Control theory

Block diagram manipulations
Compatibility
Controller design
Data structure access
Frequency domain analysis
Internal
Miscellaneous
Numerical functions
OCST demos
Obsolete
System display functions
System interface functions
System properties
Time domain analysis
System Identification

Block diagram manipulations

: Octave Controls toolbox demo: Block Diagram Manipulations demo
: Form an arbitrary complex (open or closed loop) system in state-space form from several systems.
: Filter the output of sys1 through sys2 and subtract it from the input.
: Creates linearized state space model of a Boeing 707-321 aircraft at v=80m/s.
: Creates a continuous 2nd order system with parameters: *Inputs*
: Forms the parallel connection of two systems.
: Redheffer star product or upper/lower LFT, respectively.
: returns SYS = GSYS + HSYS.
: appends new inputs and/or outputs to a system
: Close the loop from specified outputs to respective specified inputs
: Extract the purely continuous subsystem of an input system.
: *Inputs* SYS = system data structure
: Duplicate specified input/output connections of a system
: Combines two systems into a single system
: return a minimal (or reduced order) system inputs: sys: system data structure flg: 0 [default] return minimal system; state names lost : 1 return system with physical states removed that are either uncontrollable or unobservable (cannot reduce further without discarding physical meaning of states) outputs: retsys: returned system nc: number of controllable states in the returned system no: number of observable states in the returned system cflg: is_controllable(retsys) oflg: is_observable(retsys)
: Compute sys = Asys*Bsys (series connection):
: Extract specified inputs/outputs from a system
: *Inputs* VLEN=vector length, LIST= a subset of `[1:vlen]',
: scale inputs/outputs of a system.
: Return sys = Gsys - Hsys.
: Creates a system with unity gain, no states.
: State space description of a first order weighting function.

Compatibility

: use sysappend
: Connect hosts and return sockets.
: use tf2sys
: use !is_digital
: use is_digital
: use is_siso
: use lqe
: use dlqe or dkalman
: use starp
: use h2norm, hinfnorm or zgrownorm
: use ss2sys
: use sys2ss
: use tf2sys
: use sys2tf
: use tzero or tzero2
: use zp2sys
: use sys2zp

Controller design

: Octave Controls toolbox demo: H2/Hinfinity options demos
: Demonstrate the functions available for designining a discrete H_infinity controller.
: Construct the linear quadratic estimator (Kalman predictor) for the discrete time system
: Construct the linear quadratic estimator (Kalman filter) for the discrete time system
: Construct the linear quadratic regulator for the discrete time system
: Design H2 optimal controller per procedure in Doyle, Glover, Khargonekar, Francis, "State Space Solutions to Standard H2 and Hinf Control Problems", IEEE TAC August 1989
: H_infinity design demos for continuous SISO and MIMO systems and a discrete system.
: *Inputs* input system is passed as either
: Called by `hinfsyn' to see if gain G satisfies conditions in Theorem 3 of Doyle, Glover, Khargonekar, Francis, "State Space Solutions to Standard H2 and Hinf Control Problems", IEEE TAC August 1989
: Forms
: Called by `hinfsyn' to compute the H_inf optimal controller.
: Construct the linear quadratic estimator (Kalman filter) for the continuous time system
: Design a linear-quadratic-gaussian optimal controller for the system
: construct the linear quadratic regulator for the continuous time system
: Produce output for a linear simulation of a system
: Computes the matrix K such that if the state is feedback with gain K, then the eigenvalues of the closed loop system (i.e.

Data structure access

: Determines the type of system matrix.
: This function changes the sampling time (tsam) of the system.
: return the number of states, inputs, and/or outputs in the system SYS.
: Get signal names from a system
: Return the sampling time of the system SYS.
: return the initial system type of the system
: change the names of selected inputs, outputs and states.
: Update the internal representation of a system.

Frequency domain analysis

: If no output arguments are given: produce Bode plots of a system; otherwise, compute the frequency response of a system data structure
: Get default range of frequencies based on cutoff frequencies of system poles and zeros.
: Octave Controls toolbox demo: Frequency Response demo
: Used by `__freqresp__' to check that input frequency vector W is valid.
: Linear time invariant frequency response of single input systems *Inputs*
: Produce Nichols plot of a system.
: Produce Nyquist plots of a system; if no output arguments are given, Nyquist plot is printed to the screen.
: [rldata, k] = rlocus(sys[,increment,min_k,max_k]) Displays root locus plot of the specified SISO system.
: Compute transmission zeros of a continuous
: Compute the transmission zeros of a, b, c, d.

Internal

: Used internally in `abcddim'.
: used internally by bode, nyquist; compute system frequency response.
: Frequency response function - used internally by `bode', `nyquist'.
: Prints an enumerated list of strings.
: Impulse or step response for a linear system.
: used internally in syschnames item olist: index list old_names: original list names inames: new names listname: name of index list
: Used internally in syscont and sysdisc.
: return default input or output names given N, STR, M.
: return default state names given N, NZ
: Locate and mark duplicate names inputs: names: list of signal names kind: kind of signal name (used for diagnostic message purposes only) outputs: returns names with unique suffixes added; diagnostic warning message is printed to inform the user of the new signal name
: used internally in tf2sys.
: used internally in `tzero'; minimal argument checking performed
: Used internally in `zp2ss' Extract 2 values from RVALS (if possible) and construct a polynomial with those roots.

Miscellaneous

: determine axis limits for 2-d data(column vectors); leaves a 10% margin around the plots.
: Return indices of string entries in LISTVAR that match strings in STRLIST.
: no description
: function prompt([str])
: short script used in demos
: [yy,idx] = sortcom(xx[,opt]): sort a complex vector
: Append string SUFFIX to each string in the list STRLIST.
: [a1,b1] = swap(a,b)
: Return indices of signals with specified signal names inputs given a system data structure SYS, a signal type to be selected SIGTYPE (`"in"', `"out"', `"st"'), and a list of desired signal names SIGNAMELIST.

Numerical functions

: Solve the algebraic Riccati equation
: Return the solution, X of the discrete-time algebraic Riccati equation
: Return controllability grammian of discrete time system
: Solve the discrete-time Lyapunov equation
: Solve the differential Riccati equation
: Return controllability grammian M of the continuous time system dx/dt = a x + b u.
: Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart algorithm (Communications of the ACM, 1972).
: Return the pseudoinverse of X.
: Compute product of zgep incidence matrix F with vector X.
: Solve system of equations for dense zgep problem.
: Construct right hand side vector zz for the zero-computation generalized eigenvalue problem balancing procedure.
: Implementation of procedure REDUCE in (Emami-Naeini and Van Dooren, Automatica, # 1982).
: Return NONZ = number of rows of MAT whose two norm exceeds MEPS, and ZER = number of rows of mat whose two norm is less than MEPS.
: Generalized conjugate gradient iteration to solve zero-computation generalized eigenvalue problem balancing equation fx=z; called by `zgepbal'
: Apply givens rotation c,s to row vectors A, B.
: apply householder vector based on e^(m) to (column vector) y.

OCST demos

: Octave Controls toolbox demo: State Space analysis demo
: Octave Controls toolbox demo: Block Diagram Manipulations demo
: Controls toolbox demo.
: Octave Control Systems Toolbox demo/tutorial program.
: Octave Controls toolbox demo: H2/Hinfinity options demos
: Demonstrate the functions available for designining a discrete H_infinity controller.
: Octave Controls toolbox demo: Frequency Response demo
: H_infinity design demos for continuous SISO and MIMO systems and a discrete system.
: Creates linearized state space model of a Boeing 707-321 aircraft at v=80m/s.
: Octave Controls toolbox demo: Model Manipulations demo
: Octave Controls toolbox demo: Root Locus demo
: Tutorial for the use of the system data structure functions.

Obsolete

: Remove trailing blank entries and all zero entries from the string s.
: O B S O L E T E * * * D O N O T U S E!
: Determines the type of system matrix.
: O B S O L E T E: use ss2sys instead.
: Compute generalized eigenvalues of the matrix pencil (A - lambda B).
: givens rotation calculation
: Forms the series connection of two systems.
: function B = swapcols(A)
: function B = swaprows(A)
: Superseded by `syssetsignals'
: Obsolete.

System display functions

: Write formatted polynomial
: print out a system data structure in desired format
: Print formatted transfer function n(s)/d(s) to the screen.
: print formatted zero-pole form to the screen.

System interface functions

: construct a system data structure from FIR description
: Create system structure from state-space data.
: [num,den] = ss2tf(a,b,c,d) Conversion from tranfer function to state-space.
: Converts a state space representation to a set of poles and zeros.
: Extract FIR data from system data structure; see fir2sys for parameter descriptions.
: Extract state space representation from system data structure.
: Extract transfer function data from a system data structure
: Extract zero/pole/leading coefficient information from a system data structure
: Tutorial for the use of the system data structure functions.
: Conversion from tranfer function to state-space.
: build system data structure from transfer function format data
: Converts transfer functions to poles / zeros.
: Conversion from zero / pole to state space.
: Create system data structure from zero-pole data.
: Converts zeros / poles to a transfer function.

System properties

: Check for compatibility of the dimensions of the matrices defining the linear system [A, B, C, D] corresponding to
: Octave Controls toolbox demo: State Space analysis demo
: Build controllability matrix
: Computes the H2 norm of a system data structure (continuous time only)
: Computes the H infinity norm of a system data structure.
: Returns RETVAL = 1 if the dimensions of A, B, C, D are compatible, otherwise RETVAL = 0 with an appropriate diagnostic message printed to the screen.
: Logical check for system controllability.
: Test for detactability (observability of unstable modes) of (A,C).
: Determine whether a continuous time state space system meets assumptions of DGKF algorithm.
: Return nonzero if system is digital; inputs: sys: system data structure eflg: 0 [default] exit with an error if system is mixed (continuous and discrete components) : 1 print a warning if system is mixed (continuous and discrete) : 2 silent operation outputs: DIGITAL: 0: system is purely continuous : 1: system is purely discrete : -1: system is mixed continuous and discrete Exits with an error of sys is a mixed (continuous and discrete) system
: Logical check for system observability.
: Return true if TS is a valid sampling time (real,scalar, > 0)
: Return true if MYLIST is a list of individual strings.
: return nonzero if the system data structure SYS is single-input, single-output.
: Logical check for system stabilizability (i.e., all unstable modes are controllable).
: Returns 1 if the matrix A or the system SYS is stable, or 0 if not.
: Build observability matrix
: Plots the zeros and poles of a system in the complex plane.

Time domain analysis

: *Inputs*
: Convert discrete (sub)system to a purely continuous system.
: Displays eigenvalues, natural frequencies and damping ratios of the eigenvalues of a matrix P or the A-matrix of a system P, respectively.
: Returns dc-gain matrix.
: convert a multirate digital system to a single rate digital system states specified by IDX, SPREFIX are sampled at TS2, all others are assumed sampled at TS1 = `sysgettsam (SYS)'.
: Impulse response for a linear system.
: Step response for a linear system.

System Indentification

: Plot inputs and ouputs defined by the system z.
: Simulate the effects of the MISO system defined by th.
: Create a theta structure from the IIR system Ay = Bx.
: Represent the generalized Multi-Input, Single-Output (MISO) system