Pure Integrating Process

A pure integrating process has a differential equation of the form

Note that the derivative of the output, y, is only a function of the input and doesn't involve the output.

If we inject a step of size 'A' into the input, the differential equation we need to solve becomes:

This equation can be solved simply by separating the variables:

This type of process integrates the input which is applied to it. In the case of a step input, the result is a continuously increasing ramp. A common example of an integrating process is a tank where the input and output flowrates are independent of the tank level and each other - if one input changes the level in the tank will change continuously until the tank either empties or overflows.