An Introduction to System Modeling and Control

11Frequency Response Methods

11.1 Bode Diagrams

In Chapter 3 transfer functions of differential equations were introduced. For example, consider the third‐order differential equation given by

Taking the Laplace transform with zero initial conditions, i.e., , we have

resulting in the transfer function

With the input given by for it was also shown in Chapter 3 that

is a solution to the differential equation.¹

The frequency response shows how the differential equation processes any sinusoidal input It has been found that considerable insight into a system (differential equation) can ...