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It is aimed to study a hybrid quantum‐classical system in which a qubit as a quantum system coupled to a semi‐infinite 1D photonic crystal (PC) waveguide, and is controlled by a classical driving field. PC waveguides with engineering capability serve as engineered reservoirs where various manifestations of quantum mechanics can be studied. Here, the main purpose of the study is to evaluate the effect of coherent control on the dynamics of quantum Fisher information (QFI) and geometric phase (GP). It is revealed that the intensity (the Rabi frequency) of the classical field, memory time, and geometric length of the waveguide are key variables whose judicious choice aids in optimizing the estimation of the quantum parameters that are initially encoded in the qubit state. It is observed that the optical length of the waveguide and the Rabi frequency of the classical field have an interplay effect on the dynamic of the QFI and geometric phase. As an interesting finding, it is disclosed that as the Rabi frequency increases, the effect of the optical length of the waveguide fades away, and the Rabi frequency solely controls the geometric phase. Moreover, it is demonstrated that the estimation accuracy increases as the memory time decreases. On the other hand, lengthening the memory time lessens the dependency of the geometric phase on the length of the waveguide. [ABSTRACT FROM AUTHOR]