If you want to operate your mixer between 100 and 200 rpm, you can't do it with a fixed speed motor and a variable speed control.  The best variable speed controls will not effectively reduce the speed more than about 4:1, not the "advertised" speed reductions of 10:1.  Even if you were able to reduce speed by a 10:1 factor, the motor can never deliver more than constant torque.  So a one hp motor with a 10:1 speed reduction could never deliver more than 0.1 hp.
You need a motor with a gear box.  A typical single-reduction gear box would give you a 5:1 speed reduction, which should be able to get your 100 to 200 rpm with a variable speed control.  Be sure that your impeller size is appropriate for that speed range.  A 2:1 speed range may give you a 32:1 power range.

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