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Function list
Linear System Representation
Chapter
Function
Implemented
File
Number of Tests
Status
SLICOT functions
Priority (0-2)
Basic Models
tf
yes
@tf/tf.m
zpk
yes
zpk.m
ss
yes
@ss/ss.m
frd
yes
@frd/frd.m
pid
no
pidstd
no
pid2
no
dss
yes
@lti/dss.m
drss
no
filt
yes
filt.m
rss
no
Tunable Models
ltiblock.gain
no
ltiblock.pid
no
ltiblock.pid2
no
ltiblock.ss
no
ltiblock.tf
no
realp
no
AnalysisPoint
no
genss
no
genfrd
no
genmat
no
getLoopTransfer
no
getIOTransfer
no
getSensitivity
no
getCompSensitivity
no
getPoints
no
replaceBlock
no
getValue
no
setValue
no
getBlockValue
no
setBlockValue
no
showBlockValue
no
showTunable
no
nblocks
no
getLFTModel
no
Model with Time Delays
pade
no
absorbDelay
no
thiran
yes
thiran.m
hasdelay
no
hasInternalDelay
no
totaldelay
no
delayss
no
setDelayModel
no
getDelayModel
no
Model Attributes
get
yes
@iddata/get.m
set
yes
@iddata/set.m
tfdata
yes
@lti/tfdata.m
zpkdata
yes
@lti/zpkdata.m
ssdata
yes
@lti/ssdata.m
frdata
yes
@lti/frdata.m
piddata
no
pidstddata
no
piddata2
no
pidstddata2
no
dssdata
yes
@lti/dssdata.m
chgFreqUnit
no
chgTimeUnit
no
isct
yes
@lti/isct.m
isdt
yes
@lti/isdt.m
isempty
yes
built-in function
isfinite
yes
built-in function
isParametric
no
isproper
no
isreal
yes
built-in function
isiso
no
isstable
yes
@lti/isstable.m
isstatic
no
order
no
ndims
yes
built-in function
size
yes
built-in function
Model Arrays
stack
no
nmodels
no
permute
yes
built-in function
reshape
yes
built-in function
repsys
yes
repsys.m
Model Interconnection
Function
Implemented
File
Number of Tests
Status
SLICOT functions
Priority
feedback
yes
@lti/feedback.m
connect
yes
@lti/connect.m
sumblk
yes
sumblk.m
series
no
parallel
no
append
yes
append.m
blkdiag
yes
@lti/blkdiag.m
imp2exp
no
inv
yes
built-in function
lft
no
connectOptions
no
Model Transformation
Chapter
Function
Implemented
File
Number of Tests
Status
SLICOT functions
Priority
Model Type Conversion
pidstd2
no
make1DOF
no
make2DOF
no
getComponents
no
Continuous-Discrete Conversion
c2d
yes
@lti/c2d.m
d2c
yes
@lti/d2c.m
d2d
yes
@lti/d2d.m
upsample
no
c2dOptions
no
d2cOptions
no
d2dOptions
no
Model Simplification
hsvd
yes
hsvd.m
hsvplot
no
sminreal
yes
@lti/sminreal.m
balred
no
minreal
yes
@lti/minreal.m
balreal
no
modred
no
balredOptions
no
hsvdOptions
no
State-Coordinate Transformation
canon
no
prescale
yes
@lti/prescale.m
ss2ss
no
xperm
yes
@lti/xperm.m
Modal Decomposition
modsep
no
stabsep
no
freqsep
no
stabsepOptions
no
freqsepOptions
no
Linear Analysis
Chapter
Function
Implemented
File
Number of Tests
Status
SLICOT functions
Priority
Time-Domain Analysis
linearSystemAnalyzer
no
impulseplot
no
initialplot
no
lsimplot
no
stepplot
no
covar
yes
covar.m
impulse
yes
impulse.m
initial
yes
initial.m
lsim
yes
lsim.m
step
yes
step.m
lsiminfo
no
stepinfo
no
stepDataOptions
no
Frequency-Domain Analysis
bodeplot
no
nicholsplot
no
nyquistplot
no
sigmaplot
no
bode
yes
bode.m
nichols
yes
nichols.m
nyquist
yes
nyquist.m
sigma
yes
sigma.m
evalfr
no
freqresp
yes
@lti/freqresp.m
bandwidth
yes
built-in function
dcgain
yes
@lti/dcgain.m
getGainCrossover
no
getPeakGain
no
Stability Analysis
pole
yes
@lti/pole.m
zero
yes
@lti/zero.m
damp
no
dsort
no
esort
no
tzero
no
pzplot
no
iopzplot
no
allmargin
no
margin
yes
margin.m
Plot Customization
bodeoptions
no
hsvoptions
no
nicholsoptions
no
nyquistoptions
no
pzoptions
no
sigmaoptions
no
timeoptions
no
setoptions
no
getoptions
no
ctrlpref
no
updateSystem
no
Control Design
Chapter
Function
Implemented
File
Status
SLICOT functions
Priority
PID Controller Tuning
pidTuner
no
pidtune
no
pidtuneOptions
no
SISO Feedback Loops
rlocus
yes
rlocus.m
rlocusplot
no
controlSystemDesigner
no
sisoinit
no
Linear-Quadratic-Gaussian Control
lqr
yes
lqr.m
lqry
no
lqi
no
dlqr
yes
dlqr.m
lqrd
no
kalman
yes
kalman.m
kalmd
no
lqg
no
lqgreg
no
lqgtrack
no
augstate
no
norm
yes
@lti/norm.m
Pole Placement
estim
yes
estim.m
place
yes
place.m
reg
no
Matrix Computations
Function
Implemented
File
Status
SLICOT functions
Priority
lyap
yes
lyap.m
lyapchol
yes
lyapchol.m
dlyap
yes
dlyap.m
dlyapchol
yes
dlyapchol.m
care
yes
care.m
dare
yes
dare.m
gcare
no
gdare
no
ctrb
yes
ctrb.m
obsv
yes
obsv.m
ctrbf
yes
ctrbf.m
obsvf
yes
obsvf.m
gram
yes
gram.m
bdschur
no
Some very basic examples
PT1/low-pass filter step response
Code: Creating a transfer function and plotting its response
T1 = 0.4 ; # time constant
P = tf ([ 1 ], [ T1 1 ]) # create transfer function model
step ( P , 2 ) # plot step response
#add some common markers like the tangent line at the origin, which crosses lim(n->inf) f(t) at t=T1
hold on
plot ([ 0 T1 ], [ 0 1 ], "g" )
plot ([ T1 T1 ], [ 0 1 ], "k" )
plot ([ 0 T1 ], [ 1 - 1 / e 1 - 1 / e ], "m" )
hold off
Try also bode(P)!
(a first order low-pass filter has -3db magnitude at f=1/T1)