Atomic force microscopy-infrared (AFM-IR) spectroscopic imaging offers non-perturbative, molecular contrast for nanoscale characterization. The need to mitigate measurement artifacts and enhance sensitivity, however, requires narrowly-defined and strict sample preparation protocols. This limits reliable and facile characterization; for example, when using common substrates such as Silicon or glass. Here, we demonstrate a closed-loop (CL) piezo controller design for responsivity-corrected AFM-IR imaging. Instead of the usual mode of recording cantilever deflection driven by sample expansion, the principle of our approach is to maintain a zero amplitude harmonic cantilever deflection by CL control of a subsample piezo. We show that the piezo voltage used to maintain a null deflection provides a reliable measure of the local IR absorption with significantly reduced noise. A complete analytical description of the CL operation and characterization of the controller for achieving robust performance are presented. Accurate measurement of IR absorption of nanothin PMMA films on glass and Silicon validates the robust capability of CL AFM-IR in routine mapping of nanoscale molecular information.