LGR-MPC: A user-friendly software based on Legendre-Gauss-Radau pseudo spectral method for solving Model Predictive Control problems

TL;DR

This paper presents LGR-MPC, a user-friendly Python software for Model Predictive Control that leverages Legendre-Gauss-Radau spectral methods, demonstrated through various examples including analytical solutions.

Contribution

The paper introduces an accessible Python-based MPC software utilizing Legendre-Gauss-Radau spectral methods, simplifying implementation of MPC in engineering applications.

Findings

Effective in solving MPC problems with known analytical solutions

Demonstrates versatility across multiple engineering examples

Enhances accessibility of MPC technology

Abstract

Active components, such as actuators, constitute a fundamental aspect of engineering systems, affording the freedom to shape system behavior as desired. However, this capability necessitates energy consumption, primarily in the form of electricity. Thus, a trade-off emerges between energy usage and desired outcomes. While open-loop optimal control methods strive for efficiency, practical implementation is hampered by disturbances and model discrepancies, underscoring the need for closed-loop controllers. The Proportional- Integral-Derivative (PID) controller is widely favored in industry due to its simplicity, despite sub-optimal responses in many cases. To bridge this gap, Model Predictive Control (MPC) offers a solution, yet its complexity limits its broad applicability. This paper introduces user-friendly Python-based MPC software, enabling easy access to MPC. The effectiveness of this software is demonstrated through multiple examples, including those with a known analytical solution.