Nonlinear Optimal Control for Hybrid Electric Vehicles with Doubly Excited Synchronous Machine and AC/DC Converter

The article analyzes the nonlinear optimal control problem for powertrains in hybrid electric vehicles, which comprise a diesel engine, a hybrid (doubly)-excited synchronous machine (generator/motor), and an AC/DC converter. In generator functioning mode, the diesel engine provides torque for the turn motion of the synchronous machine’s rotor. Next, the AC output voltage of the hybrid excited synchronous machine is turned into DC voltage with the use of AC to DC converters and is distributed through a DC voltage bus while also being used for charging the vehicle’s batteries. The dynamic model of the HEV powertrain, being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on first-order Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the HEV powertrain a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the HEV power system under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the HEV powertrain, without the need to measure its entire state vector, the H-infinity Kalman filter is used as a robust state estimator.