We analyze three prototypical black hole (BH) X-ray binaries (XRBs), 4u1630, gro1655 and h1743, in an effort to systematically understand the intrinsic state transition of the observed accretion-disk winds between windon and windoff states by utilizing state-of-the-art {it Chandra}/HETGS archival data from multi-epoch observations. We apply our magnetically-driven wind models in the context of magnetohydrodynamic (MHD) calculations to constrain their (1) global density slope ($p$), (2) their density ($n_{17}$) at the foot point of the innermost launching radius and (3) the abundances of heavier elements ($A_{rm Fe,S,Si}$). Incorporating the MHD winds into {tt xstar} photoionization calculations in a self-consistent manner, we create a library of synthetic absorption spectra given the observed X-ray continua. Our analysis clearly indicates a characteristic bi-modal transition of multi-ion X-ray winds; i.e. the wind density gradient is found to steepen (from $p sim 1.2-1.4$ to $sim 1.4-1.5$) while its density normalization declines as the source transitions from windon to windoff state. The model implies that the ionized wind {it remains physically present} even in windoff state, despite its absent appearance in the observed spectra. Super-solar abundances for heavier elements are also favored. Our global multi-ion wind models, taking into account soft X-ray ions as well as Fe K absorbers, show that the internal wind condition plays an important role in wind transitions besides photoionization changes. % Simulated {it XRISM}/Resolve and {it Athena}/X-IFU spectra are presented to demonstrate a high fidelity of the multi-ion wind model for better understanding of these powerful ionized winds in the coming decades.
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