MODE

Equations to execution - seamlessly

MODE — Model-based Ordinary Differential Equations for MPC

MODE is a next-generation library for Model Predictive Control (MPC) that builds directly on ordinary differential equations (ODEs). By structuring control around dynamic models instead of black-box rules, MODE enables robust, transparent, and scalable control for real processes.

Why MODE?

  • Physics-based foundation: MODE uses ODEs to represent process dynamics, ensuring every controller is grounded in real behaviour.

  • Unified workflow: Model → Estimation → Prediction → Control → Deployment, all in one framework.

  • Constraint-aware: Hard and soft constraints, actuator limits, rate suppression, and economic objectives are natively supported.

  • Adaptive & resilient: Designed to handle disturbances, parameter drift, and operating envelope changes.

  • Deployable: From simulation studies to plant-floor integration, MODE bridges research and industry.

The MODE Approach

  1. Model

    • Define system states, inputs, disturbances, and outputs using ODEs.

    • Incorporate physics (mass balances, energy balances, kinetics) or data-driven terms.

    • Add algebraic constraints and auxiliary variables as needed.

  2. Estimator

    • Fuse sensor data with the model via Kalman Filters (EKF/UKF) or Moving Horizon Estimation (MHE).

    • Estimate unmeasured states and parameters online.

  3. Predictive Controller

    • Solve an optimisation problem over a prediction horizon based on the ODE model.

    • Apply optimal inputs that minimise deviations while respecting constraints.

    • Support for quadratic, nonlinear, and multi-objective cost functions.

  4. Simulator

    • Stress-test control strategies with disturbances, actuator faults, and scenario sweeps.

    • Quantify KPIs such as setpoint tracking, constraint handling, and energy efficiency.

  5. Deployment

    • Integrate with plant historians, OPC UA/MQTT protocols, or Python APIs.

    • Real-time capable with warm-start solvers and watchdog safeguards.

Example Domains

  • Mineral Processing – stabilise grinding circuits, control flotation froth levels, or regulate thickener interfaces.

  • Energy & Utilities – optimise demand response, manage storage systems, or control HVAC plants.

  • Robotics & Automation – perform trajectory tracking with torque and safety constraints.

  • Finance & Operations – apply dynamic optimisation to portfolio adjustments with turnover limits.

Example Snippet

import mode as md
# Define model
model = md.Model(dt=0.5)
x = model.state("TankLevel") # state
u = model.input("ValveOpening") # manipulated input
d = model.disturbance("FeedFlow") # disturbance
y = model.output("LevelSensor") # measurement
# ODE: dH/dt = inflow - outflow
model.ode(x, d - 0.8*u)
model.measure(y, x)
# Estimator
est = md.Estimator("ekf", model=model)
# MPC
mpc = md.MPC(model=model, horizon=30, control_horizon=10)
mpc.objective(track=y, target=2.0, weight=10)
mpc.bounds(u, lo=0, hi=100)
# Simulation
sim = md.Simulator(model, est, mpc)
sim.run(steps=100)

Key Features

  • ODE-driven control: every system starts with equations of motion or balances.

  • Estimator integration: real-time state & parameter estimation.

  • Constraint management: hard limits, fuzzy zones, rate penalties.

  • Robust optimisation: supports both linear and nonlinear MPC.

  • Diagnostics: solver status, KPI logging, constraint heatmaps.

Philosophy

MODE embraces the principle that control is strongest when built on models. By combining the predictive power of ODEs with modern optimisation, MODE delivers controllers that are both interpretable and effective.

From equations to execution – seamlessly