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Controlling buildings, towers, and other civil engineering structures for active vibration mitigation is a rapidly growing field of control systems technology. Of fundamental importance in the development of feedback control laws it is to identify the inherent dynamic characteristics of such control systems with suitable mathematical models. This brief contributes to this research field by first recognizing the existence of fixed zero dynamics in the control input channels. The discovery is subsequently incorporated into the development of specialized frequency domain identification algorithms, which also address the constrained stability of the identified model. Finally, a practical case study is presented to illustrate the important aspects of frequency domain modeling of controlled structures.