A black dye for making shirts is injected into a stream of water. The injected dye is blended into the water flow with constant speed mixers.A detector is used to monitor the dye/water concentration. The output of the detector is sent to a controller, which then sends a signal to the dye-injection valve. One needs to be careful with the location of the detector.The sensor has to be far enough away to ensure a well-mixed stream.
However, if the detector is too far away, the transport lag can destabilize the process.The regulating valve is especially designed so that the dye input rate, in milliliters per second, varies linearly with the valve position. The regulating valve thus is a first order with a time constant of τv (seconds) and a steady state gain of Kv (mL/sec.mV).The mixing process itself can be modeled as first order with a steady-state gain of Kp (ppm.sec/mL) and a time constant of τp (seconds)
Expand your mid-term report to write a report of around 4000 words maximum, excludingreferences on: “Analysis, design and implementation of a suitable feedback control strategy for a dye injection process”
The water flowrate in the pipe is 2 L/s and the pipe has a cross-sectional area of 5 cm2 . The regulating
valve is thus first order with a time constant of 0.2 s and a steady-state gain of 0.6 mLs −1 mV−1
The mixing process itself can also be modeled as first order with a steady-state gain of 0.8 ppm s mL−1 (where ppm indicates parts per million).
A previous experiment indicated that a step change in the regulating valve resulted in a response in a dye concentration that is 99.3% complete in 20 s.The magic photodetector is extremely fast, and the response is linear over a large concentration range.The optical sensor is installed at 2 meters from Dye injection.