Dynamic Characteristics

1. Dynamic Characteristics • The dynamic characteristics of sensors are due to its characteristics of being able to respond to a stimulus. • This causes error because of the delay time and time constant. • These are named dynamic error. It is the error over and above the static error. • Speed of response – how fast can it respond to a stimulus.

2. Dynamic Characteristics • To determine these quantities one applies a stimulus to the sensor and looks for response. • The stimulus might be an impulse, step or ramp (transient effects) • Sinusoidal stimulus and white noise for periodic and random dynamic errors.

3. Dynamic Characteristics • We assume that the input and output are related through a constant-coefficient linear differential equation. • The ratio of output to input can be used • Laplacian Transform of each signal and the transfer function of the sensor is used to determine the expected output. Dynamic characteristics are found by using models that involve the first and second derivative.

4. Dynamic Characteristics • We now look at a simple model of a voltage divider. • The first-order output is given in Table 1.3 • The second-order output is given by Table 1.4 • The first-order graphical results for the output are given in Fig 1.8 (next slide)

6. Dynamic Characteristics • Second order measurements are given by the differential equation: • a2 d2y(t) + a1dy(t) + a0 y(t) = 0 dt2 dt The transfer function is : Y(s) = kωn2 ___________ X(s) s2 + 2 ζωn2 s + ωn2

7. Dyanamic Characteristics • The coefficients in the transfer function are related to the constants a2 , a1 , and a0 . • The theoretical outputs for prescribed inputs are given inTable 1.5. • The second-order system response is given in Fig 1.9 (next slide.)

9. Dynamic Characteristics • Relationships for the rise time, overshoot, attenuation, natural damped angular frequency are given in the text. • The dynamic error for certain prescribed inputs are given as ed. • Discussion for an underdamped accelerometer is given as an example in the text.

11. Other Sensor Characteristics • Sensors may affect the effect to be measured, much like an ammeter affects the current to be measured. • Table 1.6 lists many of these characteristics that must be considered.

13. Input Characteristics - Impedance • Output impedance from the quantity determines the input impedance needed by the sensor. • If mismatched there is a loading error • (there are always two variables involved in a measurement of a single quantity) • Z(s) = X1(s) (effort variable) • X2 (s) (another variable)

15. Reliability • Reliability-something works without failure • Statistically described • Let λ = number of failures/time (or cycles) • Let Nf(t) be the number of failure items • Let Ns(t) be the number which survive • Then N = Nf(t) + Ns(t) • So λ = 1 dNf R (t) = lim Ns/N • dNs dt N  OO

16. Reliability • Reliability can be calculated from the failure rate • MBTF = m = 1/λ • Example 1.6 • N = 50 for t = 1000 h Nf(t) = 2 • λ = 40 failures/ million hrs • MBTF = 25,000 hrs

17. Primary Sensors • Temperature Sensors – Bimetals • Pressure Sensors • Flow Velocity & Flow Rate Sensors • Level Sensors • Force and Torque Sensors • Acceleration & Inclination Sensors • Velocity Sensors