A control system for a vehicle includes a rotary electric machine and an electronic control unit. A cooling piping is provided in a burner main body and a premixing chamber of the fuel side burner, and is connected to a heat recovery system so as to supply a cooling medium, thereby cooling the fuel side burner. A second memory decoding the position error data on the basis of the correction coefficient by the use of the computing unit and storing correction data for correcting the position data and error-containing position data generated on the basis of the encoded position error data. The carriage assembly has a first end and a second end.