Sensors differ in their response characteristics, but many follow general patterns. A first-order system is one that can be described by a first-order differential equation. A second-order system requires a second-order differential equation for its description. The thermometer is an example of a first-order system in temperature that responds directly to the heat flow induced by the difference in temperature between the sensor and the bath. A wind-measuring system consisting of a wind vane and a cup anemometer, as shown in the next illustration, involves both first-order and second-order responses. The rotor in the cup anemometer has angular momentum that resists change when the wind changes, so it is basically a first-order system in velocity with no preferred orientation or position. An exponential change between the initial and final states describes the solution to a first-order system. The wind vane is a second-order system in position that will tend to oscillate about the equilibrium position when the wind direction changes. Thus, second-order solutions include sinusoidally-varying components that describe the oscillatory nature of the system, one which often includes damping, which is represented by a damping coefficient. Many other commonly used systems fall into one of these two categories.
Drag each of the following to the type of system (first order or higher order) it represents.
The correct answers are shown below.
First Order System
Second Order System
Which of the following is(are) true of dynamic performance characteristics for a first-order system?
The correct answers are a and b.
In a first-order system, only slowly varying input fluctuations will be passed through to the output, while rapidly varying input fluctuations will be dampened or attenuated.