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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.