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Replace time delays by poles at z = 0 or phase shift
sysnd = absorbDelay(sysd)
[sysnd,G]
= absorbDelay(sysd)
sysnd = absorbDelay(sysd) absorbs all time delays of the dynamic system model sysd into the system dynamics or the frequency response data.
For discrete-time models (other than frequency response data models), a delay of k sampling periods is replaced by k poles at z = 0. For continuous-time models (other than frequency response data models), time delays have no exact representation with a finite number of poles and zeros. Therefore, use pade to compute a rational approximation of the time delay.
For frequency response data models in both continuous and discrete time, absorbDelay absorbs all time delays into the frequency response data as a phase shift.
[sysnd,G] = absorbDelay(sysd) returns the matrix G that maps the initial states of the ss model sysd to the initial states of the sysnd.
Create a discrete-time transfer function that has a time delay and absorb the time delay into the system dynamics as poles at z = 0.
z = tf('z',-1); sysd = (-.4*z -.1)/(z^2 + 1.05*z + .08); sysd.InputDelay = 3
These commands produce the result:
Transfer function: -0.4 z - 0.1 z^(-3) * ------------------- z^2 + 1.05 z + 0.08 Sampling time: unspecified
The display of sysd represents the InputDelay as a factor of z^(-3), separate from the system poles that appear in the transfer function denominator.
Absorb the delay into the system dynamics.
sysnd = absorbDelay(sysd)
The display of sysnd shows that the factor of z^(-3) has been absorbed as additional poles in the denominator.
Transfer function: -0.4 z - 0.1 ------------------------- z^5 + 1.05 z^4 + 0.08 z^3 Sampling time: unspecified
Additionally, sysnd has no input delay:
sysnd.InputDelay
ans = 0
Convert "nk" into regular coefficients of a polynomial model.
Consider the discrete-time polynomial model:
m = idpoly(1,[0 0 0 2 3]);
The value of the B polynomial, m.b, has 3 leading zeros. Two of these zeros are treated as input-output delays. Consequently:
sys = tf(m)
creates a transfer function such that the numerator is [0 2 3] and the IO delay is 2. In order to treat the leading zeros as regular B coefficients, use absorbDelay:
m2 = absorbDelay(m); sys2 = tf(m2);
sys2's numerator is [0 0 0 2 3] and IO delay is 0. The model m2 treats the leading zeros as regular coefficients by freeing their values. m2.Structure.b.Free(1:2) is TRUE while m.Structure.b.Free(1:2) is FALSE.
hasdelay | pade | totaldelay