Nonlinear optimal control for wireless power transfer and EV charging

The article treats the problem of nonlinear optimal control of wireless power transfer systems, consisting of a three-phase DC/AC inverter and a three-phase AC/DC converter (rectifier) and having as application domain the charging of electric vehicles. It is proven that the dynamic model of the wireless power transfer system is differentially flat. To apply the proposed nonlinear optimal control method, the state-space model of the wireless power transfer system undergoes approximate linearisation with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearisation takes place at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the approximately linearised model of the system, an H-infinity (optimal) feedback controller is designed. To compute the feedback gains of this controller, an algebraic Riccati equation is solved repetitively at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The nonlinear optimal control scheme achieves fast and precise tracking of setpoints by the state variables of the wireless power transfer system under moderate variations of the control inputs. To apply state estimation-based control of the wireless power transfer, the H-infinity Kalman Filter is used as a robust state observer.