Optimizing vibratory energy harvesters with differentiable data-driven control

Nonlinear vibratory energy harvesters often exhibit multiple coexisting attractors, making their control challenging and energy-intensive. Ensuring an effective transition between these attractors while minimizing control effort is crucial for maximizing power generation and maintaining system stability. This paper introduces a differentiable data-driven control strategy that optimizes energy harvester performance by leveraging a neural network (NN)-based control framework. Unlike traditional fixed-gain or surrogate modeling approaches, the proposed method directly integrates system dynamics and control power consumption into the gain adaptation process, ensuring real-time adaptability. By exploiting the differentiability of neural networks, the controller employs gradient-based optimization to continuously refine control parameters in response to changes in operating conditions. The control framework consists of an offline training phase, where the neural network learns an energy-efficient control strategy through differentiable simulations. During this phase, the neural network is trained using a large dataset of system responses to different control inputs, allowing it to learn the most energy-efficient control strategy. This trained network is then used in the online deployment phase, where the trained controller dynamically adjusts control parameters in real-time. The proposed approach minimizes control energy consumption and efficiently guides the system toward the high-energy attractor, avoiding unnecessary control effort. Our approach significantly outperforms conventional PID-based sliding mode controllers. Simulation results confirm that the differentiable controller considerably enhances energy harvesting efficiency and reduces chattering, ensuring a smooth transition to the high-energy orbit while maintaining robust system stability. The study also highlights the necessity of an adaptive control strategy, stressing the urgency of its implementation for optimal energy extraction.