Control systemsLesson 2 of 5 in the course Transfer functions and modelling

Transfer Functions: Input–Output Models, Frequency Response, and Stability

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

A transfer function describes how a system’s output relates to its input. It gives engineers a way to represent, compare, and combine components in fields such as electronics, control, chemical engineering, and imaging.

A system may be a complete device, a subsystem, or a single component. Its transfer function models the output produced for possible inputs. In a simple static case, the relationship can be shown as a graph with input on one axis and output on the other. This graph is called a transfer curve or characteristic curve.

All flashcards

What is a transfer function?
A mathematical model of how a system relates its output to its input.
What is a transfer curve?
A graph of output against input for a simple static relationship.
Why can transfer-function units differ between devices?
They depend on the physical output and input quantities being related.
How can engineers use component transfer functions?
They can combine component models to analyze larger systems, often with block diagrams.
What does a filter’s frequency response show?
How its gain and phase vary with the frequency of an input signal.

Quiz questions

  1. For a continuous-time LTI system with zero initial conditions, how is its transfer function defined?Answer: H(s)=Y(s)/X(s)H(s)=Y(s)/X(s)
  2. For a sinusoidal steady-state input, what does ∣H(jω)∣|H(j\omega)| represent?Answer: The output amplitude divided by the input amplitude.
  3. Which expression defines group delay in terms of phase ϕ(ω)\phi(\omega)?Answer: −dϕ(ω)/dω-d\phi(\omega)/d\omega
  4. What response property characterizes a Bessel filter of a given order?Answer: Maximally constant group delay.
  5. In a multiple-input, multiple-output system, what does an element of the transfer matrix relate?Answer: One input variable to one output variable.

Based on the Wikipedia article Transfer function, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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