Economic Model Predictive Control (EMPC)

The defining characteristic of EMPC is the replacement of a quadratic tracking error with a general economic cost function. This function directly encodes operational profit, energy expenditure, or material efficiency.

• Objective: Maximizes Σ (Revenue - Raw Material Cost - Energy Cost) over the prediction horizon.
• Non-Convexity: Unlike standard MPC, the economic objective is often non-convex, requiring global optimization solvers.
• Example: A chemical reactor might maximize yield * selectivity, rather than holding a specific temperature setpoint.

EMPC does not assume a steady-state optimum exists. It discovers transient economic benefits that static real-time optimization (RTO) layers miss.

• Transient Profit: The controller may drive the process through a high-profit transient path that is not a steady-state operating point.
• Time-Varying Pricing: EMPC naturally handles dynamic energy tariffs or spot-market feedstock prices as time-varying parameters in the cost function.
• Constraint Management: Operates the process persistently at active constraints that represent maximum throughput or minimum cooling limits.

Pure economic optimization can lead to unstable oscillatory behavior. EMPC enforces dissipativity constraints to guarantee closed-loop stability.

• Storage Function: A generalized energy-like function is used to constrain the system trajectory.
• Turnpike Property: Ensures the optimal economic trajectory remains near the optimal steady-state for most of the operation.
• Lyapunov Constraints: Explicit stability constraints are added to the optimization problem to prevent the controller from chasing infinite transient profit at the expense of process safety.

EMPC collapses the traditional two-layer hierarchy of RTO and MPC into a single dynamic optimization layer.

• Layer Collapse: Eliminates the inconsistency between the steady-state RTO target and the dynamic MPC execution.
• Update Frequency: EMPC solves the economic optimization at the same frequency as the control execution (seconds to minutes), not hours like traditional RTO.
• Model Consistency: Uses the same dynamic model for both economic optimization and constraint handling, ensuring feasibility.

Certain processes, like pressure swing adsorption (PSA) or simulated moving beds, have no static steady-state. EMPC is uniquely suited to optimize these periodic operations.

• Cycle Optimization: The cost function evaluates economic performance over a full cycle rather than an instantaneous state.
• Terminal Constraints: Enforces that the state at the end of the prediction horizon matches the state at the beginning to ensure repeatable cycles.
• Example: Maximizing oxygen purity per unit of energy input across a PSA cycle.

For highly exothermic or non-linear chemical processes, linear dynamic models are insufficient. Nonlinear EMPC uses first-principles or neural network models.

• Model Types: Employs deep neural networks, Gaussian process regression, or mechanistic differential-algebraic equations as the internal prediction model.
• Computational Burden: Requires non-convex nonlinear programming (NLP) solvers like IPOPT, demanding edge-compute GPUs for real-time execution.
• Constraint Handling: Rigorously handles non-linear safety constraints like reactor thermal runaway boundaries.