Benchmarking of Flatness-based Control of the Heat Equation

TL;DR

This paper benchmarks flatness-based control methods for the 1D heat equation with Neumann boundary actuation, analyzing how system parameters influence input signal computation for aluminum and steel, and assessing real-world applicability.

Contribution

It provides a systematic benchmarking of flatness-based control design for the heat equation, including parameter influence and practical scenario considerations.

Findings

Input signals are significantly affected by system and controller parameters.

The control approach is applicable to realistic scenarios involving aluminum and steel.

Parameter tuning is crucial for reliable trajectory planning.

Abstract

Flatness-based control design is a well established method to generate open-loop control signals. Several articles discuss the application of flatness-based control design of (reaction-) diffusion problems for various scenarios. Beside the pure analytical derivation also the numerical computation of the input signal is crucial to yield a reliable trajectory planning. Therefore, we derive the input signal step-by-step and describe the influence of system and controller parameters on the computation of the input signal. In particular, we benchmark the control design of the one-dimensional heat equation with Neumann-type boundary actuation for pure aluminum and steel 38Si7, and discuss the applicability of the found input signals for realistic scenarios.