Consider the vacuum filter shown in Fig. P7-1. This process is part of a waste treatment plant. The sludge enters the filter at about 5% solids. In the vacuum filter, the sludge is de-watered to about 25% solids. The filterability of the sludge in the rotating filter depends on the pH of the sludge entering the filter. One way to control the moisture of the sludge to the incinerator is by adding chemicals (ferric chloride) to the sludge feed to maintain the necessary pH. Figure P7-1 shows a proposed control scheme. The moisture transmitter has a range of 55% to 95%

When the input moisture to the filter was changed by 2.5%, the following data were obtained

(a) Draw a block diagram for the moisture control loop. Include the possible disturbances.

(b) Use fit 3 to estimate the parameters of first-order-plus-dead-time models of the two transfer functions. Redraw the block diagram showing the transfer function for each block.

(c) Give an idea of the controllability of the output moisture. What is the correct controller action?

(d) Obtain the gain of a proportional controller for minimum IAE response. Calculate the offset for a 5% change in inlet moisture.

(e) Tune a PI controller for quarter decay ratio response