Model-free control (1305.7085v2)

Abstract: "Model-free control" and the corresponding "intelligent" PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.

• The paper introduces an ultra-local model that replaces complex system models with a succinct representation for robust control.
• The methodology uses algebraic identification techniques to estimate unknown dynamics, enabling easy tuning of intelligent PID controllers.
• The simulations demonstrate that intelligent PID controllers perform reliably in systems with delays, faults, and nonlinear dynamics without recalibration.

An Expert Overview of "Model-free Control"

The paper "Model-free control" by Michel Fliess and Cédric Join presents a unified approach to model-free control (MFC) techniques, specifically emphasizing intelligent PID controllers (iPIDs), which include intelligent proportional-integral-derivative (PID), proportional-integral (PI), and proportional (P) controllers. These controllers have found application across diverse sectors such as intelligent transportation systems and energy management, indicating their broad utility in various practical implementations.

Theoretical Framework

At the core of the proposed model-free control is the use of an "ultra-local model" which replaces complex mathematical models with a simpler representation: $y^{(\nu)} = F + \alpha u$ where $y^{(\nu)}$ is the $\nu$-th derivative of the output $y$, $\alpha$ is a constant parameter, and $F$ encapsulates the unknown dynamics and disturbances. This framework allows for intelligent controllers that are remarkably straightforward to implement and tune, even in the presence of noise and disturbances.

The paper discusses the significance of choosing appropriate values for $\nu$ and $\alpha$, highlighting that low orders of differentiation are usually adequate, and the precise value of $\alpha$ can be determined empirically. For estimation purposes, $F$ is treated as a piecewise constant function and can be efficiently estimated using algebraic identification techniques.

Numerical Results and Practical Applications

Several numerical simulations are provided to illustrate the efficacy of these controllers. For instance, the authors demonstrate the application of iPIDs in handling systems with infinite dimensions, such as those modeled by partial differential equations (PDEs), including systems with heat equations and varying delays. The iPIDs offer substantial advantages over traditional PIDs, particularly in ease of tuning and maintaining performance without resorting to detailed plant models.

The numerical results underscore the practicality and robustness of the model-free control approach compared to traditional PID controllers. These simulations address cases with known system components, changes in system dynamics, actuator faults, and complex nonlinear systems. The iPID controllers adapt quickly to these scenarios without necessitating recalibration or detailed system models.

Implications and Future Directions

The implications of this research touch both theoretical and practical realms. From a theoretical perspective, it challenges the conventional emphasis on precise modeling, suggesting a paradigm shift towards model-free strategies, especially when implementing control systems in industrial applications. Practically, the ability to apply control strategies without detailed models may lead to more cost-effective and faster deployment of control systems across various industries.

The paper posits that further research is needed to extend the findings to multivariable systems and to enhance the understanding of complexities such as delays and non-minimum phase characteristics. Moreover, it prompts reflection on the broader implications for the field of control theory, potentially altering the focus from rigorous system modeling to leveraging empirical insights and simplifying control synthesis.

In conclusion, the work by Fliess and Join highlights the practical utility of model-free control strategies through intelligent PID implementation, offering a compelling alternative to conventional model-based control methods. This approach provides an accessible pathway for robust control across a wide range of complex and uncertain systems, paving the way for new developments in the field of automatic control.