Feedback Control Systems Demystified: Volume 1 Designing PID Controllers by Jack W. Lewis

Author:Jack W. Lewis [Lewis, Jack W.]
Language: eng
Format: azw3
Publisher: Surber Press
Published: 2014-03-28T16:00:00+00:00

We set this to zero in order to obtain the homogeneous solution. That is

The homogeneous solution always has at least one solution of the form

where A and r are unknown constants. We can readily see that (4.19) is a solution. Differentiate (4.19) once.

Substitute this derivative and (4.19) into (4.18).

Divide both sides of (4.20) by Aert.

Equation (4.21) must hold for all time if (4.19) is to be a solution to (4.18) for all time. Therefore (4.21) requires that

That gives the homogeneous solution as

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