A Generalized Lyapunov Stability Theorem for Discrete-time Systems Based on Quadratic Difference Forms

Process units may operate different time scales (for example, reactors with different volumes) thus requiring plantwide control systems with multiple sampling rates to avoid over or under sampling. Moreover, it may be preferable to sample critical variables at a higher rate than non-critical ones to decrease capital. Motivated by the above considerations, this paper addresses the issue of distributed multirate model predictive control design for chemical process networks. In order to ensure the closed-loop stability and achieve a minimum performance, dissipativity-based constraints are included in the design of the individual local controllers.

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“…Kojima and Takaba,[5], then extended it to the discrete time case, introducing QdFs. Defining the extended inputs and outputs as:…”

Section: Background and Preliminariesmentioning

confidence: 99%

Multirate dissipativity-based distributed MPC

Zheng

Tippett

Bao

et al. 2013

2013 Australian Control Conference

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“…The well-known Lyapunov conditions (see, e.g., p. 2913 of [33]) are used to develop further algebraic specifications for stability, that will be instrumental for the synthesis of controllers. For ease of reference, these conditions are recalled as follows:…”

Section: Lyapunov Stabilitymentioning

confidence: 99%

“…Remark 1. Please notice that when dealing with higher order linear systems, it is only required a condition on the Lyapunov function Q K to be non negative, rather than positive definite, please see [33].…”

Section: Lyapunov Stabilitymentioning

confidence: 99%

Data-Driven Control of LVDC Network Converters: Active Load Stabilization

Ruiz-Martinez

Mayo-Maldonado

Escobar

et al. 2020

IEEE Trans. Smart Grid

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This paper addresses the (model-free) data-driven control of power converters, acting as distributed generators, in low voltage direct current (LVDC) networks (e.g. DC microgrids, DC distributed power systems, DC buses wit multiple sources and loads, etc.). Since traditional stand-alone control design, cannot guarantee stability when converters are connected to a network, it is proposed a deterministic solution that does not require the network model-an approach purely based on measurement data. This is a suitable way to overcome common issues when using a model-based approach, e.g. the use of an excessive number of variables and equations, the presence of un-modeled dynamics, unknown parameters and/or the lack of first principle model equations. To corroborate the advantages of the proposed approach, the present work addresses an extreme but also realistic scenario: weak networks with active loads, such as constant power loads (CPLs). It is also shown that the proposed scheme guarantees stability in a rigorous deterministic way-using a Lyapunov approach based on coefficient matrices directly constructed from data. Simulation results using a multibus LVDC distribution network, based on PSCAD/EMTDC, are provided as proof of concept. Index Terms-Data-driven control, distributed generators, LVDC networks, DC microgrids, DC buses, oscillations, stability, constant power loads. Recent contributions of model-based approaches include: [11]-[13], where feedback control techniques are proposed to stabilize power converters in the presence of CPLs. In [2],

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“…An important result concerning QdFs is that the forward difference of a QdF is itself a QdF. That is, Q ϕ ðt þ 1ÞÀQ ϕ ðtÞ ¼ Q ∇ϕ , where ∇ϕðζ; ηÞ ¼ ðζη À 1Þϕðζ; ηÞ, Kojima and Takaba (2005). This facilitates operations of QdFs using efficient polynomial matrix methods.…”

Section: Preliminariesmentioning

confidence: 99%