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Publication# A Robust Data-Driven Controller Design Methodology With Applications to Particle Accelerator Power Converters

Résumé

A new data-driven approach using the frequency response function (FRF) of a system is proposed for designing robust-fixed structure digital controllers for particle accelerators' power converters. This design method ensures that the dynamics of a system are captured and avoid the problem of unmodeled dynamics associated with parametric models. The H ∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a two degree of freedom RST controller. This controller is robust with respect to the frequency-dependent uncertainties of the FRF. A convex optimization algorithm is implemented to obtain the controller parameters. The effectiveness of the method is illustrated by considering two case studies that require robust controllers for achieving the desired performance.

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Concepts associés

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Concepts associés (6)

Robustesse (ingénierie)

En ingénierie, la robustesse d'un système se définit comme la « stabilité de sa performance ».
On distingue trois types de systèmes :

- les systèmes non-performants, qui ne remplissent pas les fonct

Régulateur PID

Le régulateur PID, appelé aussi correcteur PID (proportionnel, intégral, dérivé) est un système de contrôle permettant d’améliorer les performances d'un asservissement, c'est-à-dire un système ou pr

Parameter

A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element

Publications associées (6)

Chargement

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The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems.
In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions.
The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity.
This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance).
The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies.

Gorka Galdos Sanz de Galdeano, Alireza Karimi

The flexible transmission benchmark was proposed in the European Journal of Control to evaluate some robust digital control approaches in 1995. With progress in convex optimization algorithms new methods for robust controller design are developed. A recently proposed fixed-order robust controller design method is applied to this benchmark problem and the results are compared with the existing results. The proposed method is based on open-loop shaping with frequency-domain constraints on the closed-loop sensitivity functions in the Nyquist diagram. The method needs only the frequency response of the model and can consider the multimodel uncertainty. A controller is designed by a convex optimization algorithm that meets all the required performance specifications for the benchmark with the lowest controller complexity.

A new method for H-infinity gain-scheduled controller design by convex optimization is proposed that uses only frequency-domain data. The method is based on loop shaping in the Nyquist diagram with constraints on the weighted infinity-norm of closed-loop transfer functions. This method is applied to a benchmark for adaptive rejection of multiple narrow-band disturbances. First, it is shown that a robust controller can be designed for the rejection of a sinusoidal disturbance with known frequency. The disturbance model is fixed in the controller, based on the internal model principle, and the other controller parameters are computed by convex optimization to meet the constraints on the infinity-norm of sensitivity functions. It is shown next that a gain scheduled-controller can be computed for a finite set of disturbance frequencies by convex optimization. An adaptation algorithm is used to estimate the disturbance frequency which adjusts the parameters of the internal model in the controller. The simulation and experimental results show the good performance of the proposed control system.