The only 1ph AC induction motors that use RPM control are typically shaded poles motors, fans etc, and this is done with a Triac style controller, most of the cap start/run motors do not control well this way due to dropping out of run at low rpm or on load.
There are some PSC motors as shown in your pic that also have a Triac style controller but generally again it is fan usage only, no good for the application you need.
You are probably better off to get a DC motor off ebay or ex treadmill type.
M.