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Sampled-Data Controller Synthesis for Dissipative Linear Periodic Jump-Flow Systems with Design Applications

Q: How does the proposed technique compare to other existing methods for sampled-data controller synthesis

The proposed technique for sampled-data controller synthesis using dissipative linear periodic jump-flow systems offers several advantages over existing methods. One key advantage is the ability to design controllers that render the closed-loop system dissipative with respect to quadratic supply functions, including passivity and an upper bound on the system's H∞-norm as special cases. This provides a more comprehensive approach to controller synthesis, considering both stability and performance criteria simultaneously. Additionally, by modeling the sampled-data control system as a linear periodic jump-flow system and utilizing differential linear matrix inequalities (DLMIs), the proposed technique allows for tractable conditions in terms of a single Linear Matrix Inequality (LMI). This reduces computational complexity and facilitates efficient controller design.

Q: What are the practical implications of achieving dissipativity in control systems

Achieving dissipativity in control systems has significant practical implications across various applications. Firstly, dissipativity ensures energy balance within the system, leading to stable behavior and robust performance. By constraining energy dissipation through quadratic storage functions and supply functions, dissipativity guarantees that the system remains bounded under disturbances or uncertainties. This property is crucial for ensuring safe operation of complex systems where stability is paramount. Furthermore, dissipativity enables better understanding and analysis of hybrid dynamical systems like sampled-data control systems. It provides insights into how energy flows through different components of the system, allowing for effective control design strategies based on energy considerations. Overall, achieving dissipativity enhances the predictability, robustness, and efficiency of control systems in real-world applications.

Q: How can these results be extended to more complex control design problems beyond the ones discussed in the paper

These results can be extended to more complex control design problems beyond those discussed in the paper by applying similar techniques to address specific requirements or constraints in different scenarios. For instance: Nonlinear Systems: The methodology can be adapted to handle nonlinearities by incorporating nonlinear models or approximations into the LPJF framework. Robust Control: Extending these results to robust control design involves incorporating uncertainty models into DLMIs for synthesizing controllers that are resilient against variations or disturbances. Networked Control Systems: Addressing network-induced delays or packet losses requires modifying the LPJF representation to account for communication constraints while ensuring stability and performance objectives are met. Multi-Agent Systems: Applying these techniques to multi-agent systems involves developing distributed controllers that coordinate agents' actions while maintaining overall system stability. By customizing parameters such as storage functions, supply functions, and weighting filters based on specific requirements of each application domain, these results can be tailored to tackle diverse challenges in advanced control engineering fields effectively.

Conceptos Básicos

Linear-matrix-inequality-based techniques are proposed for sampled-data controller synthesis to render closed-loop systems dissipative, with applications in passivity and H∞-norm minimization.

Resumen

The paper introduces techniques for designing sampled-data controllers to achieve dissipativity using linear periodic jump-flow system models. Three applications are presented: passivity-based controller synthesis, filter matching, and controller redesign. The results show improved closed-loop behavior compared to traditional discretization methods.

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arxiv.org

Estadísticas

The vast majority of controller implementations have shifted from analogue to digital controllers over the last century.
SDCS design was successful in the 90s due to a technique called 'lifting'.
SDCS can be modeled as linear periodic jump-flow systems (LPJF).
LPJF systems enable designing controllers using Riccati differential and difference equations.
DLMIs can be turned into numerically tractable LMIs by approximating unknown variables.
LPJF systems can be made dissipative with respect to quadratic storage functions.

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Sampled-Data Controller Synthesis using Dissipative Linear Periodic Jump-Flow Systems with Design Applications

by L. M. Spin,M... a las arxiv.org 03-14-2024

https://arxiv.org/pdf/2304.01878.pdf

Sampled-Data Controller Synthesis using Dissipative Linear Periodic Jump-Flow Systems with Design Applications

Consultas más profundas

How does the proposed technique compare to other existing methods for sampled-data controller synthesis

The proposed technique for sampled-data controller synthesis using dissipative linear periodic jump-flow systems offers several advantages over existing methods. One key advantage is the ability to design controllers that render the closed-loop system dissipative with respect to quadratic supply functions, including passivity and an upper bound on the system's H∞-norm as special cases. This provides a more comprehensive approach to controller synthesis, considering both stability and performance criteria simultaneously. Additionally, by modeling the sampled-data control system as a linear periodic jump-flow system and utilizing differential linear matrix inequalities (DLMIs), the proposed technique allows for tractable conditions in terms of a single Linear Matrix Inequality (LMI). This reduces computational complexity and facilitates efficient controller design.

What are the practical implications of achieving dissipativity in control systems

Achieving dissipativity in control systems has significant practical implications across various applications. Firstly, dissipativity ensures energy balance within the system, leading to stable behavior and robust performance. By constraining energy dissipation through quadratic storage functions and supply functions, dissipativity guarantees that the system remains bounded under disturbances or uncertainties. This property is crucial for ensuring safe operation of complex systems where stability is paramount.
Furthermore, dissipativity enables better understanding and analysis of hybrid dynamical systems like sampled-data control systems. It provides insights into how energy flows through different components of the system, allowing for effective control design strategies based on energy considerations. Overall, achieving dissipativity enhances the predictability, robustness, and efficiency of control systems in real-world applications.

How can these results be extended to more complex control design problems beyond the ones discussed in the paper

These results can be extended to more complex control design problems beyond those discussed in the paper by applying similar techniques to address specific requirements or constraints in different scenarios. For instance:

Nonlinear Systems: The methodology can be adapted to handle nonlinearities by incorporating nonlinear models or approximations into the LPJF framework.
Robust Control: Extending these results to robust control design involves incorporating uncertainty models into DLMIs for synthesizing controllers that are resilient against variations or disturbances.
Networked Control Systems: Addressing network-induced delays or packet losses requires modifying the LPJF representation to account for communication constraints while ensuring stability and performance objectives are met.
Multi-Agent Systems: Applying these techniques to multi-agent systems involves developing distributed controllers that coordinate agents' actions while maintaining overall system stability.

By customizing parameters such as storage functions, supply functions, and weighting filters based on specific requirements of each application domain, these results can be tailored to tackle diverse challenges in advanced control engineering fields effectively.