Motor controller operates without tachometer feedback
Bruce Trump, Burr-Brown Corp, Tucson, AZ -- 12/9/1999
Speed controllers have long exploited the reverse-EMF characteristics of
dc motors to control their speed. These linear driver circuits use power op amps
to create a negative resistance drive to the motor that counteracts the voltage
drop in the motor's series resistance (Reference 1). The circuit in Figure 1 shows an implementation of this type of speed control using a PWM drive, which reduces power dissipation in the drive circuitry.Control voltage VIN sets the speed, and IC1, Q1, and R3 convert VIN to a 0- to 200-µA current. The current source controls the duty cycle of the PWM driver, IC2, at Pin 3. D1, D2, and R5 prevent the circuit from pulling the control input too low, which can cause an inversion in the control loop.
Motor current flows through the internal switching transistor in IC2 out the common terminal and through the current-sense resistor, RS. The circuit filters and scales the voltage across the sense resistor to provide positive feedback to the input circuitry through R2. With the proper amount of positive feedback, an increase in motor load increases motor current, which increases duty-cycle drive to maintain constant speed.
The equation of speed balance is

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