Optical tachometers that produce a frequency proportional to RPM are popular feedback sources for precision analog motor speed control. This usually involves a frequency-to-voltage converter (FVC) to convert the tachometer output to a voltage that’s then input to a conventional servo. Though it typically works fine, it’s unnecessarily complicated and requires a tachometer with a relatively high pulse/revolution characteristic to allow for both a reasonably fast loop response and adequate ripple filtering in the FVC.

The circuit shown circumvents those problems by replacing the usual FVC with period-to-voltage converter A2. The motor speed setpoint is adjusted with R1 as follows: The voltage on integrator A2 (V_{r}) is a negative-going sawtooth with slope given by I_{r}/C1. I_{r} = (V3 - V1)R1/(R2R3), so if 1/F_{m} is the period of the tachometer pulses, the peak-to-peak swing of V_{r} = (V3 - V1)R1/(F_{m }R2R3C1).

During the positive half-cycles of the tachometer square wave, S3 connects C3 to A2 so that the voltage on C3 tracks the sawtooth. On every negative square-wave transition, C3 is connected to the summing point of A4. This happens in such a way that if V_{r} < (V3 - V1), then a positive increment of charge is deposited on the summing point. This tends to drive A4 negative and thus reduce the voltage applied to the motor, slowing it down._{}

By contrast, if V_{r} > (V3 - V1), then a negative increment is dumped onto C4 and the motor voltage and speed are increased. The net result is for A4 to converge on the single motor voltage that makes F_{m} = R1/(R2R3C1) because only then is V_{r} = (V3 - V1). Consequently, the equilibrium tachometer frequency and therefore motor speed is directly proportional to R1 and independent of the absolute values of V1 and V3, removing any requirement for precision voltage references. Only the stability of the ratios of R1, R2, R3, and C1 contribute significantly to the error budget of the controller. Therefore, V_{s} supply voltages from 20 V to 35 V give the same accuracy.

Dc stability of the controller is assured by the relationships derived previously and by the error integration performed by A4. But, as in all servos, dynamic convergence is another matter. Damping of the system response and stable, over-shoot-free response to perturbation are provided by the C4/C5 ratio and R4 x C5 time constant. The values for these parts, shown in the figure, worked well in the prototype. Different motors connected to different loads might require tweaking of these values. In general, the greater the C4/C5 ratio and R4 x C5 time constant, the greater net damping and tolerance of high load inertia.

One additional consideration is what happens if the motor stops and F_{m} = 0. Because the feedback path depends on charge transfers between C3 and C4, and since these transfers cease if F_{m} = 0, some means is needed to “jump-start” the servo. Comparator A3 does this by slewing A4 positive whenever V_{r} is allowed to ramp below V4. Accurate charge transfers in normal operation are promoted by the crisp square wave produced by Schmitt trigger S1.

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