From Reference Model Selection to Controller Validation: Application to Loewner Data-Driven Control

Abstract

The choice of a reference model in data-driven control techniques is a critical step. Indeed, it should represent the desired closed-loop performances and be achievable by the plant at the same time. In this paper, we propose a method to build such a reference model, both reproducible by the system and having a desired behaviour. It is applicable to Linear Time-Invariant (LTI) monovariable systems and relies on the estimation of the plant's instabilities through a data-driven stability analysis technique. The L-DDC (Loewner Data Driven Control) algorithm is used to illustrate the impact of the choice of the reference model on the control design process. Finally, the proposed choice of specifications allows to use a controller validation technique based on the small-gain theorem.

Interpolation-based irrational model control design and stability analysis

“…As explained in [9], the reference model choice is a key factor for the LDDC success, as for any other model reference control techniques. Indeed, this latter should not only represent a desirable closed-loop behaviour, but also an achievable dynamic of the considered system (i.e.…”

“…In the general case, the right half plane poles and zeros of the system are estimated in [9] in order to build an achievable reference model on the basis of the initial specifications given by the user. This is made possible through a data-driven stability analysis introduced in [6] and the associated estimation of instabilities presented in [5].…”

“…One of the major challenges in this data-driven control strategy is to preserve internal stability. While the ideal controller is known to be stabilising thanks to the choice of an achievable reference model, see [9], there is no guarantee regarding the reduced-order controllers. Therefore, it is necessary to analyse the internal stability during the controller reduction step.…”

Interpolatory-based data-driven pulsed fluidic actuator control design and experimental validation

“…In opposition to the spectral energy density, the cross (or inter-correlated) spectral density is a complex number which gain represents the interaction power and which arguments represents the phase between u prbs (t k ) and y prbs (t k ). Now the open-loop data have been collected and treated, the Loewner Data-Driven Control (L-DDC) process [3], detailed in the following, can be deployed.…”

“…The main objective of the present contribution is therefore to provide practitioners and experimental researchers a simple but yet effective methodology and practical workflow to implement pulsed fluid actuators flow controllers directly from experiments. While the contribution is more methodological rather than theoretical, authors believe that the interpolatory-based data-driven control design process presented in this paper solves practical problems faced by practitioners, namely, the complete PFA controller design using open-loop data collected directly on the experimental setup only (technical details can be found in [3,4]).…”