COMPUTING SCIENCE

# Everything Is Under Control

Can control theory save the economy from going down the tubes?

# Control Freaks

On first acquaintance, the idea of feedback control seems straightforward enough. Consider the design of a cruise-control system for an automobile. A minimal version measures the current speed of the car, compares it with the desired speed, then adjusts the throttle by an amount proportional to the difference. If the car slows somewhat—perhaps on an upgrade—the controller senses the discrepancy and opens the throttle wider, so that the car regains some of the lost speed.

But there is more to control theory than this simple proportional-feedback mechanism. A drawback of pure proportional control is that the car never quite attains the requested speed; as the error diminishes, so does the feedback signal, and the system settles into a state with some nonzero offset from the correct velocity. The offset can be eliminated by another form of feedback, based not on the error itself but on the integral of the error with respect to time. In effect, the integral measures the cumulative error, which keeps growing if the speed differs even slightly from the set point. Thus integral control ensures that over the long term the net error approaches zero and the average speed converges on the set-point speed.

Yet integral control has drawbacks of its own. Suppose the car cannot maintain a commanded speed of 60 on an upgrade; an integral controller might compensate by going 80 on the other side of the hill, which could get you a speeding ticket. More generally, integral control has a tendency to overshoot and oscillate around the set point. A remedy is to add still another form of feedback, based on the time derivative of the error signal. Derivative feedback opposes rapid changes in speed and thus tends to damp out oscillations.

**IN THIS SECTION**

EMAIL TO A FRIEND :

# Comments

In the last section, the author says Sims of Yale imposed the policies of the modern Fed on the economy of the 1930s and vice versa and that swapping strategies had little effect on the outcome. Writ...

posted by David Hawla

May 5, 2009 @ 4:50 PM

In response to David Hawla:
Thanks for that note of clarification. Of course you're correct. Sims looked at two broad periods, roughly 1919-1939 and 1949-1998. Obviously there was a lot of variation ...

posted by Brian Hayes

May 6, 2009 @ 9:13 AM

Engineering is about physical, hence logically but not necessarily numerically quantifiable laws. Expansion tanks (cf savings) allow a hydraulic system to expand and contract as required, but of cour...

posted by David Taylor

June 30, 2009 @ 9:26 AM

**Of Possible Interest**

**Feature Article**: Twisted Math and Beautiful Geometry

**Spotlight**: First Person: Exploring the Unconscious Brain

**Feature Article**: Social Media Monitors the Largest Fish in the Sea

**Other Related Links**