Identification of effective transport physics and optimal feedback control: Experimental demonstration on a 1600-fan wind generator

Abstract

Distributed-input distributed-output (DIDO) systems arise in numerous engineering applications where large numbers of actuators generate spatially distributed physical fields that are monitored by distributed sensors. Developing physically interpretable models that enable real-time optimal control of these systems remains challenging because of the high dimensionality and strong spatial coupling between inputs and outputs. In this work, we propose a physics-based framework for modeling and closed-loop optimal control of DIDO systems from experimental input-output data. First, an effective partial differential equation (PDE) is selected among candidate transport models and discretized on the actuator grid to obtain a minimum-grid representation. Second, the PDE is solved in closed form, which yields an input-output operator with only four physically interpretable parameters. Third, the operator is incorporated into an iterative, constrained quadratic program that accounts for the actuator limits. The framework is demonstrated on the inner 40 x 40 section of the world's highest-resolution Fan Array Wind Generator (FAWG), comprising 1600 independently controlled fans with 36 distributed velocity measurements. The model describes the spatial interaction between the 1600 actuators and the measured velocity field with normalized mean absolute prediction errors of 11-20% for representative actuation patterns. The closed-loop controller reproduces all three prescribed two-dimensional velocity fields with a normalized mean absolute error below 2.3% in fewer than 10 iterations.