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This paper refers to the results of a study on the usefulness of simulation techniques based on both modeling and experiments of electro-hydraulic systems using an on-off solenoid valve controlled by pulse width modulation for an automatic transmission. By this simulation, the pressure dynamics in a hydraulic circuit and the movement of a clutch piston were analyzed assuming the flow of the hydraulic circuit to be a one-dimensional compressible flow, and considering the non-linear spring characteristics of a clutch. As a result, in comparison with the experiments, the validity of this calculation has been confirmed.