You could start with this:
help tf
TF Construct transfer function or convert to transfer function.
Construction:
SYS = TF(NUM,DEN) creates a continuous-time transfer function SYS with
numerator NUM and denominator DEN. SYS is an object of type TF when
NUM,DEN are numeric arrays, of type GENSS when NUM,DEN depend on tunable
parameters (see REALP and GENMAT), and of type USS when NUM,DEN are
uncertain (requires Robust Control Toolbox).
SYS = TF(NUM,DEN,TS) creates a discrete-time transfer function with
sample time TS (set TS=-1 if the sample time is undetermined).
S = TF('s') specifies the transfer function H(s) = s (Laplace variable).
Z = TF('z',TS) specifies H(z) = z with sample time TS.
You can then specify transfer functions directly as expressions in S
or Z, for example,
s = tf('s'); H = exp(-s)*(s+1)/(s^2+3*s+1)
SYS = TF creates an empty TF object.
SYS = TF(M) specifies a static gain matrix M.
You can set additional model properties by using name/value pairs.
For example,
sys = tf(1,[1 2 5],0.1,'Variable','q','IODelay',3)
also sets the variable and transport delay. Type "properties(tf)"
for a complete list of model properties, and type
help tf.<PropertyName>
for help on a particular property. For example, "help tf.Variable"
provides information about the "Variable" property.
By default, transfer functions are displayed as functions of 's' or 'z'.
Alternatively, you can use the variable 'p' in continuous time and the
variables 'z^-1', 'q', or 'q^-1' in discrete time by modifying the
"Variable" property.
Data format:
For SISO models, NUM and DEN are row vectors listing the numerator
and denominator coefficients in descending powers of s,p,z,q or in
ascending powers of z^-1 (DSP convention). For example,
sys = tf([1 2],[1 0 10])
specifies the transfer function (s+2)/(s^2+10) while
sys = tf([1 2],[1 5 10],0.1,'Variable','z^-1')
specifies (1 + 2 z^-1)/(1 + 5 z^-1 + 10 z^-2).
For MIMO models with NY outputs and NU inputs, NUM and DEN are
NY-by-NU cell arrays of row vectors where NUM{i,j} and DEN{i,j}
specify the transfer function from input j to output i. For example,
H = tf( {-5 ; [1 -5 6]} , {[1 -1] ; [1 1 0]})
specifies the two-output, one-input transfer function
[ -5 /(s-1) ]
[ (s^2-5s+6)/(s^2+s) ]
Arrays of transfer functions:
You can create arrays of transfer functions by using ND cell arrays
for NUM and DEN above. For example, if NUM and DEN are cell arrays
of size [NY NU 3 4], then
SYS = TF(NUM,DEN)
creates the 3-by-4 array of transfer functions
SYS(:,:,k,m) = TF(NUM(:,:,k,m),DEN(:,:,k,m)), k=1:3, m=1:4.
Each of these transfer functions has NY outputs and NU inputs.
To pre-allocate an array of zero transfer functions with NY outputs
and NU inputs, use the syntax
SYS = TF(ZEROS([NY NU k1 k2...])) .
Conversion:
SYS = TF(SYS) converts any dynamic system SYS to the transfer function
representation. The resulting SYS is always of class TF.
See also TF/EXP, FILT, TFDATA, ZPK, SS, FRD, GENSS, USS, DYNAMICSYSTEM.
Documentation for tf
doc tf
Other uses of tf
control/tf DynamicSystem/tf rffilter.rffilter/tf
dsp.AllpassFilter/tf idParametric/tf signal/tf
dsp.Channelizer/tf mpc/tf StaticModel/tf
dsp.NotchPeakFilter/tf
help rlocfind
RLOCFIND Find root locus gains for a given set of roots.
[K,POLES] = RLOCFIND(SYS) is used for interactive gain
selection from the root locus plot of the SISO system SYS
generated by RLOCUS. RLOCFIND puts up a crosshair cursor
in the graphics window which is used to select a pole location
on an existing root locus. The root locus gain associated
with this point is returned in K and all the system poles for
this gain are returned in POLES.
[K,POLES] = RLOCFIND(SYS,P) takes a vector P of desired root
locations and computes a root locus gain for each of these
locations (i.e., a gain for which one of the closed-loop roots
is near the desired location). The j-th entry of the vector K
gives the computed gain for the location P(j), and the j-th
column of the matrix POLES lists the resulting closed-loop poles.
See also RLOCUS.
Other uses of rlocfind
DynamicSystem/rlocfind
