Design of robust decentralised controllers for MIMO plants with delays through network structure exploitation

ABSTRACT

A methodology is proposed for the design of robust controllers for retarded and neutral-type time-delay systems, focusing on decentralised and overlapping fixed-order controllers for Multiple Input Multiple Output (MIMO) systems. The methodology is grounded in a direct optimisation approach and relies on the minimisation of spectral abscissa and ${\mathcal{H}}_{\mathrm{\infty }}$ cost functions, as a function of the controller or design parameters. First, an approach applicable to generic MIMO systems is presented, which imposes a suitable sparsity pattern with the possibility of fixing elements in the controller parameterisation. Second, if the system to be controlled has the structure of a network of coupled identical subsystems, then it is shown that this structure can be exploited by an improved algorithm for the design of decentralised controllers, thereby improving computational efficiency and scalability with the number of subsystems. Several numerical examples illustrate the effectiveness of the methodology, and its extension towards consensus type problems.

KEYWORDS:

• Robust control
• structured controllers
• time-delay systems
• large-scale interconnected systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In order to simplify notations and shorten the equations, we denote by $u=K\left(s\right)y$ the application of a feedback controller coupling $y\left(t\right)$ to $u\left(t\right)$, whose transfer function is given by $K\left(s\right)$.

Additional information

Funding

This work was supported by the project C14/17/072 of the Onderzoeksraad, KU Leuven Research Council, by the project G0A5317N of the Research Foundation-Flanders (Fonds Wetenschappelijk Onderzoek – Vlaanderen), and by the project UCoCoS funded by the European Union's Horizon 2020 Framework Programme under the Marie Sklodowska-Curie Grant Agreement No 675080.