A control systems design toolbox for Julia.
To install, in the Julia REPL:
- 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
- State-space identification
- 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()) ss(SparseMatrix())
- Continuous time systems are simulated with continuous time solvers from
- Freqresp now returns frequencies in the first dimension.
lsim(sys, u::Function)syntax has changed from
u(x,t)to be consistent with
feedback(P,C)no longer returns
feedback(P*C). The behavior is changed to
feedback(P1, P2) = P1/(1+P1*P2).
Simulatorprovides 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
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
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"])
See the examples folder