Laplace Transforms for Processes

While this book only uses Laplace transforms when the alternative would be overly complex, they are used in many text books and by control system vendors. So that they can be recognised, the transforms for the common types of process are listed here. 

As shown in the example in this chapter, inverse response is caused by two competing processes - the faster of which takes the process first in a direction opposite to the steady state. We can approximate this as two first-order processes with gains of opposite sign, so that the combined effect is given by 

If T3 is less than 0 then the process will show inverse response. If T3 is greater than 0 then the process will show PV overshoot and T3 is said to add lead to the process. 

Ziegler, J.G. and Nichols, N.B. (1942) Optimum settings for automatic controllers. Transactions oftheASME, 64, 759-768. 

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