Selecting the tube current when using iterative reconstruction is challenging due to the varying relationship between contrast, noise, spatial resolution, and dose across different algorithms. This study proposes a task-based automated exposure control (AEC) method using a generalized detectability index (d'gen). The proposed method leverages existing AEC methods that are based on a prescribed noise level. The generalized d'gen metric is calculated using look-up tables of task-based modulation transfer function and noise power spectrum. Look-up tables were generated by scanning a 20-cmdiameter American College of Radiology (ACR) phantom and reconstructing with a reference reconstruction algorithm and four levels of an in-house iterative reconstruction algorithm (IR1-4). This study tested the validity of the assumption that the look-up tables can be approximated as being independent of dose level. Preliminary feasibility of the proposed d'gen-AEC method to provide a desired image quality level for different iterative reconstruction algorithms was evaluated for the ACR phantom. The image quality ((d'gen) resulting from the proposed d'gen-AEC method was 3.8 (IR1), 3.9 (IR2), 3.9 (IR3), 3.8 (IR4) compared to the desired d'gen of 3.9 for the reference image. For comparison, images acquired to match the noise standard deviation of the reference image demonstrated reduced image quality (d'gen). of 3.3 for IR1, 3.0 for IR2, 2.5 for IR3, and 1.8 for IR4). For all four iterative reconstruction methods, the d'gen-AEC method resulted in consistent image quality in terms of detectability index at lower dose than the reference scan. The results provide preliminary evidence that the proposed d'gen-AEC can provide consistent image quality across different iterative reconstruction approaches.