Dragne, F., Alirand, M., Neves, W., and Lagnier, J., "ESC Hydraulic Circuit Modeling and Model Reduction in the Aim of Reaching Real Time Capability," SAE Technical Paper 2013-36-0013, 2013, doi:10.4271/2013-36-0013.
An ESC hydraulic modulator contains on/off valves and proportional valves. A complex model of one proportional valve is detailed and used as a basis for model reduction the activity index technique. One interesting aspect is that the technology of the proportional valves remains (i.e. ball valves under conical seat). As such, the parameters are physical parameters forming the ones to master (manufacturing tolerances) by the supplier to also master the dynamic behavior of the system. Once this has been done, a complete model of half an ESC braking circuit is built including the pump, the reservoir, the pipes and hoses as well as the calipers. The activity index technique is thus reused on the circuit to further reduce it to finally obtain a modeling level acceptable for real time purpose. The simple model is thus compared to the complex one and the experiments in term of accuracy on typical manoeuvers like braking for low adherence surface, J-Turn and acceleration… The simple ESC hydraulic model is finally coupled to a vehicle model to analyze the capability the complete model (vehicle + braking circuit) has to run real time. As a conclusion, even if HiL benches for testing ESC control logic are always using a hydraulic circuit as hardware, the approach from complex to simple models gives new possibilities for a complete virtual process including continuity in modeling assumptions for MiL, SiL and HiL. This may open possible collaborations for model exchanges of plant models between OEMs and suppliers to improve the virtual process for developing and validating ESC control logic.