Nonlinear optimal control of a four-wheel autonomous electric vehicle driven by a VSI-fed BLDC motor

The article proposes a nonlinear optimal control method for a four-wheel autonomous vehicle driven by a VSI-fed BLDC motor. The dynamic model of the autonomous EV is formulated by integrating the state-space descriptions of the four-wheel autonomous ground vehicle, of the three-phase permanent magnet brushless DC motor, and of the three-phase DC/AC inverter which is connected to batteries. It is proven that the dynamic model of the autonomous EV is differentially flat. Next, the state-space description of the autonomous EV undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the system’s Jacobian matrices. The linearization takes place at each sampling instance around a temporary operating point which is defined by the present value of the EV’s state vector and by the last sampled value of the EV’s control inputs vector. For the approximately linearized model of the system an H-infinity feedback controller is designed. To select the feedback gains of the H-infinity controller an algebraic Riccati equation is solved 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 method ensures precise following of reference paths in the XY plane by the autonomous EV, as well as convergence of all state variables of the EV to the targeted setpoints. The variations of the control inputs are kept moderate. The proposed nonlinear optimal control method is a simple yet efficient solution for the design of low-cost autonomous electric vehicles.