Nuts & Volts - January 2005

error. In the circuit in Figure 7, the integrator is performing the same task. It is integrating the error. It then provides a correction signal to the motor. We can summarize integral action in a few sentences:

1. An error must be present!

2. The integral section accumulates the error. A small error can become a large correction over a period of time.

3. As the error is accumulated, the motor is forced to correct the error.

4. Finally, the integrator will overshoot the set-point. It must produce an error opposite of the original in order to discharge the capacitor.

The final PID component is the derivative. Recall that the output of the differentiator was proportional to the slope of a wave. The same type of action is occurring in this circuit. When the motor starts to turn, the voltage measured by the resistor will be increasing or decreasing. If we have a voltage changing over a period of time, we have a ramp! The slope of this ramp changes with the speed of the motor. If the motor is going fast, the slope is high (i.e., voltage is changing fast for a given amount of time). Consequently, the output of the derivative stage will be high. The differentiator has the following attributes:

1. The motor must be moving!

2. The differentiator will have a high output voltage when the motor is moving fast and a low voltage when the motor is moving slow.

3. This signal is applied in such a way as to slow down the motor.

4. If the motor is not moving, the differentiator has 0 output voltage.

The connections for the differentiator are different than the proportional and integral sections. The differentiator receives its input directly from the resistor. It, therefore, measures only the speed at which the motor is moving. It does not care about the set-point. This is done to prevent large derivative drive signals when the set-point is changed. Again, the differentiator only responds to the speed of the motor.

Schematic

Figure 8 contains a simplified schematic of a servo motor PID control system. This schematic is an adaptation of the PID controller presented by Professor Jacob in his book, Industrial Control Electronics. This type of system has the advantage of easy tuning. This circuit is also

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