ModelPredictiveControl.jl

A model predictive control package for Julia.

The package depends on ControlSystemsBase.jl for the linear systems and JuMP.jl for the solving.

Installation

To install the ModelPredictiveControl package, run this command in the Julia REPL:

using Pkg; Pkg.add("ModelPredictiveControl")

To construct model predictive controllers (MPCs), we must first specify a plant model that is typically extracted from input-output data using system identification. The model here is linear with one input, two outputs and a large time delay in the first channel:

\mathbf{G}(s) = \frac{\mathbf{y}(s)}{\mathbf{u}(s)} = 
\begin{bmatrix}
    \frac{2e^{-20s}}{10s + 1} \\[3pt]
    \frac{10}{4s +1}
\end{bmatrix}

We first construct the plant model with a sample time $T_s = 1$ s:

using ModelPredictiveControl, ControlSystemsBase
G = [ tf( 2 , [10, 1])*delay(20)
      tf( 10, [4,  1]) ]
Ts = 1.0
model = LinModel(G, Ts)

Our goal is controlling the first output $y_1$, but the second one $y_2$ should never exceed 35:

mpc = LinMPC(model, Mwt=[1, 0], Nwt=[0.1])
mpc = setconstraint!(mpc, ymax=[Inf, 35])

The keyword arguments Mwt and Nwt are the output setpoint tracking and move suppression weights, respectively. A setpoint step change of five tests mpc controller in closed-loop. The result is displayed with Plots.jl:

using Plots
ry = [5, 0]
res = sim!(mpc, 40, ry)
plot(res, plotry=true, plotymax=true)

StepChangeResponse

See the manual for more detailed examples.

Features

Legend

implemented feature
planned feature

Model Predictive Control Features

linear and nonlinear plant models exploiting multiple dispatch
supported objective function terms:
- output setpoint tracking
- move suppression
- input setpoint tracking
- economic costs (economic model predictive control)
explicit predictive controller for problems without constraint
soft and hard constraints on:
- output predictions
- manipulated inputs
- manipulated inputs increments
- terminal states to ensure nominal stability
custom manipulated input constraints that are a function of the predictions
supported feedback strategy:
- state estimator (see State Estimation features)
- internal model structure with a custom stochastic model
automatic model augmentation with integrating states for offset-free tracking
support for unmeasured model outputs
feedforward action with measured disturbances that supports direct transmission
custom predictions for:
- output setpoints
- measured disturbances
easy integration with Plots.jl
optimization based on JuMP.jl:
- quickly compare multiple optimizers
- nonlinear solvers relying on automatic differentiation (exact derivative)
additional information about the optimum to ease troubleshooting

State Estimation Features