Function reference

The Python Control Systems Library control provides common functions for analyzing and designing feedback control systems.

System creation

ss(A, B, C, D[, dt])	Create a state space system.
tf(num, den[, dt])	Create a transfer function system.
frd(d, w)	Construct a frequency response data model
zpk(zeros, poles, gain[, dt])	Create a transfer function from zeros, poles, gain.
rss([states, outputs, inputs, strictly_proper])	Create a stable random state space object.
drss([states, outputs, inputs, strictly_proper])	Create a stable, discrete-time, random state space system
NonlinearIOSystem(updfcn[, outfcn, params])	Nonlinear I/O system.

System interconnections

append(sys1, sys2, [..., sysn])	Group models by appending their inputs and outputs.
connect(sys, Q, inputv, outputv)	Index-based interconnection of an LTI system.
feedback(sys1[, sys2, sign])	Feedback interconnection between two I/O systems.
interconnect(syslist[, connections, ...])	Interconnect a set of input/output systems.
negate(sys)	Return the negative of a system.
parallel(sys1, sys2, [..., sysn])	Return the parallel connection sys1 + sys2 (+ ... + sysn).
series(sys1, sys2, [..., sysn])	Return the series connection (sysn * ... *) sys2 * sys1.

Frequency domain plotting

bode_plot(syslist[, omega, plot, ...])	Bode plot for a system
describing_function_plot(H, F, A[, omega, ...])	Plot a Nyquist plot with a describing function for a nonlinear system.
nyquist_plot(syslist[, omega, plot, ...])	Nyquist plot for a system
gangof4_plot(P, C[, omega])	Plot the "Gang of 4" transfer functions for a system
nichols_plot(sys_list[, omega, grid])	Nichols plot for a system
nichols_grid([cl_mags, cl_phases, ...])	Nichols chart grid

Note: For plotting commands that create multiple axes on the same plot, the individual axes can be retrieved using the axes label (retrieved using the get_label method for the matplotliib axes object). The following labels are currently defined:

• Bode plots: control-bode-magnitude, control-bode-phase

• Gang of 4 plots: control-gangof4-s, control-gangof4-cs, control-gangof4-ps, control-gangof4-t

Time domain simulation

forced_response(sys[, T, U, X0, transpose, ...])	Simulate the output of a linear system.
impulse_response(sys[, T, X0, input, ...])	Compute the impulse response for a linear system.
initial_response(sys[, T, X0, input, ...])	Initial condition response of a linear system
input_output_response(sys, T[, U, X0, ...])	Compute the output response of a system to a given input.
step_response(sys[, T, X0, input, output, ...])	Compute the step response for a linear system.
phase_plot(odefun[, X, Y, scale, X0, T, ...])	Phase plot for 2D dynamical systems

Control system analysis

dcgain(sys)	Return the zero-frequency (or DC) gain of the given system
describing_function(F, A[, num_points, ...])	Numerical compute the describing function of a nonlinear function
frequency_response(sys, omega[, squeeze])	Frequency response of an LTI system at multiple angular frequencies.
get_input_ff_index(sys)	Return the input feedforward passivity (IFP) index for the system.
get_output_fb_index(sys)	Return the output feedback passivity (OFP) index for the system.
ispassive(sys[, ofp_index, ifp_index])	Indicate if a linear time invariant (LTI) system is passive.
margin(sysdata)	Calculate gain and phase margins and associated crossover frequencies
stability_margins(sysdata[, returnall, ...])	Calculate stability margins and associated crossover frequencies.
phase_crossover_frequencies(sys)	Compute frequencies and gains at intersections with real axis in Nyquist plot.
poles(sys)	Compute system poles.
zeros(sys)	Compute system zeros.
pzmap(sys[, plot, grid, title])	Plot a pole/zero map for a linear system.
root_locus(sys[, kvect, xlim, ylim, ...])	Root locus plot
sisotool(sys[, initial_gain, xlim_rlocus, ...])	Sisotool style collection of plots inspired by MATLAB's sisotool.
StateSpace.__call__(x[, squeeze, warn_infinite])	Evaluate system's frequency response at complex frequencies.
TransferFunction.__call__(x[, squeeze, ...])	Evaluate system's transfer function at complex frequencies.

Matrix computations

care(A, B, Q[, R, S, E, stabilizing, ...])	Solves the continuous-time algebraic Riccati equation
ctrb(A, B)	Controllabilty matrix
dare(A, B, Q, R[, S, E, stabilizing, ...])	Solves the discrete-time algebraic Riccati equation
dlyap(A, Q[, C, E, method])	Solves the discrete-time Lyapunov equation
lyap(A, Q[, C, E, method])	Solves the continuous-time Lyapunov equation
obsv(A, C)	Observability matrix
gram(sys, type)	Gramian (controllability or observability)

Control system synthesis

acker(A, B, poles)	Pole placement using Ackermann method
create_statefbk_iosystem(sys, K[, ...])	Create an I/O system using a (full) state feedback controller
dlqr(A, B, Q, R[, N])	Discrete-time linear quadratic regulator design
h2syn(P, nmeas, ncon)	H_2 control synthesis for plant P.
hinfsyn(P, nmeas, ncon)	H_{inf} control synthesis for plant P.
lqr(A, B, Q, R[, N])	Linear quadratic regulator design
mixsyn(g[, w1, w2, w3])	Mixed-sensitivity H-infinity synthesis.
place(A, B, p)	Place closed loop eigenvalues
rootlocus_pid_designer(plant[, gain, sign, ...])	Manual PID controller design based on root locus using Sisotool

Model simplification tools

minreal(sys[, tol, verbose])	Eliminates uncontrollable or unobservable states in state-space models or cancelling pole-zero pairs in transfer functions.
balred(sys, orders[, method, alpha])	Balanced reduced order model of sys of a given order.
hsvd(sys)	Calculate the Hankel singular values.
modred(sys, ELIM[, method])	Model reduction of sys by eliminating the states in ELIM using a given method.
era(YY, m, n, nin, nout, r)	Calculate an ERA model of order r based on the impulse-response data YY.
markov(Y, U[, m, transpose])	Calculate the first m Markov parameters [D CB CAB ...] from input U, output Y.

Nonlinear system support

describing_function(F, A[, num_points, ...])	Numerical compute the describing function of a nonlinear function
find_eqpt(sys, x0[, u0, y0, t, params, iu, ...])	Find the equilibrium point for an input/output system.
linearize(sys, xeq[, ueq, t, params])	Linearize an input/output system at a given state and input.
input_output_response(sys, T[, U, X0, ...])	Compute the output response of a system to a given input.
ss2io(*args, **kwargs)	Create an I/O system from a state space linear system.
summing_junction([inputs, output, ...])	Create a summing junction as an input/output system.
tf2io(sys[, ...])	Convert a transfer function into an I/O system
flatsys.point_to_point(sys, timepts[, x0, ...])	Compute trajectory between an initial and final conditions.

Stochastic system support

correlation(T, X[, Y, squeeze])	Compute the correlation of time signals.
create_estimator_iosystem(sys, QN, RN[, P0, ...])	Create an I/O system implementing a linqear quadratic estimator
dlqe(A, G, C, QN, RN, [, N])	Linear quadratic estimator design (Kalman filter) for discrete-time systems.
lqe(A, G, C, QN, RN, [, NN])	Linear quadratic estimator design (Kalman filter) for continuous-time systems.
white_noise(T, Q[, dt])	Generate a white noise signal with specified intensity.

Utility functions and conversions

augw(g[, w1, w2, w3])	Augment plant for mixed sensitivity problem.
bdschur(a[, condmax, sort])	Block-diagonal Schur decomposition
canonical_form(xsys[, form])	Convert a system into canonical form
damp(sys[, doprint])	Compute natural frequency, damping ratio, and poles of a system
db2mag(db)	Convert a gain in decibels (dB) to a magnitude
isctime(sys[, strict])	Check to see if a system is a continuous-time system
isdtime(sys[, strict])	Check to see if a system is a discrete time system
issiso(sys[, strict])	Check to see if a system is single input, single output
issys(obj)	Return True if an object is a system, otherwise False
mag2db(mag)	Convert a magnitude to decibels (dB)
modal_form(xsys[, condmax, sort])	Convert a system into modal canonical form
observable_form(xsys)	Convert a system into observable canonical form
pade(T[, n, numdeg])	Create a linear system that approximates a delay.
reachable_form(xsys)	Convert a system into reachable canonical form
reset_defaults()	Reset configuration values to their default (initial) values.
sample_system(sysc, Ts[, method, alpha, ...])	Convert a continuous time system to discrete time by sampling
ss2tf(sys)	Transform a state space system to a transfer function.
ssdata(sys)	Return state space data objects for a system
tf2ss(sys)	Transform a transfer function to a state space system.
tfdata(sys)	Return transfer function data objects for a system
timebase(sys[, strict])	Return the timebase for a system
timebaseEqual(sys1, sys2)	Check to see if two systems have the same timebase
unwrap(angle[, period])	Unwrap a phase angle to give a continuous curve
use_fbs_defaults()	Use Feedback Systems (FBS) compatible settings.
use_matlab_defaults()	Use MATLAB compatible configuration settings.
use_numpy_matrix([flag, warn])	Turn on/off use of Numpy matrix class for state space operations.