Analysis and Control of an Energy Harvesting Model

The energy harvesting process is highly nonlinear and one must understand the dynamics of this process in order to control it effectively. The main reason for this nonlinearity is the fact that the process is governed by second order nonlinear differential equations. In this work, these equations are modified into first order ODE and bifurcation and multiobjective nonlinear model predictive control (MNLMPC) calculations are performed on an energy harvesting model. MATCONT (a MATLAB program) was used for the bifurcation analysis while PYOMO was used for the MNLMPC calculations in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of a Hopf bifurcation point, which is eliminated using an activation factor involving the tanh function. The Hopf bifurcation causes limit cycles, which adversely affect both safety and productivity. The MNLMPC calculations provide the optimal control profiles for maximizing the voltage produced.