Design of L2 stable fixed-order decentralised controllers in a network of sampled-data systems with time-delays

Deesh Dileep (Corresponding author), Jijju Thomas, Laurentiu Hetel, Nathan van de Wouw, Jean Pierre Richard, Wim Michiels

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

A methodology is proposed for the design of sampled-data fixed-order decentralised controllers for Multiple Input Multiple Output (MIMO) Linear Time-Invariant (LTI) time-delay systems. Imperfections in the communication links between continuous-time plants and controllers arising due to transmission time-delays, aperiodic sampling, and asynchronous sensors and actuators are considered. We model the errors induced due to the control imperfections using an operator approach leading to a simple L2 stability criterion. A frequency domain-based direct optimisation approach towards controller design is proposed in this paper. This approach relies on the minimisation of cost functions, for stability and robustness against control imperfections, as a function of the controller or design parameters. First, the proposed method towards controller design is applied to generic MIMO LTI systems with time-delays. Second, when the delay system to be controlled has the structure of a network of coupled quasi-identical subsystems, we use a scalable algorithm to design identical decentralised controllers through network structure exploitation. Quasi-identical subsystems are identical subsystems that have non-identical uncertainties or control imperfections. By exploiting the structure, we improve the computational efficiency and scalability with the number of subsystems. The methodology has been implemented in a publicly available software, which supports system models in terms of delay differential algebraic equations. Finally, the effectiveness of the methodology is illustrated using a numerical example.

Original languageEnglish
Pages (from-to)73-85
Number of pages13
JournalEuropean Journal of Control
Volume56
DOIs
Publication statusPublished - Nov 2020

Keywords

  • Decentralized control
  • Network structure exploitation
  • Robust controller design
  • Sampled-data control
  • Time-delay systems

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