Control of the common rail pressure in gasoline engines through an extended state observer based MPC

Abstract

In this paper, a model predictive control (MPC) solution, assisted by extended state observer (ESO), is proposed for the common rail pressure control in gasoline engines. The rail pressure dynamic, nonlinear with large uncertainty, is modeled as a simple first order system. The discrepancy of the model from the real plant is lumped as “total disturbance”, to be estimated in real-time by ESO and then mitigated in the nonlinear MPC, assuming the total disturbance does not change in the prediction horizon. The nonlinear MPC problem is solved using the Newton/generalized minimum residual (GMRES) algorithm. The proposed ESO-MPC solution, is compared with the conventional proportional-integral-differential (PID) controller, based on the high-fidelity model provided in the benchmark problem in IFAC-E-CoSM. Results show the following benefits from using ESO-MPC relative to PID (benchmark): 1) the disturbance rejection capability to fuel inject pulse step is improved by 12% in terms of recovery time; 2) the transient response of rail pressure is improved by 5% in terms of the integrated absolute tracking error; and 3) the robustness is improved without need for gain scheduling, which is required in PID. Additionally, increasing the bandwidth of ESO allows reducing the complexity of the model implemented in MPC, while maintaining the disturbance rejection performance at the cost of high noise-sensitivity. Therefore, the ESO-MPC combination offers a simpler and more practical solution for common rail pressure control, relative to the standard MPC, which is consistent with the findings in simulation.