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Reinforcement learning (RL) is a promising, upcoming topic in automatic control applications. Where classical control approaches require a priori system knowledge, data-driven control approaches like RL allow a model-free controller design procedure, rendering them emergent techniques for systems with changing plant structures and varying parameters. While it was already shown in various applications that the transient control behavior for complex systems can be sufficiently handled by RL, the challenge of non-vanishing steady-state control errors remains, which arises from the usage of control policy approximations and finite training times. To overcome this issue, an integral action state augmentation (IASA) for actor-critic-based RL controllers is introduced that mimics an integrating feedback, which is inspired by the delta-input formulation within model predictive control. This augmentation does not require any expert knowledge, leaving the approach model free. As a result, the RL controller learns how to suppress steady-state control deviations much more effectively. Two exemplary applications from the domain of electrical energy engineering validate the benefit of the developed method both for reference tracking and disturbance rejection. In comparison to a standard deep deterministic policy gradient (DDPG) setup, the suggested IASA extension allows to reduce the steady-state error by up to 52 $\%$ within the considered validation scenarios.