Passivity-based PI control of first-order systems with I/O communication delays: a frequency domain analysis

ABSTRACT

In this paper, the proportional integral (PI) control of first-order linear passive systems through a delayed communication channel is revisited in light of the relative stability concept called σ-stability. Treating the delayed communication channel as a transport partial differential equation (PDE), the passivity of the overall control-loop is guaranteed, resulting in a closed-loop system of neutral nature. Spectral methods are then applied to the system to obtain a complete stability map. In particular, we perform the $\mathcal{D}$-subdivision method to declare the exact σ-stability regions in the space of PI parameters. This framework is then utilised to analytically determine the maximum achievable exponential decay rate σ* _d of the system while achieving the PI tuning as explicit function of σ* _d and system parameters.

KEYWORDS:

• Time-delay systems
• passivity-based control
• linear systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. A formal proof of this fact follows from the analysis of ∂σ/∂ω = 0 using the implicit function theorem, the reader is referred to Ramírez, Garrido, and Mondié (2015) for further details in the case of delay-based control of first-order systems.

Additional information

Funding

Consejo Nacional de Ciencia y Tecnología [grant number 180725].