Transfer Function

What is Transfer Function?

The ratio of a linear system's output to its input in the Laplace domain, assuming zero initial conditions, condensing an entire differential equation into a single algebraic expression. Where its poles sit in the complex plane determines almost everything about the system's stability and dynamic response.

The five clues

Engineerdle #60 described Transfer Function with five clues, revealed one at a time from hardest to most direct. Each clue points at a different property of the concept.

1. 01A single expression that captures how a whole system responds.
2. 02It's a ratio, taken in the Laplace domain.
3. 03Output divided by input, with all initial conditions assumed zero.
4. 04Its poles tell you almost everything about stability.
5. 05G(s) = Output(s)/Input(s) — the s-domain ratio describing a linear system's input-output behaviour.

More Control Systems concepts

• Ziegler-Nichols MethodPuzzle #48
• OvershootPuzzle #43
• Phase MarginPuzzle #38
• Laplace TransformPuzzle #33