH could swing from 12 to 2 pH during the regeneration of a demineralization system or an area pump out. The disturbances could be fast because of plug flow, batch sequences, manual operations, and the stick-slip action of control valves. If pH control is not your thing and it is “High Time We Went” per the Joe Cocker song I am listening to, here is the escape clause.

“Besides embedded process models saving projects a chunk of money, improving plant performance, and justifying better controls and valves by studying the dynamics and integrated functionality of the process and automation system design, you can learn neat stuff like:”

(1) Speed besides size is important
(2) Feedforward signals can do more harm than good
(3) Feedforward head starts based on deltas can help
(4) Linearization of the process variable can be robust and useful
(5) Valve stick-slip can be the upset that keeps on giving

If you are caught within the gravitational pull of this study, I can’t guarantee it is not a black hole that sucks you into another dimension.

A process model constructed and embedded in the DCS was used to study a conventional pH and a reagent demand control system with and without feedforward control. In all cases the control loop was in the recirculation line of a vessel to provide a fast feedback correction of abrupt and large disturbances. The feed and reagents were injected at the inlet of a static mixer just before the recirculation stream reentered the vessel. Middle signal selection of 3 pH electrodes was used to inherently ignore a single sensor failure of any type, reduce measurement noise, ignore spikes and slow sensors, and facilitate online diagnostics and calibration. The inline control loop was extremely fast. The transportation delay was only about 2 seconds. The largest potential source of deadtime was injection delay associated with opening and closing of the reagent control valves but this was minimized by coordinated action of close coupled isolation valves at the injection point. Insuring model fidelity for a pH system simply came down to matching the slopes of the model’s titration curve with the slopes of the plant’s lab titration curve. The following file shows the model and lab titration curves on slides 1 and 2 and the control system on slide 3. Not readable is the slope of 0.015 at 2 and 12 pH.
pH System02 Study Results

First you need to get good lab curves by taking samples of the influent at key times such as steps in a batch sequence when acids or bases are used or during unusual operations such as the pump out of containment areas. The samples should be at the process temperature and titrated with the same reagents used in the automation system. The sample time, temperature, and volume and reagent type and strength must be noted and reagent addition volumes and pH must be tabularized. The typical graphical plots of titration curves showing a vertical line between 3 and 11 pH are next to useless.

The feedforward signal and linearized process variable for reagent demand control were created by use of the same signal characterizer block where the input array was pH values and the output array were corresponding X-axis values per the titration curve. The X-axis was scaled 0 to 100% for the Y-axis and the pH measurement scale of 2 to 12 pH. The first input to the signal characterizer for feedforward control was influent pH. The first input to the signal characterizer for reagent demand (feedback control) was static mixer outlet pH. The second input to both signal characterizers was the pH set point.

Since influent pH measurement errors as small as 0.04 at 2 and 12 pH can cause feedforward errors of 20% or more per the titration curve, it was decided that continuous adjustment by means of a pH feedforward signal could be making large incorrect changes in the reagent flow. It was reasoned that large changes computed in feedforward signal due to large changes in influent flow or pH could be useful as a delta head start to pre-position the valves for the start of a large upset and then let the feedback controller do its thing. This proved to be the case although the feedforward was complicated by the blend of the recirculation stream with the influent at the inlet to the static mixer. Unfortunately, the accuracy of the feedforward curve depended on the accuracy of the titration curve.

Reagent demand control does not deteriorate significantly for changes in the titration curve because only relative changes in the slope are important for linearization and any information is usually better than no information about the shape of the curve. Reagent demand control uses the X-axis of the titration curve scaled as a 0-100% process variable and set point. This control ignores the pH fluctuations near neutrality because these correspond to very small changes in reagent demand due to the steep slope. Reagent demand control also recognizes the true distance of the influent from the set point, which is important for startup and well as disturbances.

Results of the auto tuner showed that the pH controller gain needed to be very low (e.g. 0.02) because of the high process gain from the steep slope of the titration curve at the 7 pH set point. The reagent demand controller gain could be 10 times larger (e.g. 0.25) – see slides 5 and 6 for screen prints of auto tuner results.

A comparison of the conventional pH and reagent demand control is shown on slide 7. The spikes in the static mixer pH are caused by 0.4% stick-slip of the water valves. If the resolution of the water valves was improved from 0.4% to 0.1%, the spikes went away. If the resolution of the acid and base valves upstream or at the static mixer deteriorated from the specified 0.1% to 0.4%, there were many more spikes from the limit cycles of these valves. Normally, a 0.5% resolution control is consider good. This is not so for high process gains. Neutralization systems with pH set points near neutrality are excellent indicators of actual valve resolution and a perpetual stick-slip limit cycle. If you want to know more, check out “Improving pH System Design and Performance” at the Emerson Global Users Exchange this September and the Chemical Processing article on control valves last October.
http://www.chemicalprocessing.com/articles/2007/200.html