Stochastic optimal control of a tri-stable energy harvester with the P-SSHI circuit under colored noise

In this paper, the stochastic optimal control of a piecewise electromechanically coupled tri-stable energy harvester (TEH) driven by colored noise is investigated. For the purpose of efficient DC supply, the P-SSHI circuit is chosen as the harvesting circuit connected to the TEH. Based on the statistical linearization and the moment method, the analytical expressions of the stationary response moments and the mean harvested power are derived. Then, the stochastic optimal control problem of the TEH is considered from the perspective of extremum optimization of the multivariable function. The effects of colored noise and system parameters on harvesting performance and control effectiveness are further explored. The results show that the time constant ratio can improve the harvested DC power but weaken the rectification efficiency of the circuit, which plays an opposite role to the inversion factor. The electromechanical-coupled coefficient is beneficial to the enhancement of DC power, but it is not conducive to the effectiveness of the control method. The control effectiveness of the rectification efficiency can be optimized by choosing an appropriate noise intensity. The harvesting performance of controlled TEH is significantly higher than that without control. The Monte Carlo simulations (MCS) well support the theoretical results. Graphical abstract: [Figure not available: see fulltext.].