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We present accurate electromechanical measurements on a balanced push-pull dielectric elastomer actuator, demonstrating submicrometer accurate position control. An analytical model based on a simplified pure-shear dielectric elastomer film with prestretch is found to capture the voltage-displacement behavior, with reduced output due to the boundary conditions. Two complementary experiments show that actuation coefficients of 0.5-1 nm/V-2 are obtainable with the demonstrated device, enabling motion control with submicrometer accuracy in a voltage range below 200 V.