Describing function analysis of relay with hysteresis
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Describing Function analysis of nonlinear systems – Prof Elio USAI – March 2008
Describing Function – Harmonic balance
The armonic balance equation is a necessary condition for the existence of
limit cycles in the nonlinear system
The approximate analysis gives good estimates if the low-pass filter
hypothesis is strongly verified. It is a good tools for engineers
The harmonic balance equation is similar to the characteristic polynomial
function, i.e. it leads to the Nyquist condition for closed-loop stability
The Describing Function is a linear approximation of the static nonlinearity
limited to the first harmonic
( ) ( ) ω
ω ,
1
N
U
G
j
=
−
In most cases the Describing Function is not a function of the frequency and
this simplifies the verification of the harmonic balance equation by means of
the Nyquist plot of the transfer function
Describing Function – Harmonic balance
The armonic balance equation is a necessary condition for the existence of
limit cycles in the nonlinear system
The approximate analysis gives good estimates if the low-pass filter
hypothesis is strongly verified. It is a good tools for engineers
The harmonic balance equation is similar to the characteristic polynomial
function, i.e. it leads to the Nyquist condition for closed-loop stability
The Describing Function is a linear approximation of the static nonlinearity
limited to the first harmonic
( ) ( ) ω
ω ,
1
N
U
G
j
=
−
In most cases the Describing Function is not a function of the frequency and
this simplifies the verification of the harmonic balance equation by means of
the Nyquist plot of the transfer function
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