README.md

ModelPredictiveControl.jl

An open source model predictive control package for Julia.

The package depends on ControlSystemsBase.jl for the linear systems, JuMP.jl for the optimization and DifferentiationInterface.jl for the derivatives.

Installation

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

using Pkg; Pkg.add("ModelPredictiveControl")

Getting Started

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 (a transfer function matrix, with $s$ as the Laplace variable):

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

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)

See the manual for more detailed examples.