Exercise 6: Controller Tuning

Answers to Question 3

If the relationship between heating fluid flow and reactor temperature is assumed to be linear what is the relationship?

The equation for a straight line is

Temp = aFlow + b

So now we have to evaluate a and b. We know two points on the line

Flow = 2 kg/s, Temp = 140 ^oC
Flow = 4 kg/s, Temp = 173 ^oC

and so the equation can be evaluated to be:

Temp = 16.5 Flow + 107

What is the value of the dimensional process gain and what are its dimensions?

Dimensional process gain = 16.5 ^oC(kg/s)

The units are temperature/flow

What is the dimensionless process gain?

To get this multiply the dimensional gain by (kg/s per flow %) and divide by (^oC per temperature %).

Valve scaling is 0.1 (kg/s per flow %)
Temperature range is 200 ^oC
Temperature scaling is 2 (^oC per temperature %)

Dimensionless gain = 16.5 * 0.1 / 2 = 0.825

Easier way...

The dimensionless gain really has units of temperature range % / flow range %.

Change in temperature is 33 degrees which is 16.5% of range
Change in flow is 20%
Dimensionless gain = 16.5/20 = 0.825

If the reactor temperature is to be controlled at 180^oC using a proportional-only controller, what percentage manual offset would you recommend?

For the answer to this question determine what flow will give a temperature of 180 ^oC and convert this to a valve position.

180 = 16.5 Flow + 107
Flow = 4.42 kg/s

This represents 44.2% of the valve range and this must be the controller output with zero error to achieve the required temperature.

Experimental tuning of the process suggests the use of a dimensionless controller gain, standardised to a unity gain process, of 2.4. To what proportional band setting does this correspond?

The standard gain refers to a process with unity gain. Divide this by the process gain to get the actual required dimensionless gain:

2.4/0.825 = 2.91

This process has a gain of 0.825, which is less than one, so the required controller gain will need to be greater than the standard gain, so you need to divide by the process gain to increase it.

Proportional band is the reciprocal of dimensionless gain, expressed as a percentage:

PB = 1/2.91 * 100 = 34%

A theoretical investigation of the process suggests a dimensional controller gain of 0.2kg/s/^oC. What proportional band does this represent?

This uses the same approach as the more involved procedure for the third part of this question above.

Dimensionless gain = dimensional gain {(kg/s)/^oC } * {^oC/temp%} / {(kg/s)/flow%

= 0.2 * 2 / 0.1

= 4

So PB = 100/4 = 25%

Please move Back to previous page