Offset–free data–driven predictive control

This paper presents a tutorial overview of model predictive control (MPC), subspace predictive control (SPC) and data–enabled predictive control (DeePC), with emphasis on offset–free design. Based on recent results on offset–free SPC design and on the relation between SPC and DeePC, we show that when incremental inputs are used in the identification step (SPC) or in the Hankel matrix (DeePC), the resulting data– driven predictive controllers are offset–free. Moreover, they are equivalent with offset–free MPC in the deterministic case. For noisy data the equivalence does not hold and a regularized version of the DeePC algorithm is necessary. We show that regularized DeePC can be formulated as a Tikhonov regularized least squares problem. This enables systematic tuning of the regularization parameter. We compare the performance of the offset–free data–driven predictive controllers in an application example from high–precision mechatronics.