This　paper　investigates　enhanced　damping　for　protecting　bridge　stay　cables　from　excessive　vibration　using　a　newly　developed　self-sensing　magnetorheological　(MR)　damper.　The　semi-active　control　strategy　for　effectively　operating　the　self-sensing　MR　damper　is　formulated　based　on　the　linear-quadratic-Gaussian　(LQG)　control　by　further　considering　a　collocated　control　configuration,　limited　measurements　and　nonlinear　damper　dynamics.　Due　to　its　attractive　feature　of　sensing-while-damping,　the　self-sensing　MR　damper　facilitates　the　collocated　control.　On　the　other　hand,　only　the　sensor　measurements　from　the　self-sensing　device　are　employed　in　the　feedback　control.　The　nonlinear　dynamics　of　the　self-sensing　MR　damper,　represented　by　a　validated　Bayesian　NARX　network　technique,　are　further　accommodated　in　the　control　formulation　to　compensate　for　its　nonlinearities.　Numerical　and　experimental　investigations　are　conducted　on　stay　cables　equipped　with　the　self-sensing　MR　damper　operated　in　passive　and　semi-active　control　modes.　The　results　verify　that　the　collocated　self-sensing　MR　damper　facilitates　smart　damping　for　inclined　cables　employing　energy-dissipative　LQG　control　with　only　force　and　displacement　measurements　at　the　damper.　It　is　also　demonstrated　that　the　synthesis　of　nonlinear　damper　dynamics　in　the　LQG　control　enhances　damping　force　tracking　efficiently,　explores　the　features　of　the　self-sensing　MR　damper,　and　achieves　better　control　performance　over　the　passive　MR　damping　control　and　the　Heaviside　step　function-based　LQG　control　that　ignores　the　damper　dynamics.　©　2016　IOP　Publishing　Ltd.