he project is to design a controller for a mixer.

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 v (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 p (seconds).

CT = Controller CC = Control Valve Q = Water flow rate L = Distance from Dye injection to optical sensor

Write a report of 2,500 words maximum, excluding references (this is a report with a literature review, hypothesis, and proposal for workings) using the above description on:

Feedback control strategy for a dye injection process

Consider/discuss the following in the report:

1. Problem statement

Provide a description of the problem at hand. Clarify where such units are used and identify the typical control objectives. What are the requirements? Tight control, relaxed control, fast control

Discuss safety and economic requirements.

The variables should be identified and categorised into manipulated variables, disturbance variables and process variables.

2. Modelling and block diagrams

For the process variable draw an open loop block diagram showing all blocks (process dynamics, disturbance dynamics), final control elements, and sensors. At this stage no controller is shown. Name each block and signal in the block diagram.

Explain how a model could be obtained from the differential equations and/or by experiment for each block in the block diagram. You may write the first principle equations that lead to develop the transfer functions. You are expected to discuss how in practice you can experiment to obtain the transfer functions or verify the ones obtained from first principle.

Present the type of transfer functions to expect for each block (order, deadtime or not, sign of the gain).

3. Control strategies (single loop, cascade, feedforward)

For each process variable describe the different possible control strategies, feedback, feedforward, cascade, or any combination of these, and compare them. For each control strategy provide a block diagram clarifying it.

Recommend one control strategy for each process variable.

4. Features of P, PI, PID

Describe P, PI, PID controllers. For each controller, provide its formula and transfer function. Provide a comparison of the controllers and present the expected results (reaction curves). Clearly specify when to use each controller type.

Recommend which ones to use for the case at hand.