The 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 $TV($seconds$)$ and a steady state gain of $Kv(mL.s-1.mV-1).$

The mixing process itself can be modeled as first order with a steady$-$state gain of $Kp$

$($ppm$.$s$.$mL$-1)$ and a time constant of $Tp($seconds$).$

"Analysis, design and implementation of a suitable feedback control strategy for a

dye injection process."

The water flowrate in the pipe is $2\frac{L}{s}$ and the pipe has a cross$-$sectional area of $5cm2.$

The regulating valve is thus first order with a time constant of $0\mathrm{.}2s$ and a steady$-$state

gain of $0\mathrm{.}6mL.s-1.mV-1.$

The mixing process itself can also be modeled as first order with a steady$-$state gain of

$0\mathrm{.}8ppm.s.mL-1($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 $99\mathrm{.}3\%$ complete in $20s.$

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.

Add the following to your mid$-$term report:

Transfer functions

Estimate the process transfer functions that can be in the following form

The process transfer function is $Gp=K\frac{p}{?}(($aubaR $*s+1)$

The control valve transfer function is: $Ga=$KvI $($taubal $*s+1)$

The transport lag due to the distance between Dye injection and the optical sensor is

accounted for by: $Gm=K{m}^{**}{e}^{-t{d}^{**}(s)}$

Determine $Kp,p,Kv,v,Km,td$ from the information given above.

What do you expect the disturbances transfer functions to look like? Propose suitable

ones

What would the open loop step response be i$.$e$.$ the Process Reaction curve function

Gprc $=$ GaGpGm?

To do the empirical tuning we need to fit a first order function with deadtime ig$.$

Gprc ~~$\frac{K^{**}{e}^{-a}s}{bs+1}$ to the Gprc found in step $4$

Find $K,a,$ and $b$ in step $5$ by "tuning" in MATLAB. This can be done by plotting the

step response in step $4.$ And then "guessing" the values of $K,a,$ and $b$ and then plotting

the step response in MATLAB and comparing the $2$ plots and then modifying $K,a,$ and $b$

until a good match is obtained

Then use Cohen$-$coon method $($shown in the table below$)$ to determine the PID

parameters. Compare the parameters to those obtained using MATLAB's pidtune

function

Gprc $=K^{**}{e}^{-t}d\frac{s}{{}^{**}}s+1$