Ratio of output to input in the Laplace domain; characterises a linear system completely.
A transfer function G(s)=Y(s)/U(s) for zero initial conditions describes a linear system's input-output behaviour. Its poles set stability and speed, zeros shape the response. Series blocks multiply and feedback gives G/(1+GH).
G(s)=1/(τs+1) is a first-order low-pass.
A transfer function summarises a linear system in one expression, so you can predict its response to any input without re-solving the equations.
Ratio of output to input in the Laplace domain; characterises a linear system completely.
A transfer function summarises a linear system in one expression, so you can predict its response to any input without re-solving the equations.
Take the Laplace transform of the equation with zero initial conditions, then divide the output transform by the input transform.
Its roots, the poles, determine stability and natural behaviour of the system.
Typical applications include designing a filter that meets a required cutoff and attenuation, predicting the output of a sensor amplifier chain and specifying the gain needed for a feedback loop.
Study "Laplace transform" first (topic 67 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Poles: denominator roots. Stable if poles in the left half-plane. Frequency response G(jω).
G(s)=1/(τs+1) is a first-order low-pass.
The next topic is "Systems of ODEs", which builds directly on this one.
It is classed as Intermediate in Engineering Mathematics (topic 68 of 104). It is an intermediate topic. Work through the beginner topics in Engineering Mathematics first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.