Model Predictive Control Tuning by Inverse Matching for a Wave Energy Converter

Abstract

This paper investigates the application of a method to find the cost function or the weight matrices to be used in model predictive control (MPC) such that the MPC has the same performance as a predesigned linear controller in state-feedback form when constraints are not active. This is potentially useful when a successful linear controller already exists and it is necessary to incorporate the constraint-handling capabilities of MPC. This is the case for a wave energy converter (WEC), where the maximum power transfer law is well-understood. In addition to solutions based on numerical optimization, a simple analytical solution is also derived for cases with a short prediction horizon. These methods are applied for the control of an empirically-based WEC model. The results show that the MPC can be successfully tuned to follow an existing linear control law and to comply with both input and state constraints, such as actuator force and actuator stroke.

Model Analysis for the Implementation of a Fast Model Predictive Control Scheme on the Absorption/Stripping CO2 Capture Plants

“…Weights are tuned in MPC-based control schemes to successfully attain the required setpoints. The values of Q and R cannot be identical for all control strategies as each controller strategy’s weights are tuned for the maximum performance . Fast MPC 1 and 2 are based on two distinct models in the current study.…”

Self-tuning, load-mitigating feedback control of a 3-DOF point absorber

“…It has been shown that simple feedback controllers can approximate complex conjugate controllers over finite frequency bands [26] [27]. Because realistic seastates are generally band-limited [11], these controllers can offer commensurate performance at substantially reduced implementation complexity.…”

“…from which the optimal gains for a complex conjugate controller follow immediately from Eq. 7 and 3 for a single frequency [26]. Because realistic seas are narrowbanded, the approximation of optimal complex conjugate control at a single frequency results in a high fractional power capture [11], though the ideal single frequency at which power capture is maximized does not share the closed-form solution of the monochromatic case and is instead determined via optimization.…”

A practical approach to wave energy modeling and control

“…A similar approach has also been presented more recently in [43]. Another consideration, as shown in [44], is that model predictive controllers (MPCs) can be designed to track such feedback controllers in order to handle constraints without any need for wave prediction. The question of nonlinear dynamics has received significant interest within the WEC community [45][46][47][48].…”