Artificial-reference tracking MPC with probabilistically validated performance on industrial embedded systems

TL;DR

This paper presents an efficient MPC implementation for industrial embedded systems that incorporates practical features and probabilistic performance validation, demonstrated on a nonlinear reactor control scenario.

Contribution

It introduces a structure-exploiting first-order method for MPC tailored to embedded systems, with integrated practical features and a probabilistic validation framework.

Findings

Successful implementation on a PLC in a hardware-in-the-loop setup.

Probabilistic validation shows reliable constraint adherence over long-term operation.

Efficient control of a nonlinear reactor with limited computational resources.

Abstract

Industrial embedded systems are typically used to execute simple control algorithms due to their low computational resources. Despite these limitations, the implementation of advanced control techniques such as Model Predictive Control (MPC) has been explored by the control community in recent years, typically considering simple linear formulations or explicit ones to facilitate the online computation of the control input. These simplifications often lack features and properties that are desirable in real-world environments. In this article, we present an efficient implementation for embedded systems of MPC for tracking with artificial reference, solved via a recently developed structure-exploiting first-order method. This formulation is tailored to a wide range of applications by incorporating essential practical features at a small computational cost, including integration with an offset-free scheme, back-off parameters that enable constraint tightening, and soft constraints that preserve feasibility under disturbances or plant-model mismatch. We accompany this with a framework for probabilistic performance validation of the closed-loop system over long-term operation. We illustrate the applicability of the approach on a Programmable Logic Controller (PLC), incorporated in a hardware-in-the-loop setup to control a nonlinear continuous stirred-tank reactor. The behavior of the closed-loop system is probabilistically validated with respect to constraint violations and the number of iterations required at each time step by the MPC optimization algorithm.