In　order　to　suppress　the　random　noise　in　the　suspension　gap　signals　during　the　operation　of　the　maglev　train,　the　tracking　differentiator　(TD)　was　designed　and　implemented　to　filter　the　gap　signals,　and　then　the　feedback　controller　based　on　the　proposed　TD　was　designed　to　realize　the　stable　suspension.　First,　without　complex　nonlinear　operations　existed　in　Han’s　TD　(fhan-TD),　a　simple　time-optimal　control　law　equipped　with　the　linearity　property　was　proposed　by　using　the　back-stepping　approach.　This　approach　can　determine　the　boundary　curves　and　characteristic　curves,　and　then　the　control　sequences　located　in　the　reachable　region　and　linear　region　can　be　calculated.　With　the　proposed　control　sequences,　a　new　TD　with　the　simple　property　can　be　given.　Second,　with　the　state　variables　named　gap　signal　and　speed　signal,　a　second-order　state　equation　was　established,　and　the　single-point　suspension　control　system　model　according　to　the　real-life　maglev　train　structure　was　created.　Finally,　in　view　of　the　PID　(Proportional　Integral　Derivative)　controller,　the　proposed　TD　was　added　to　filter　the　gap　signals.　By　combining　the　PID　controller　and　the　proposed　TD,　the　suspension　feedback　controller　framework　was　proposed　to　ensure　the　stable　suspension.　Simulation　results　show　that　the　proposed　TD　performs　well　in　signal　tracking　and　differentiation　acquisition.　Compared　with　the　traditional　fhan-TD,　when　the　input　signal　is　noisy　sine　wave　or　noisy　square　wave,　the　filtering　performance　of　proposed　TD　is　improved　by　37.5%　and　33.87%,　and　the　phase　lag　is　reduced　by　5.04%　and　30.34%,　respectively.　Experiments　carried　out　on　the　maglev　train　platform　show　that　the　proposed　TD　can　suppress　random　noise　existed　in　the　gap　outputs　effectively.　During　the　suspension　stage　of　maglev　train,　the　proposed　controller　can　reduce　the　overshoot　by　6.57%,　and　can　shorten　the　adjustment　time　by　0.11　s.　This　verifies　the　effectiveness　and　practicability　of　the　proposed　TD　and　its　corresponding　PID　strategy.　The　new　TD　and　its　feedback　controller　have　good　reference　value　for　engineering　implementation.　©　2023,　Central　South　University　Press.　All　rights　reserved.