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## ME- 495 Mechanical and Thermal Systems Lab Fall 2011

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**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.**COMPONENTS OF SYSTEM RESPONSE**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)**Dynamic Characteristics of Simplified Mechanical Systems**Generalized Equation of Motion for a Spring Mass Damper System(1-axis) • F(t) = general excitation force • = fundamental circular forcing frequency**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 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**FIRST ORDER SYSTEM(I.B) Harmonically Excited**F(t) = Fo cosWt**First Order System – Harmonically Excited –**ExampleTemperature Probe Example**(II) SECOND ORDER SYSTEM(II.A) Step Input**• Step input • F=0 when t<0 • F=Fo when t>0 • Underdamped Eq:**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 cosWt**MICROPHONE EXAMPLE**Second Order System – Harmonically Excited ExampleMicrophone Example