In-domain control of a heat equation: an approach combining zero-dynamics inverse and differential flatness

TL;DR

This paper presents a novel control scheme for in-domain heat equation control, combining zero-dynamics inverse and differential flatness, validated through convergence analysis and numerical simulations.

Contribution

It introduces a new control approach that integrates zero-dynamics inverse with flat system control for in-domain heat equation regulation.

Findings

Control scheme converges and is solvable.

Numerical simulations confirm effectiveness.

Approach handles complex in-domain actuation.

Abstract

This paper addresses the set-point control problem of a heat equation with in-domain actuation. The proposed scheme is based on the framework of zero dynamics inverse combined with flat system control. Moreover, the set-point control is cast into a motion planing problem of a multiple-input, multiple-out system, which is solved by a Green's function-based reference trajectory decomposition. The validity of the proposed method is assessed through convergence and solvability analysis of the control algorithm. The performance of the developed control scheme and the viability of the proposed approach are confirmed by numerical simulation of a representative system.