Dye Mixer Dynamics and Control
experiment water flows from the mains through a rotameter and a
needle valve into a flow system consisting of three 300 ml
Erlenmeyer flasks. Ball valves allow for flow through three vessels
in series, through one vessel only, or through a combination of
vessels. The effluent passes through a special flow cuvette in a
Spec 20 spectrophotometer, the signal from which is digitized and
processed by a LabVIEW. A solution of methylene blue dye is held in
a 20 L polyethylene carboy, flows to a magnetic drive centrifugal
pump, and then through a stepper-motor driven needle valve to mix
with the water feed stream. The computer controls the dye solution
valve via a stepper motor.
The first mode of operation involves using a syringe to inject a pulse of dye into the feed stream. The flow system response is digitized, plotted, and then the mean residence time (and thus the system volume) are calculated. The students can repeat the calculation using a spreadsheet, since the dye concentration vs. time data are written to a file. Each run takes only one or two minutes.
Next, a BASIC program is used to carry out an iterative nonlinear regression algorithm which estimates two parameters of a model of the flow system. Some of the water flows through three flasks and some through only one; the program is able to estimate the fraction passing through the three-flask portion, an otherwise unmeasurable quantity. This provides the students with a very simple and concrete introduction to modeling and parameter estimation.
In a second mode the water feed rate and flow system configuration are set, the dye feed pump is turned on, and the computer executes a PID control program. The students set the desired effluent dye concentration (the set point) and the algorithm adjusts the valve position to drive the effluent concentration to the set point, and thus the error to zero. The students are able to specify the three PID gains and the set point, and observe the nature of the control, which can range from sluggish to good to damped oscillatory to limit cycle oscillations. One nice result is to observe good control using a single flask only, and then see the system become unstable as two flasks are added to the flow path. This demonstrates clearly how additional delay in a loop can make control more difficult.
An important feature of the experiment is that the students can see directly all elements of a PID feedback control loop in action, including the passage of the dye through the flow system, the operation of the control valve, and the spectrophotometer response. They can also look at the statements in the program that implement the PID controller.
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