Select Category: Examples Linear Time Invariant Models Model Data Access Model Conversions Model Interconnections Model Characteristics Model Simplification Time Domain Analysis Frequency Domain Analysis Pole Placement Optimal Control Robust Control Matrix Equation Solvers Model Reduction Controller Reduction Experimental Data Handling System Identification Overloaded LTI Operators Overloaded IDDATA Operators Miscellaneous

Examples

MDSSystem	Run the example for robust control of a mass-damper-spring system.
optiPID	Numerical optimization of a PID controller using an objective function.
Anderson	Frequency-weighted coprime factorization controller reduction [1].
Madievski	Demonstration of frequency-weighted controller reduction.
VLFamp	Calculations on a two stage preamp for a multi-turn, air-core solenoid loop antenna for the reception of signals below 30kHz.

Linear Time Invariant Models

dss	Create or convert to descriptor state-space model.
filt	Create discrete-time transfer function model from data in DSP format.
frd	Create or convert to frequency response data.
ss	Create or convert to state-space model.
tf	Create or convert to transfer function model.
zpk	Create transfer function model from zero-pole-gain data.

Model Data Access

@lti/dssdata	Access descriptor state-space model data.
@lti/filtdata	Access discrete-time transfer function data in DSP format.
@lti/frdata	Access frequency response data.
@lti/get	Access key values of LTI objects.
@lti/set	Set or modify properties of LTI objects.
@lti/ssdata	Access state-space model data.
@lti/tfdata	Access transfer function data.
@lti/zpkdata	Access zero-pole-gain data.

Model Conversions

@lti/c2d	Convert the continuous LTI model into its discrete-time equivalent.
@lti/d2c	Convert the discrete LTI model into its continuous-time equivalent.
@lti/d2d	Resample discrete-time LTI model to sampling time TSAM.
@lti/prescale	Scale state-space model.
@lti/xperm	Reorder states in state-space models.
@ss/ss2ss	Applies the similarity transformation T to a state-space model

Model Interconnections

append	Group LTI models by appending their inputs and outputs.
@lti/blkdiag	Block-diagonal concatenation of LTI models.
@lti/connect	Name-based or index-based interconnections between the inputs and outputs of LTI models.
@lti/feedback	Feedback connection of two LTI models.
@lti/lft	Linear fractional tranformation, also known as Redheffer star product.
@lti/mconnect	Arbitrary interconnections between the inputs and outputs of an LTI model.
@lti/parallel	Parallel connection of two LTI systems.
@lti/series	Series connection of two LTI models.
sumblk	Create summing junction S from string FORMULA for name-based interconnections.

Model Characteristics

ctrb	Return controllability matrix.
ctrbf	If Co=ctrb(A,B) has rank r <= n = SIZE(A,1), then there is a similarity transformation Tc such that Tc = [t1 t2] where t1 is the controllable subspace and t2 is orthogonal to t1
damp	Calculate natural frequencies, damping ratios and poles.
dsort	Sort discrete-time poles by magnitude (in decreasing order).
esort	Sort continuous-time poles by real part (in decreasing order).
@lti/dcgain	Compute the DC gain of LTI system.
gram	'gram (SYS, "c")' returns the controllability gramian of the (continuous- or discrete-time) system SYS. 'gram (SYS, "o")' returns the observability gramian of the (continuous- or discrete-time) system SYS. 'gram (A, B)' returns the con...
hsvd	Hankel singular values of the stable part of an LTI model.
@lti/isct	Determine whether LTI model is a continuous-time system.
isctrb	Logical check for system controllability.
isdetectable	Logical test for system detectability.
@lti/isdt	Determine whether LTI model is a discrete-time system.
@lti/isminimumphase	Determine whether LTI system has asymptotically stable zero dynamics.
isobsv	Logical check for system observability.
@lti/issiso	Determine whether LTI model is single-input/single-output (SISO).
isstabilizable	Logical check for system stabilizability.
@lti/isstable	Determine whether LTI system is stable.
@lti/norm	Return H-2 or L-inf norm of LTI model.
obsv	Return observability matrix.
obsvf	If Ob=obsv(A,C) has rank r <= n = SIZE(A,1), then there is a similarity transformation Tc such that To = [t1;t2] where t1 is c and t2 is orthogonal to t1
@lti/pole	Compute poles of LTI system.
pzmap	Plot the poles and zeros of an LTI system in the complex plane.
@lti/size	LTI model size, i.e. number of outputs and inputs.
@lti/zero	Compute zeros and gain of LTI model.

Model Simplification

@lti/minreal	Minimal realization or zero-pole cancellation of LTI models.
@lti/sminreal	Perform state-space model reduction based on structure.

Time Domain Analysis

covar	Return the steady-state covariance.
gensig	Generate periodic signal.
impulse	Impulse response of LTI system.
imp_invar	Converts analog filter with coefficients B and A and/or SYS_IN to digital, conserving impulse response.
initial	Initial condition response of state-space model.
lsim	Simulate LTI model response to arbitrary inputs.
ramp	Ramp response of LTI system.
step	Step response of LTI system.

Frequency Domain Analysis

bode	Bode diagram of frequency response.
bodemag	Bode magnitude diagram of frequency response.
@lti/freqresp	Evaluate frequency response at given frequencies.
margin	Gain and phase margin of a system.
nichols	Nichols chart of frequency response.
nyquist	Nyquist diagram of frequency response.
sensitivity	Return sensitivity margin MS.
sgrid	Display an grid in the complex s-plane.
sigma	Singular values of frequency response.
zgrid	Display an grid in the complex z-plane.

Pole Placement

acker	Calculates the state feedback matrix of a completely controllable SISO system using Ackermann's formula
place	Pole assignment for a given matrix pair (A,B) such that 'p = eig (A-B*F)'.
reg	Form regulator from state-feedback and estimator gains
rlocus	Display root locus plot of the specified SISO system.
rlocusx	Interactive root locus plot of the specified SISO system SYS.

Optimal Control

augstate	Append state vector x of system SYS to output vector y.
dlqe	Kalman filter for discrete-time systems.
dlqr	Linear-quadratic regulator for discrete-time systems.
estim	Return state estimator for a given estimator gain.
kalman	Design Kalman estimator for LTI systems.
lqe	Kalman filter for continuous-time systems.
lqg	Linear-quadratic gaussian (LQG) design
lqgreg	Form LQG regulator
lqgtrack	Form LQG servo controller
lqi	Linear-quadratic integral control.
lqr	Linear-quadratic regulator.
lqry	Linear-quadratic regulator with output weighting.

Robust Control

augw	Extend plant for stacked S/KS/T problem.
fitfrd	Fit frequency response data with a state-space system.
h2syn	H-2 control synthesis for LTI plant.
hinfsyn	H-infinity control synthesis for LTI plant.
mixsyn	Solve stacked S/KS/T H-infinity problem.
mktito	Partition LTI plant P for robust controller synthesis.
ncfsyn	Loop shaping H-infinity synthesis.

Matrix Equation Solvers

care	Solve continuous-time algebraic Riccati equation (ARE).
dare	Solve discrete-time algebraic Riccati equation (ARE).
dlyap	Solve discrete-time Lyapunov or Sylvester equations.
dlyapchol	Compute Cholesky factor of discrete-time Lyapunov equations.
lyap	Solve continuous-time Lyapunov or Sylvester equations.
lyapchol	Compute Cholesky factor of continuous-time Lyapunov equations.

Model Reduction

bstmodred	Model order reduction by Balanced Stochastic Truncation (BST) method.
btamodred	Model order reduction by frequency weighted Balanced Truncation Approximation (BTA) method.
hnamodred	Model order reduction by frequency weighted optimal Hankel-norm (HNA) method.
spamodred	Model order reduction by frequency weighted Singular Perturbation Approximation (SPA).

Controller Reduction

btaconred	Controller reduction by frequency-weighted Balanced Truncation Approximation (BTA).
cfconred	Reduction of state-feedback-observer based controller by coprime factorization (CF).
fwcfconred	Reduction of state-feedback-observer based controller by frequency-weighted coprime factorization (FW CF).
spaconred	Controller reduction by frequency-weighted Singular Perturbation Approximation (SPA).

Experimental Data Handling

iddata	Create identification dataset of output and input signals.
@iddata/cat	Concatenate iddata sets along dimension DIM.
@iddata/detrend	Detrend outputs and inputs of dataset DAT by removing the best fit of a polynomial of order ORD.
@iddata/diff	Return K-th difference of outputs and inputs of dataset DAT.
@iddata/fft	Transform iddata objects from time to frequency domain using a Fast Fourier Transform (FFT) algorithm.
@iddata/filter	Filter output and input signals of dataset DAT.
@iddata/get	Access key values of iddata objects.
@iddata/ifft	Transform iddata objects from frequency to time domain.
@iddata/merge	Concatenate experiments of iddata datasets.
@iddata/nkshift	Shift input channels of dataset DAT according to integer NK.
@iddata/plot	Plot signals of iddata identification datasets on the screen.
@iddata/resample	Change the sample rate of the output and input signals in dataset DAT by a factor of 'p/q'.
@iddata/set	Set or modify keys of iddata objects.
@iddata/size	Return dimensions of iddata set DAT.

System Identification

arx	Estimate ARX model using QR factorization.
moen4	Estimate state-space model using combined subspace method: MOESP algorithm for finding the matrices A and C, and N4SID algorithm for finding the matrices B and D.
moesp	Estimate state-space model using MOESP algorithm.
n4sid	Estimate state-space model using N4SID algorithm.

Overloaded LTI Operators

@lti/ctranspose	Conjugate transpose or pertransposition of LTI objects.
@lti/end	End indexing for LTI objects.
@lti/horzcat	Horizontal concatenation of LTI objects.
@lti/inv	Inversion of LTI objects.
@lti/minus	Binary subtraction of LTI objects.
@lti/mldivide	Matrix left division of LTI objects.
@lti/mpower	Matrix power of LTI objects.
@lti/mrdivide	Matrix right division of LTI objects.
@lti/mtimes	Matrix multiplication of LTI objects.
@lti/plus	Binary addition of LTI objects.
@lti/repmat	Form a block transfer matrix of SYS with M copies vertically and N copies horizontally.
@lti/subsasgn	Subscripted assignment for LTI objects.
@lti/subsref	Subscripted reference for LTI objects.
@lti/times	Hadamard/Schur product of transfer function matrices.
@lti/transpose	Transpose of LTI objects.
@lti/uminus	Unary minus of LTI object.
@lti/uplus	Unary plus of LTI object.
@lti/vertcat	Vertical concatenation of LTI objects.

Overloaded IDDATA Operators

@iddata/end	End indexing for IDDATA objects.
@iddata/horzcat	Horizontal concatenation of iddata datasets.
@iddata/subsasgn	Subscripted assignment for iddata objects.
@iddata/subsref	Subscripted reference for iddata objects.
@iddata/vertcat	Vertical concatenation of iddata datasets.

Miscellaneous

@ss/display	Display routine for SS objects.
db2mag	Convert Decibels (dB) to Magnitude.
doc_control	Open online documentation of the Control package in the system's standard browser.
mag2db	Convert Magnitude to Decibels (dB).
options	Create options struct OPT from a number of key and value pairs.
pid	Return the transfer function C of the PID controller in parallel form with first-order roll-off.
pidstd	Return the transfer function C of the PID controller in standard form with first-order roll-off.
repsys	Form a block transfer matrix of SYS with M copies vertically and N copies horizontally.
strseq	Return a cell vector of indexed strings by appending the indices IDX to the string STR.
test_control	Execute all available tests at once.
thiran	Approximation of continuous-time delay using a discrete-time allpass Thiran filter.
BMWengine	Model of the BMW 4-cylinder engine at ETH Zurich's control laboratory.
Boeing707	Creates a linearized state-space model of a Boeing 707-321 aircraft at V=80 m/s (M = 0.26, GA0 = -3 deg, ALPHA0 = 4 deg, KAPPA = 50 deg).
WestlandLynx	Model of the Westland Lynx Helicopter about hover.