Many systems are subject to periodic disturbances and exhibit repetitive behaviour. Model-based repetitive control employs knowledge of such periodicity to attenuate periodic disturbances and has seen a wide range of successful industrial implementations. The aim of this paper is to develop a data-driven repetitive control method. In the developed framework, linear periodically time-varying (LPTV) behaviour is lifted to linear time-invariant (LTI) behaviour. Periodic disturbance mitigation is enabled by developing an extension of Willems’ fundamental lemma for systems with exogenous disturbances. The resulting Data-enabled Predictive Repetitive Control (DeePRC) technique accounts for periodic system behaviour to perform attenuation of a periodic disturbance. Simulations demonstrate the ability of DeePRC to effectively mitigate periodic disturbances in the presence of noise.

In recent years, the amount of data available from systems has drastically increased, motivating the use of direct data-driven control techniques that avoid the need of parametric modeling. The aim of this paper is to analyze closed-loop aspects of these approaches in the presence of noise. To analyze this, a unified formulation of several approaches, including Data-enabled Predictive Control (DeePC) and Subspace Predictive Control (SPC) is obtained and the influence of noise on closed-loop predictors is analyzed. The analysis reveals potential closed-loop correlation problems, which are closely related to well-known results in closed-loop system identification, and consequent control issues. A case study reveals the hazards of noise in data-driven control.

Light Detection and Ranging (LIDAR)-assisted Model Predictive Control (MPC) for wind turbine control has received much attention for its ability to incorporate future wind speed disturbance information in a receding horizon optimal control problem. However, the growth of wind turbine sizes results in increasing system complexity and system interactions, and complicates the design of model-based controllers like MPC. Together with increasing data availability, this obstacle motivates the use of direct data-driven predictive control approaches like Subspace Predictive Control (SPC). An SPC implementation is developed that both does not suffer from traditional, potentially detrimental closed-loop identification bias and incorporates past and future (not necessarily periodic) disturbance information. Simulations of the presented method for above-rated wind turbine rotor speed regulation using pitch control demonstrate the capabilities of the data-driven SPC algorithm for increasing degrees of wind speed disturbance information in the developed framework.

Direct data-driven control has attracted substantial interest since it enables optimization-based control without the need for a parametric model. This paper presents a new Instrumental Variable (IV) approach to Data-enabled Predictive Control (DeePC) that results in favorable noise mitigation properties, and demonstrates the direct equivalence between DeePC and Subspace Predictive Control (SPC). The methodology relies on the derivation of the characteristic equation in DeePC along the lines of subspace identification algorithms. A particular choice of IVs is presented that is uncorrelated with future noise, but at the same time highly correlated with the data matrix. A simulation study demonstrates the improved performance of the proposed algorithm in the presence of process and measurement noise.