A Control Systems Toolbox for Julia
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mfalt Merge pull request #164 from JuliaControl/fixfeedback
Fixed feedback and added Polynomial constructors for simpler code
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A control systems design toolbox for Julia.


To install, in the Julia REPL:




Support for Julia 0.7/1.0 added.


  • LTISystem types are now more generic and can hold matrices/vectors of arbitrary type. Examples (partly pseudo-code):

Similar for tf,zpk etc.

  • Continuous time systems are simulated with continuous time solvers from OrdinaryDiffEq.jl
  • Freqresp now returns frequencies in the first dimension.
  • Breaking: lsim(sys, u::Function) syntax has changed from u(t,x) to u(x,t) to be consistent with OrdinaryDiffEq
  • Breaking: feedback(P,C) no longer returns feedback(P*C). The behavior is changed to feedback(P1, P2) = P1/(1+P1*P2).
  • Type Simulator provides lower level interface to continuous time simulation.
  • Example autodiff.jl provides an illustration of how the new generic types can be used for automatic differentiation of a cost function through the continuous-time solver, which allows for optimization of the cost function w.r.t. PID parameters.


All functions have docstrings, which can be viewed from the REPL, using for example ?tf .

A documentation website under developement is available at http://juliacontrol.github.io/ControlSystems.jl/latest/.

Some of the available commands are:

Constructing systems

ss, tf, zpk, ss2tf


pole, tzero, norm, norminf, ctrb, obsv, gangoffour, margin, markovparam, damp, dampreport, zpkdata, dcgain, covar, gram, sigma, sisomargin


care, dare, dlyap, lqr, dlqr, place, pid, leadlink, laglink, leadlinkat, rstd, rstc, dab

Time and Frequency response

step, impulse, lsim, freqresp, evalfr, bode, nyquist


lsimplot, stepplot, impulseplot, bodeplot, nyquistplot, sigmaplot, marginplot, gangoffourplot, pidplots, pzmap, nicholsplot, pidplots, rlocus, leadlinkcurve


minreal, sminreal, c2d


This toolbox works similar to that of other major computer-aided control systems design (CACSD) toolboxes. Systems can be created in either a transfer function or a state space representation. These systems can then be combined into larger architectures, simulated in both time and frequency domain, and analyzed for stability/performance properties.


Here we create a simple position controller for an electric motor with an inertial load.

using ControlSystems

# Motor parameters
J = 2.0
b = 0.04
K = 1.0
R = 0.08
L = 1e-4

# Create the model transfer function
s = tf("s")
P = K/(s*((J*s + b)*(L*s + R) + K^2))
# This generates the system
# TransferFunction:
#                1.0
# ---------------------------------
# 0.0002s^3 + 0.160004s^2 + 1.0032s
#Continuous-time transfer function model

# Create an array of closed loop systems for different values of Kp
CLs = TransferFunction[kp*P/(1 + kp*P) for kp = [1, 5, 15]];

# Plot the step response of the controllers
# Any keyword arguments supported in Plots.jl can be supplied
stepplot(CLs, label=["Kp = 1", "Kp = 5", "Kp = 15"])