Controllers balance performance with closed-loop stability

Vance J. VanDoren Ph.D., P.E., consulting editor -- Control Engineering, 5/1/2000

If high-speed response is not required, any continuous process can be controlled easily enough. A feedback controller need only measure the process variable, determine if it has deviated too far from the setpoint, apply the necessary corrective effort, wait to see if the error goes away, and repeat as necessary. This closed-loop control procedure will eventually have the desired effect provided the controller is sufficiently patient.

A child playing on a swingset uses closed-loop instability to keep the swing going.

Unfortunately, patience is not generally considered a virtue in process control. A typical controller will apply a whole series of corrective efforts well before its initial efforts have finished affecting the process. Waiting for the process to settle out every time the controller makes a move generally leaves the process out of spec for so long that the controller becomes virtually useless.

Not so fast

On the other hand, a controller that tries to eliminate errors too quickly can actually do more harm than good. It may end up over-correcting to the point that the process variable overshoots the setpoint, causing an error in the opposite direction. If this subsequent error is larger than the original, the controller will continue to over-correct until it starts oscillating from 100% effort to 0% and back again.

This condition is commonly called closed-loop instability or simply hunting. An aggressive controller that drives the closed-loop system into sustained oscillations is even worse than its overly patient counterpart because process oscillations can go on forever. The process variable will always be too high or too low. Worse still, the oscillations can sometimes grow in magnitude until pipes start bursting and tanks start overflowing.

Stabilizing techniques

The Ziegler-Nichols closed-loop method is arguably the most straightforward approach for designing stable control loops. It applies to PID controllers, which can be made more or less aggressive by adjusting their proportional (P), integral (I), and derivative (D) gains. The higher the gains, the harder the controller works to eliminate errors.

Ziegler and Nichols found that if they gradually turned up the proportional gain on a P-only controller it would eventually start over-correcting and force the process into sustained oscillations. By reducing the gain by 50% at that point, the loop would become stable again. Simple enough!

Less obvious is how to add integral and derivative action to make the controller even more responsive without risking closed-loop instability. Ziegler and Nichols determined through trial and error that increasing the integral and derivative gains in a prescribed manner would actually allow the proportional gain to be increased to as much as 75% of the value that caused instability. Their famous 'tuning rules' allowed control engineers for the first time to design two-term (PI) and three-term (PID) controllers that would keep the closed-loop system stable, yet fast enough to eliminate errors in a timely manner.

A child on a swingset, for example, uses closed-loop instability to keep the swing going. By applying a control action while the swing is still in motion (i.e., by 'pumping'), the child can force the swing back and forth past its resting position. Conversely, a process controller would try to keep the closed-loop system stable by forcing the magnitude of Q to grow ever smaller.