On the controller form for linear hyperbolic MIMO systems with dynamic boundary conditions

TL;DR

This paper introduces an algebraic method to derive controller forms for linear hyperbolic MIMO systems with boundary coupling, extending existing approaches and proposing a new flatness-based computation scheme.

Contribution

It develops a generalized hyperbolic controller form for MIMO systems and introduces a novel algebraic, flatness-based algorithm for its computation.

Findings

The algebraic approach successfully derives controller forms for complex MIMO hyperbolic systems.

The proposed flatness-based scheme effectively computes the controller form in an algebraic setting.

The method is demonstrated on a motivating example, validating its applicability.

Abstract

This contribution develops an algebraic approach to obtain a controller form for a class of linear hyperbolic MIMO systems, bidirectionally coupled with a linear ODE system at the unactuated boundary. After a short summary of established controller forms for SISO and MIMO ODE as well as SISO hyperbolic PDE systems, it is shown that the approach to state a controller form for SISO systems cannot easily be transferred to the MIMO case as it already fails for a very simple example. Next, a generalised hyperbolic controller form with different variants is proposed and a new flatness-based scheme to compute said form is presented. Therein, the system is treated in an algebraic setting where quasipolynomials are used to express the predictions and delays in the system. The proposed algorithm is then applied to the motivating example.