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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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Signal Response of Measurand?
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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
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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 = S o /S i –S min <S i <S max Overloaded in this range.
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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
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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
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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
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Dynamic Characteristics of Simplified Mechanical Systems F(t) = general excitation force = fundamental circular forcing frequency Generalized Equation of Motion for a Spring Mass Damper System(1-axis)
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(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 –F o =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 –P A =initial magnitude of process at t=0 – = time constant = /k 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.
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Figure (a) depicts progressive process Figure (b) depicts decaying process
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F(t) = Fo cos t (I)FIRST ORDER SYSTEM (I.B) Harmonically Excited
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PHASE LAG
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First Order System – Harmonically Excited – Example T emperature Probe Example
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TEMPERATURE PROBE EXAMPLE - Continued
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Step input –F=0 when t<0 –F=F o when t>0 Underdamped Eq: (II) SECOND ORDER SYSTEM (II.A) Step Input
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OVERDAMPED SECOND ORDER SYSTEM = / C >1 This represents both damped and under-damped cases.
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(II) SECOND ORDER SYSTEM (II.B) Harmonically Excited F(t) = Fo cos t
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MICROPHONE EXAMPLE Second Order System – Harmonically Excited Example Microphone Example
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MICROPHONE EXAMPLE
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