Docstoc

s

Document Sample
s Powered By Docstoc
					              Transfer Functions

1.   Transfer functions
2.   Standard process inputs
3.   First-order systems
4.   Simulink example
5.   Integrating systems
                 Transfer Functions
l   The transfer function
    » Represent relation between input U(s) & output Y(s) in the
      Laplace domain
                                     U(s)            Y(s)
    » Usually denoted as G(s)                G(s)
                                     Input           Output
    » Y(s) = G(s)U(s)
                                            Transfer
    » Only applicable to linear models!     function
l   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
           Transfer Function Example
l   Stirred tank heater


l   Steady-state equation:

l   Initial conditions:

l   Subtract steady-state equation
        Transfer Function Example cont.
l   Laplace transform


l   Rearrange noting that T’(0) = 0




l   Definitions




l   Transfer functions – 1st-order system
       Properties of Transfer Functions

l   Additive property
    » Y(s) = G1(s)U1(s)+ G2(s)U2(s)


l   Multiplicative property
    » Y2(s) = G1(s)G2(s)U(s)


l   ODE equivalence
                 Standard Process Inputs
l   Step input




l   Ramp input




l   Rectangular pulse input   l   Sinusoidal input
                   System Order
l   General transfer function


l   System order
    » Order of the denominator polynomial D(s)
    » Generally equal to the number of ODEs from which
      G(s) was derived
l   First-order system


l   Second-order system
                First-Order System
l   Standard form




l   Stirred tank heater




l   Step response
Ramp Response
Sinusoidal Response
       Simulink Example: sininput.mdl

l   First-order system:

l   Sinusoidal input:

l   Simulink simulation
                 Integrating Systems
l   Liquid storage tank


l   Deviation model


l   Laplace domain


l   Step response



    » Integrating systems do not have a steady-state gain

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:0
posted:6/24/2013
language:English
pages:12