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.

✨ Features

🎯 Model Predictive Control Features

• 🏭️ Plant Model: Linear or nonlinear models exploiting multiple dispatch.
• ⛳️ Objectives: Tracking for inputs/outputs, move suppression, terminal costs, and economic costs.
• ⏳️ Horizons: Distinct prediction/control horizons with custom move blocking.
• 📸 Linearization: Auto-differentiation for exact Jacobians.
• ⚙️ Adaptive MPC: Manual model updates or automatic successive linearization.
• 🏎️ Explicit MPC: Specialized for unconstrained problems.
• 🚧 Constraints: Soft/hard limits on inputs, outputs, increments, and terminal states.
• 🔁 Feedback: Internal model or state estimators (see features below).
• 📡 Feedforward: Integrated support for measured disturbances.
• 🔮 Preview: Custom predictions for setpoints and measured disturbances.
• 📈 Offset-Free: Automatic model augmentation with integrators.
• 📊 Visuals: Easy integration with Plots.jl.
• 🧩 Solvers: Optimization via JuMP.jl (quadratic & nonlinear) and derivatives via DifferentiationInterface.jl.
• 📝 Transcription: Direct single/multiple shooting and trapezoidal collocation.
• 🩺 Troubleshooting: Detailed diagnostic information about optimum.
• ⏱️ Real-Time: Optimized for low memory allocations with soft real-time utilities.

🔭 State Estimation Features

• 🔍️ Estimators: Many Kalman filters, Luenberger, and Moving Horizon Estimator (MHE).
• 🎛️ Customization: Ability to use custom/external state estimates.
• 🌊 Disturbances: Estimate unmeasured disturbances via integrators on inputs/outputs.
• 🛣️ Bumpless Transfer: Smooth transitions from manual to automatic control.
• ⌚️ Timing: Estimators available in filter (current) or predictor (delayed) forms.
• 🏷️ MHE Types: Formulations for both linear (quadratic optimization) and nonlinear plants.
• 🛡️ MHE Constraints: Tunable soft/hard constraints on state and noise estimates.