Adjustable Speed Drives (ASD) need to have the at least the torque and velocity regulators tuned. The tension regulator if used will also need to be tuned. Tuning can be done with Auto-Tune or done manually. Tuning is a process of setting regulator gains to give a desired response. In web handling, tuning applies a ** step function** (sudden increase) to the setpoint. The desired response is a curve that rises rapidly and then more slowly approaches the new setpoint. The desired response follows an exponential curve. The diagram below shows several typical responses to a step.

Less desirable responses include:

*Instability**Oscillatory*(hunting)*Over-Shoot**Accuracy**Steady State Error**Dead Time*

There are industry accepted measurements and calculations that can be used to describe the undesirable traits and to characterize the desired exponential response.

The only useful measurement for *instability* and *oscillatory* systems is the *Period* (seconds) or *Frequency* (Hz= 1/Period), *Angular Frequency* (2π*Frequency radians/second).

The desired response is measured by its *time constant* in seconds. The time constant is the time to reach 63% of the setpoint. The time constant can be converted to *bandwidth* in Radians/second. *Bandwidth* and *time constant* are inversely related.

*Over-Shoot* is measured as a percentage of the step size. Measure the highest peak and compare with the setpoint value. A *Critically-Damped* system is the fastest exponential response without over-shoot. *Over-Damped* systems look identical to the Critically-Damped response, except they have a greater time constant/lower Bandwidth. *Under-Damped* systems have overshoot.

*Dead time* is undesirable and always limits regulator response.

The chart below shows typical responses. The response may be of a torque regulator, speed regulator or tension regulator. The chart shows an ideal response with time constant of 0.5 seconds, an under-damped response with 30% overshoot and an over-damped response.

**Important assumptions**

The discussion above assumes the system is a single loop, second order, type 1 (single integrating). This applies to drives used in web handling. The ideal is a true approaching exponential curve defined by this equation.

1-e^{-t/τ}

## Comments