control

control

4.0.0 2024-01-04

Control package for GNU Octave including system analysis and control synthesis. The package uses routines of the SLICOT-Reference library.

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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)'.
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.
lqr Linear-quadratic regulator.

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.