ME- 495 Mechanical and Thermal Systems Lab Fall 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 = S o /S i –S min <S i <S max 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 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 –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.

Figure (a) depicts progressive process Figure (b) depicts decaying process

F(t) = Fo cos  t (I)FIRST ORDER SYSTEM (I.B) Harmonically Excited

PHASE LAG

First Order System – Harmonically Excited – Example T emperature Probe Example

TEMPERATURE PROBE EXAMPLE - Continued

Step input –F=0 when t<0 –F=F o when t>0 Underdamped Eq: (II) SECOND ORDER SYSTEM (II.A) Step Input

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 cos  t

MICROPHONE EXAMPLE Second Order System – Harmonically Excited Example Microphone Example

MICROPHONE EXAMPLE