Control Engineering

Can a control increase system performance?
June 4, 2007

The short answer is: “Absolutely not.”

The long answer is: “Absolutely not,” with an explanation.

Let’s start with what performance is, really. According to the 7th (out of 8) definition from Dictionary.com:

performance – noun, the manner in which or the efficiency with which something reacts or fulfills its intended purpose.

I submit that we generally measure perfomance by quantifying some dimension of what a system is supposed to do, such as the speed of a vehicle, the power put out by a motor, the centripetal force applied by an airplane’s wings in a turn, the compound annual growth rate of the U.S. economy, etc. The highest value the system is physically capable of achieving is an intrinsic property of the system, and may be determined either theoretically or by actual test. The actual value is some other value determinable by measurement right now. In general, we can define a relative performance value as the ratio of the actual performance to the maximum performance.

“Maximum” means it can’t do any more.

Relative performance is a positive definite quantity between zero and 1.

A control is an auxiliary subsystem added to the original (uncontrolled) system to modify its performance. It does so by reducing performance below the maximum.

The throttle on an automobile engine reduces its power output below what it would produce if the throttle were removed.

A clutch reduces the coupling between a drive train’s input and output below what it would be if there was only a solid shaft.

Sometimes, however, a control appears to induce the action the performance number measures. For example, the control surfaces on an aircraft induce flight attitude changes that make the craft turn. No controls, in that case, means no action. One might be deluded by this behavior into imagining that the control creates the action and that more control might mean more action.

That, however, isn’t so. If you carefully analyse such controls, you will find that they create the action by redirecting something that has its own physical limitation. In the turning-aircraft example, the craft’s ailerons rotate the fuselage around its roll axis, while the pilot (in this maneuver) uses the rudder to rotate the craft around its yaw axis. This changed attitude (called a bank) redirects part of the wing’s lift to create the required centripetal force. The whole procedure robs lift to pay for side force. The limit is, therefore, the amount of lift taken away before the aircraft falls out of the sky.

You can (and, in fact, must) increase airspeed to create additional lift, but that, too, has its limits. There’s a little thing called called maximum maneuvering speed (V_a) published for every aircraft. V_a is the airspeed at which the lift force at the stall angle of attack (beyond which airflow separates and the wing loses lift) equals the aircraft’s structural limit minus some safety margin.

If you make a maximum-deflection turn at higher than V_a, the aircraft will make a nasty “eeek” sound as the wings start to separate from the fuselage. If you try it at less than V_a, the wing stalls and won’t turn any tighter. More robust controls won’t do anything but get you to the limit faster.

In short, control systems cannot increase performance, only impede it.

That said, controls can help you when full performance will lead to bad results. Remove the throttle, and your aircraft will exceed V_a with you helplessly along for the ride.

Posted by on June 4, 2007 | Comments (1)