Without getting tangled in a horde of details, PID (proportional-integral- derivative) control enables you to benefit from the fast response of solid-state adjustable-speed drives by tuning the electrical system to the mechanical characteristics. By doing so, you obtain the optimum system performance for maximum productivity and quality.

To understand how this works, let’s look at a simple yet typical example. A motor turns a long shaft that is connected to a heavy roll, *Figure 1*. If we clamp the motor end of the shaft and use a long lever on the roll end, we can turn (wind-up) the shaft a few degrees. If we then release the roll end, the roll oscillates. The frequency of this oscillation is the natural frequency of the system. The stiffer the system, the higher the system resonant frequency.

During steady-state operation, this system frequency is rarely noticed. However, during transient conditions — accelerating, decelerating, and during sudden load changes — the system frequency can raise havoc with the machine. This can occurr during a transient condition when the load oscillates above and below the desired speed — an *unstable* condition.

With a modern drive, a motor can apply torque to a shaft almost instantaneously. Sensitive measuring instruments show that a shaft winds up — the motor-end of the shaft turns before the roll end. However, for maximum system performance, a drive should change the speed and torque as fast as the process and machine can accept the change without oscillating or operating in an unstable condition. Achieving that optimum point is where PID control enters the picture. PID control often enables higher machine performance than a drive can deliver without PID.

### What it is

PID stands for three basic control elements — proportional plus integral plus derivative. Each contributes to optimizing machine (system) operation.

**Proportional**. To illustrate how the proportional section works, consider the roll application in *Figure 1*, and assume that the roll is part of a process with changeable loads. By putting a velocity transducer on the shaft, the drive controller can compare the actual speed with the required speed. (The difference between the two values is the *error* signal.) If the roll slows down (or speeds up) the drive can apply torque to increase (or decrease) the roll speed back to the required level. The question is, “How much corrective torque should be applied and how quickly?”

To determine this, let’s first establish that the ratio of output torque to error signal is *gain*. In this case, the ratio is constant so the output is *proportional* to the error. Thus we have the “P” in the PID control.

To get the best velocity control in the example (assuming this is a small machine, not a rolling mill), we set the drive to deliver the maximum torque as fast as possible by setting the proportional gain at maximum. In some systems, this is fine. In others, we get a machine with a soprano voice. The machine starts talking to us by complaining that it doesn’t like all that “go juice” coming out of the amplifier and causing the motor to produce all that torque. The “voice” of the system is a combination of frequencies, composed mostly of the natural system frequency. This machine has become unstable. The proportional part of the PID control is set too high, so the voice is calmed by reducing this gain setting.

Here’s why the singing. The mechanical system couldn’t keep up with the corrections initiated by the control, *Figure 2*. The control overshots the mark, then undershoots. The electrical signal and the mechanical components get out of phase and the singing starts. This is analogous to releasing the lever and letting the roll oscillate.

**Integral.** Fortunately, there are circuits that can enable more proportional gain, for higher machine performance, without the dire consequences. This circuit is an integrator that alters the drive’s frequency response (quantified on a Bode plot, PTD, 4/90). The magnitude of the integrator’s contribution is defined by the *integral gain.*

Continuing our example, by having integral gain, we can increase the proportional gain so the system just starts to go unstable (sings), then reduce it slightly. Next, increase the integral gain until the system goes unstable; back it off slightly; return to the proportional gain and increase it again to just below the unstable point. The proportional gain is now higher than it was without the integral gain, and the system responds faster without operating in an unstable condition.

**Differential.** At first glance, it may seem that systems need only P and I. But systems also change their operating characteristics during operation. Typical example: An eccentric driving a linear travel mechanism that has significant changes in the reflected inertia during the operating cycle. Winders and unwinders, which change inertia as the roll diameter changes, are other examples.

In both types of systems, as the inertia changes, the speed begins to overshoot then undershoot the desired speed until it settles out.

Reducing the acceleration rate reduces the magnitude of the speed deviations, but the number of speed deviation cycles remains the same.

Therefore, a method to anticipate conditions is desirable for both of these types of systems. Enter the *differential* part of PID. This capability measures the *rate of change* of the difference between the desired speed and the actual speed (this difference is the error signal) then the PID controller changes the drive gain to anticipate changes.

In turn, the differential gain adjustment, which is adjusted during setup, determines the magnitude of the change of drive gain per unit of error signal. This adjustment is also selected to reduce or eliminate the speed oscillations during changes in load inertia or similar operating characteristic. If the gain is set too high, the drive is sluggish. The optimum setting is often one overshoot and one undershoot before the speed stabilizes.

The WR^{2} compensation included in dedicated winder controls is a differential gain adjustment.

This differential portion of the PID control is sensitive to noise in the control and feedback circuits. Unlike the integral portion, which reduces the influence of noise, the differential portion accentuates any noise and can cause faulty machine operation.

### Digital PID

Some fully digital adjustable-speed drives offer the capability to program the values for the PID settings. This, too, requires a thorough machine analysis, or use of the trial-and-error method for the first machine. Then these values can be used for duplicate systems. You should review the instruction manual for a specific drive to establish the details of this method.

### Caveat

Although the PID control capability offers additional opportunities to maximize the performance of many systems, it can generate laziness. Engineers may be tempted to omit a major step — optimize the design of the machine itself. The final system can be no better than the system mechanics.

For maximum productivity, the best design requires analyzing many factors including viscous damping, backlash, windage, friction, reflected inertia, and all the other factors that influence the total productivity, not just the speed oscillations.

**John H. Davison** is a technical marketing and sales consultant in the Pittsburgh suburb of Bethel Park, Pa.

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