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Transfer Functions

Transfer Functions. The transfer functionRepresent relation between input U(s)

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Transfer Functions

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    1. Transfer Functions Transfer functions Standard process inputs First-order systems Simulink example Integrating systems

    2. Transfer Functions The transfer function Represent relation between input U(s) & output Y(s) in the Laplace domain Usually denoted as G(s) Y(s) = G(s)U(s) Only applicable to linear models! Deviation variables Defined as difference between variable and its steady-state value Transfer functions always specified in terms of deviation variables Y(s) = G(s)U(s) Usually often omit primes for notational simplicity

    3. Transfer Function Example Stirred tank heater Steady-state equation: Initial conditions: Subtract steady-state equation

    4. Transfer Function Example cont. Laplace transform Rearrange noting that T(0) = 0 Definitions Transfer functions 1st-order system

    5. Properties of Transfer Functions Additive property Y(s) = G1(s)U1(s)+ G2(s)U2(s) Multiplicative property Y2(s) = G1(s)G2(s)U(s) ODE equivalence

    6. Standard Process Inputs Step input Ramp input Rectangular pulse input

    7. System Order General transfer function System order Order of the denominator polynomial D(s) Generally equal to the number of ODEs from which G(s) was derived First-order system Second-order system

    8. First-Order System Standard form Stirred tank heater Step response

    9. Ramp Response

    10. Sinusoidal Response

    11. Simulink Example: sininput.mdl First-order system: Sinusoidal input: Simulink simulation

    12. Integrating Systems Liquid storage tank Deviation model Laplace domain Step response Integrating systems do not have a steady-state gain

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