Direct data-driven H2 – H∞ loop-shaping

Abstract

In this paper, a direct data-driven approach is proposed to tune fixed-order controllers for unknown stable LTI plants in a mixed-sensitivity loop-shaping problem. The method requires a single set of input-output samples and it is based on simple convex optimization techniques; moreover, it guarantees internal stability as the data-length tends to infinity. Compared to a standard model-based approach, the proposed methodology theoretically guarantees the same asymptotical performance in case of correct parameterization, whereas the direct data-driven formulation is less conservative in case of undermodeling. The effectiveness of the method is illustrated via some numerical examples.

A Data-Driven Approach to Mixed-Sensitivity Control With Application to an Active Suspension System

“…Moreover, the constraint γ (ρ) < 1 may affect closed-loop performance, if the optimal solution is close to the boundary defined by the real constraint. A simple situation where this fact may happen has been presented in [15]. It must be mentioned that the formulation (7) is only one of possible solutions and that different results could be achieved in different situations.…”

“…As far as the authors are aware, this is the first time where the noniterative data-driven philosophy is applied to the mixed-sensitivity loop-shaping problem. A preliminary version of this work can be found in [15]. An iterative data-driven solution to the problem has instead been presented in [16].…”

Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

“…In papers such as [17], a significant study related to this present work evinces the design of an H-infinity loop shaping controller with weighting function optimization by linear matrix inequalities. Then in [18], a data-driven H2-H infinity loop shaping controller is presented. In studies such as [19], an H-infinity loop shaping controller is designed for linear parameter varying plant.…”

An Improved DC Motor Position Control Using Differential Evolution Based Structure Specified H∞ Robust Controller

“…The author in [31] showed an H∞ loop shaping controller synthesis with weighting function optimization. A data-driven H2H∞ loop shaping is shown in [32]. In [33], the author tried to implement H2/H∞ robust control to control the DC motor.…”