Specifications

Model Conversion
2-41
for discrete-time models.
Automatic Conversion
Some algorithms operate only on one type of LTI model. For example, the
algorithm for zero-order-hold discretization with
c2d can only be performedon
state-space models. Similarly, commands like
tfdata expect one particular
type of LTI models (TF). For convenience, such commands automatically
convert LTI models to the appropriate or required model type. For example, in
sys = ss(0,1,1,0)
[num,den] = tfdata(sys)
tfdata first converts the state-space model sys to an equivalent transfer
function in order to return numerator and denominator data.
Note that conversions to state-space models are not uniquely defined. For this
reason, automatic conversions to state space are disabled when the result
depends on the choice of state coordinates, for example, in commands like
initial or kalman.
Caution About Model Conversions
When manipulating or converting LTI models, keep in mind that:
•The three LTI model types TF, ZPK, and SS, are not equally well-suited for
numerical computations. In particular, the accuracy of computations using
high-ordertransferfunctionsis oftenpoor.Therefore,itis oftenpreferableto
workwiththe state-space representation. In addition,itisoften beneficial to
balance and scale state-space models using
ssbal. You get this type of
balancing automatically when you convert any TF or ZPK model to state
space using
ss.
•Conversions to the transfer function representation using
tf may incur a
lossofaccuracy.Asaresult,the transferfunction poles may noticeably differ
from the poles of the original zero-pole-gain or state-space model.
•Conversions to state space are not uniquely defined in the SISOcase, nor are
they guaranteed to produce a minimal realization in the MIMO case. For a
given state-space model
sys,
Hz
()
DCzIA–
()
1–
B+=