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Design of \(\mathcal{L}_2\) stable fixed-order decentralised controllers in a network of sampled-data systems with time-delays. (English) Zbl 1455.93006
Summary: 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 \(\mathcal{L}_2\) 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.
Reviewer: Reviewer (Berlin)
MSC:
93A14 Decentralized systems
93C35 Multivariable systems, multidimensional control systems
93B70 Networked control
93C57 Sampled-data control/observation systems
93C43 Delay control/observation systems
93C05 Linear systems in control theory
Software:
HANSO
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