Robust H∞ force control of a solenoid actuator using experimental data and finite element method

In this paper, the robust force control of a solenoid actuator is studied. Such control problem is of interest in the study of gear shifting control in electric vehicles (EVs) equipped with an automated manual transmission (AMT). Experimental system identification together with the finite element method (FEM) is the approach considered in this paper to model the dynamic behavior of the solenoid actuator as well as the system uncertainties. Using experimental system identification, a dynamic model of the actuator is obtained and a nonlinear algebraic model of the electromagnetic force versus current and air gap is proposed. Using the properties of the magnetic materials and the geometry of the actuator, an FEM analysis is performed using Magnet® - Infolytica software - to obtain the dynamics of the nominal system and verify the system identification result. Considering the inherent uncertainty of the physical parameter involved in the actuation system as well as the measurement errors, an uncertainty analysis is performed to obtain the dynamic uncertainty model of the solenoid system. Moreover, considering the application of such actuator in the gear shifting process, the closed-loop performance objectives are defined with respect to the desired gear shifting quality. Knowing both the nominal system model and the uncertainty model, an H∞ robust controller is designed. The performance of the resulting robust closed-loop control system is examined for the nominal and perturbed systems and is shown to satisfy the objectives.