A control systems design toolbox for Julia.

To install, in the Julia REPL:

Pkg.add("ControlSystems")

• Poles and zeros are "not sorted" as in Julia versions < 1.2, even on newer versions of Julia. This should imply that complex conjugates are kept together.

• We now support systems with time delays. Example:

sys = tf(1, [1,1])*delay(1)
stepplot(sys, 5) # Compilation time might be long for first simulation
nyquistplot(sys)

• Delayed systems (frequency domain)
• Delayed systems (time domain)
• Systems with uncertainty
• Robust PID optimization

New state-space type HeteroStateSpace that accepts matrices of heterogeneous types: example using StaticArrays.

System identification using ControlSystemIdentification.jl is now available. The readme together with a series of notebooks serve as documentation.

• State-space identification
• ARX/PLR
• Transfer-function estimation using spectral methods
• Impulse-response estimation

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):

ss(1)
ss(1.)
ss(1im)
ss(ForwardDiff.Dual(1.))
ss(GPUArray([1]))
ss(SparseMatrix([1]))

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 is available at http://juliacontrol.github.io/ControlSystems.jl/latest/.

Some of the available commands are:

ss, tf, zpk

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

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

pid, stabregionPID, loopshapingPI, pidplots

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"])

See the examples folder