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MEC524 — Chapter 2
System Representation
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Transfer Function — Classical Approach

The ratio of the Laplace transform of output to input, assuming zero initial conditions. It describes the input-output ratio in the s-Domain.

◆ Diagram
Transfer Function — Classical ApproachG(s) = Output(s) / Input(s)Laplace-transformed ratio, zero initial conditionsInput U(s)G(s)Output Y(s)Analogy: The Vending Machine$Input?InternalsHidden🥤OutputOnly cares about input → output relationshipNo need to understand internal mechanics — just the ratio G(s)Classical control: what goes in, what comes out
◆ Key Points
01.G(s) = Y(s) / U(s) — zero initial conditions assumed
02.Properties: Order (highest power of s), Type (powers at origin), Rank (n − m)
03.Ideal for single-input single-output (SISO) systems
04.Analogy: Vending machine — input (coin) → output (soda), no internal knowledge needed
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Ch 1: Control Systems Ch 3: Mathematical Modeling