ControlSystems.jl

A control systems design toolbox for Julia.

Installation

To install, in the Julia REPL:

using Pkg; Pkg.add("ControlSystems")

News

2022-07 v1.0

• Breaking: Frequency-responses have changed data layout to ny×nu×nω from the previous nω×ny×nu. This is for performance reasons and to be consistent with time responses. This affects downstream functions bode and nyquist as well.
• Breaking: baltrunc and balreal now return the diagonal of the Gramian as the second argument rather than the full matrix.
• Breaking: The pid constructor no longer takes parameters as keyword arguments. pid has also gotten some new features, the new signature is pid(P, I, D=0; form = :standard, Ts=nothing, Tf=nothing, state_space=false). This change affects downstream functions like placePI, loopshapingPI, pidplots.
• Breaking: The semantics of broadcasted multiplication between two systems was previously inconsistent between StateSpace and TransferFunction. The new behavior is documented under Multiplying systems in the documentation.

Documentation

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

A documentation website is available at http://juliacontrol.github.io/ControlSystems.jl/latest/ and an introductory video is available here.

Some of the available commands are:

Constructing systems

ss, tf, zpk, delay

Analysis

poles, tzeros, norm, hinfnorm, linfnorm, ctrb, obsv, gangoffour, margin, markovparam, damp, dampreport, zpkdata, dcgain, covar, gram, sigma, sisomargin

Synthesis

are, lyap, lqr, place, leadlink, laglink, leadlinkat, rstd, rstc, dab, balreal, baltrunc

PID design

pid, stabregionPID, loopshapingPI, pidplots, placePI

Time and Frequency response

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

Plotting

bodeplot, nyquistplot, sigmaplot, plot(lsim(...)), plot(step(...)), plot(impulse(...)), marginplot, gangoffourplot, pzmap, nicholsplot, pidplots, rlocus, leadlinkcurve

Other

minreal, sminreal, c2d

Usage

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.

Example

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
using Plots
plot(step.(CLs, 5), label=["Kp = 1" "Kp = 5" "Kp = 15"])

Additional examples

See the examples folder and ControlExamples.jl and several examples in the documentation.