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.