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Ionic polymer-metal composites (IPMCs) form an important category of electroactive polymers (also known as artificial muscles) and have built-in actuation and sensing capabilities. A dynamic, physics-based model is presented for IPMC actuators, which is amenable to model reduction and control design. This model is represented as an infinite- dimensional transfer function relating the bending displacement to the applied voltage. It is obtained by deriving the exact solution to the governing partial differential equation (PDE) in the Laplace domain for the actuation dynamics, where the effects of the distributed surface resistance and the dynamics of the cantilever beam are incorporated. The physical model is expressed in terms of fundamental material parameters and actuator dimensions, and is thus geometrically scalable. It can be easily reduced to low-order models for real-time control design. As an example, an Hinfin controller is designed based on the reduced model and applied to tracking control. Experimental results are provided to validate the proposed model.