Engineering Measurements

MENG $231$

Home Work #$2$

Measurement System Behavior $-$ Dynamic System Response

$Q_1$ : Ideally, sensors respond immediately to changes in the parameter being measured. However,

sensors need some time to adjust to changes, and often show oscillations that take some time to

stabilize.

In a report format, discuss the dynamic system response of sensors and their associated electronic

circuits. The dynamic system response of the system is typically tested with different types of

inputs. Briefly explain such types. Provide one physical example representing either Zero$-$order,

First$-$order, or Second$-$order measurement system, along with analysis demonstrating one type

of input. Identify the parameters that control the behavior and response of a measurement system.

Note: Students may work in groups of maximum $3$ members to conduct the work. No word$/$page

limit is required for the report $($at least $2-3$ pages$).$

Supplementary Notes

The input measured variable $x$ can be either static $($steady$)$ or dynamic $($unsteady$).$ If the input is

static, the output is generally some factor $C$ times the input $x,y=C.x,$ where $C$ is called the static

sensitivity of the measuring system. $(y$ has a linear relationship with $x).$

For time$-$dependent $($dynamic$)$ measurements, the behavior is described by a differential equation.

Such systems are known as dynamic systems, and their behavior is therefore called dynamic

system response, featuring some nonlinear relationship like $y=C_{1}x+C_2{x}^2.$

The relationship between input and output for a general measuring system can be expressed as an

ordinary differential equation $($ODE$).$ The order of a dynamic system is determined by the order

ODE. Now, if the input $x$ is not constant, but changes with time $($dynamic$),x=x(t),$ the output $y$

would respond instantaneously to changes in $x,y(t)=Cx(t),$ which is called $\text{'}$an ideal measuring

system'. The order of an ideal dynamic system is zero, i$.$e$.,n=0,$ called zero$-$order dynamic

system, with most of real systems are first