Real-time State Estimation for an Adaptive Vibration Energy Harvesting System

Moving horizon estimation (MHE) has proven to be an efficient optimization-based technique to address the problem of joint state and parameter estimation with nonlinearities in system dynamics and constraints. This work aims to propose the application of MHE for a specific nonlinear vibration setup, often used to analyze energy harvesting concepts in the laboratory environment. Using a simulated energy harvesting scenario exhibiting a strongly nonlinear behavior, we focus on the estimation of unmeasured system states and a time-varying structural parameter that can be utilized to maximize the harvested energy, or in structural health monitoring. To exploit the recent algorithmic developments in embedded optimization, we implement the proposed scheme on a low-cost embedded computing platform using automatic code generation. A hardware-in-the-loop setup is used in order to investigate the performance of the real-time MHE scheme, and to quantify the associated computational effort. The results demonstrated in this paper, suggest the real-time feasibility of MHE, and certain practical advantages over a standard Kalman filtering in a vibration energy harvesting system.