This paper describes a system identification method and the development of a closed-loop controller for a Hydraulically Amplified Self-healing Electrostatic (HASEL) actuator. Our efforts focus on developing a reliable and consistent way to identify system models for these soft robotic actuators using high-speed videography based motion tracking. Utilizing a mass-spring-damper model we are able to accurately capture the behavior of a HASEL actuator. We use the resulting plant model to design a Proportional-Integral controller that demonstrates improved closed-loop tracking and steady-state error performance.