Calculus with no math
When did you last use calculus on the job? My guess is never. So why do all the control theory textbooks bombard us with equations and expect us to understand how that relates to our real world processes? In these days of computer aided design and analysis tools – the need to solve a differential equation has been all but eliminated. This means that most engineers have lost touch with the concept of calculus, and how it applies to the real world. This is a shame because in many engineering disciplines and particularly in process control – the ability to visualise a problem mathematically is what really separates the real pros from the rest of the crowd. In fact even the humble PID contains those scary sounding calculus terms Integral and Derivative. This section aims to give you a feel for what these terms really mean. This will give you a real edge when understanding what’s going on in your controller.

Derivatives
Go into the control room of a process plant and ask the operator: “What’s the derivative of reactor 4’s pressure?”

And the response will typically be: “Bugger off smart arse!”

However go in and ask: “What’s the rate of change of reactor 4’s pressure?”

And the operator will examine the pressure trend and say something like: “About 5 PSI every 10 minutes” He’s just performed calculus on the pressure trend! (don’t tell him though or he’ll want a pay rise) So derivative is just a mathematical term meaning rate-of-change. That’s all there is to it. Testing your understanding

Suppose you have a box of electronics that calculates the derivative of its input signal. Its output is connected to an analogue meter which reads zero when vertical, negative to the left and positive to the right. Look at the diagram below and draw on it where the meter would be pointing for each of the 4 input signals.

Scroll Down for the answer…

Were you right? If not – remember that the absolute value of the input signal does not matter,