ME- 495 Mechanical and Thermal Systems Lab Fall 2011
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ME- 495 Mechanical and Thermal Systems Lab Fall 2011 Chapter 5: MEASURING SYSTEM RESPONSE Professor: Sam Kassegne, PhD, PE
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ME- 495 Mechanical and Thermal Systems Lab Fall 2011. Chapter 5: MEASURING SYSTEM RESPONSE Professor: Sam Kassegne, PhD, PE. Signal. Response of Measurand?. RESPONSE. - PowerPoint PPT Presentation
Transcript of ME- 495 Mechanical and Thermal Systems Lab Fall 2011
ME- 495Mechanical and Thermal
Systems LabFall 2011
Chapter 5: MEASURING SYSTEM RESPONSE
Professor: Sam Kassegne, PhD, PE
Signal
Response of Measurand?
RESPONSE• System Response: an evaluation of the systems
ability to faithfully sense, transmit and present all pertinent information included in the measurand and exclude all else:
• Key response characteristics/components are:– Amplitude response– Frequency response– Phase response– Slew Rate
COMPONENTS OF SYSTEM RESPONSE
1) Amplitude response: • ability to treat all input
amplitudes uniformly– Overdriving – exceeding
an amplifiers ability to maintain consistent proportional output
– Gain = Amplification = So/Si
– Smin<Si<Smax
Overloaded in this range.
2) Frequency Response
• ability to measure all frequency components proportionally
• Attenuation: loss of signal frequencies over a specific range
Attenuated in this range.
COMPONENTS OF SYSTEM RESPONSE
3) Phase Response
• amplifiers ability to maintain the phase relationships in a complex wave.
• This is usually important for complex waves unlike amplitude and frequency responses which are important for all types of input wave forms. Why?
COMPONENTS OF SYSTEM RESPONSE
• 4) Delay/Rise time: time delay between start of step but before proper output magnitude is reached.
• Slew rate: maximum rate of change that the system can handle (de/dt) (i.e. for example 25 volts/microsecond)
COMPONENTS OF SYSTEM RESPONSE
Dynamic Characteristics of Simplified Mechanical Systems
• F(t) = general excitation force = fundamental circular forcing frequency
n
n
2n
2n
1nnn
o
2
2
c
A
Btan
BACn
)tncos(C2
A)t(F
Ksdt
ds
dt
sdm
g
1)t(F
Generalized Equation of Motion for a Spring Mass Damper System(1-axis)
(I)FIRST ORDER SYSTEM(I.A) Step Forced
If mass = 0, we get a first-order system.
E.g. Temperature sensing systems
• F(t)=0 for t<0
• F(t) = F0 for t >= 0– t=time, k=deflection constant– s=displacement, =damping coefficient
– Fo=amplitude of input force
• This can be reduced to the general form:
(after integration over time and simplification)– P=magnitude of any first order system at time t
– P=limiting magnitude of the process as t
– PA=initial magnitude of process at t=0
= time constant = /k
ksdt
ds)t(F
t
A ePPPP
The above equation could be used to define processes such as a heated/cooled bulk or mass, such as temperature sensor subjected to a step-temperature change, simple capacitive-resistive or inductive-resistive circuits, and the decay of a radioactive source.
Figure (a) depicts progressive process
Figure (b) depicts decaying process
1f2_as_works__&0_and_1G_ideally
)f2(tan)f(_:becomes_response_phase
kttancons_time
T
1)Hz(frequencyf
k
FF_of_ntdisplaceme_staticP
process_dynamic_periodic_the_of_amplitude_imummaxP
)f2(1
1
P
P)f(G
1
os
d
2s
d
F(t) = Fo cost
(I)FIRST ORDER SYSTEM(I.B) Harmonically Excited
ksdt
ds)t(F
PHASE LAG
First Order System – Harmonically Excited – ExampleTemperature Probe Example
TEMPERATURE PROBE EXAMPLE - Continued
TEMPERATURE PROBE EXAMPLE - Continued
• Step input– F=0 when t<0
– F=Fo when t>0
• Underdamped Eq:
(II) SECOND ORDER SYSTEM(II.A) Step Input
Ksdt
ds
dt
sdm
gtF
c
2
21)(
OVERDAMPED SECOND ORDER SYSTEM
= / C >1
This represents both damped and under-damped cases.
(II) SECOND ORDER SYSTEM(II.B) Harmonically Excited
F(t) = Fo cost
MICROPHONE EXAMPLE
Second Order System – Harmonically Excited ExampleMicrophone Example
MICROPHONE EXAMPLE
