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 above shows several typical responses to a step.
Less desirable responses include:
- Oscillatory (hunting)
- 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 above 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.
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