Zeros and gain of SISO dynamic system
Zeros of Transfer Function
Compute the zeros of the following transfer function:
sys = tf([4.2,0.25,-0.004],[1,9.6,17]); Z = zero(sys)
Z = 2×1 -0.0726 0.0131
Zeros and Gain of Transfer Function
Calculate the zero locations and zero-pole gain of the following transfer function:
sys = tf([4.2,0.25,-0.004],[1,9.6,17]); [z,gain] = zero(sys)
z = 2×1 -0.0726 0.0131
gain = 4.2000
The zero locations are expressed in because the time unit of the transfer function (
H.TimeUnit) is seconds.
Zeros and Gain of Models in an Array
For this example, load a 3-by-1 array of transfer function models.
3x1 array of transfer functions. Each model has 1 outputs and 1 inputs.
Find the zeros and gain values of the models in the array.
[Z, gain] = zero(sys); Z(:,:,1,1)
ans = 0x1 empty double column vector
ans = 1
zero returns an array each for the zeros and the gain values respectively. Here,
gain(:,:,1,1) corresponds to the zero and the gain value of the first model in the array, that is,
sys — Dynamic system
dynamic system model | model array
Dynamic system, specified as a SISO dynamic system model, or an array of
SISO dynamic system models. Dynamic systems that you can use include
continuous-time or discrete-time numeric LTI models such as
tf (Control System Toolbox),
zpk (Control System Toolbox), or
ss (Control System Toolbox) models.
sys is a generalized state-space model
genss or an uncertain state-space model
zero returns the zeros of the
current or nominal value of
sys is an array of models,
returns the zeros of the model corresponding to its subscript
sys. For more
information on model arrays, see Model Arrays (Control System Toolbox).
J1,...,JN — Indices of models in array whose zeros you want to extract
Indices of models in array whose zeros you want to extract, specified as a
positive integer. You can provide as many indices as there are array
sys. For example, if
sys is a 4-by-5 array of dynamic system models, the
following command extracts the zeros for entry (2,3) in the array.
Z = zero(sys,2,3);
Z — Zeros of the dynamic system
column vector | array
Zeros of the dynamic system, returned as a column vector or an array. If
A single model, then
Zis a column vector of zeros of the dynamic system model
A model array, then
Zis an array containing the zeros of each model in
Z is expressed as the reciprocal of the time units
sys.TimeUnit. For example, zero is expressed
in 1/minute if
gain — Zero-pole-gain of the dynamic system
Zero-pole-gain of the dynamic system, returned as a scalar. In other
gain is the value of
the model is written in
zpk (Control System Toolbox) form.
syshas internal delays,
zerosets all internal delays to zero, creating a zero-order Padé approximation. This approximation ensures that the system has a finite number of zeros.
zeroreturns an error if setting internal delays to zero creates singular algebraic loops. To assess the stability of models with internal delays, use
To calculate the transmission zeros of a multi-input, multi-output (MIMO) system, use
tzero(Control System Toolbox).
- Pole and Zero Locations (Control System Toolbox)