What response behaviours can dynamic measurement systems display?

  • Measurement systems respond differently to inputs due to their inherent properties such as resistance, capacitance, mass and dead time.
  • The dynamic response of an instrument is typically described as either zero, first, or second-order:
    • The order of an ideal dynamic system is zero but this does exist in clinical practice
    • Most clinical measurement systems behave as either first-order or second-order dynamic systems
  • Each order can be modelled by using differential equations of increasing complexity
Zero-Order
First-Order
Second-Order
Description
  • The displayed value tracks the measured value exactly
  • The system is characterised as having:
    • No inertia
    • No damping
  • The displayed value moves towards the true value exponentially
  • The system is characterised as having:
    • Time-dependent storage or dissipative ability
    • No inertia
  • The displayed value oscillate around the true value before coming to steady-state
  • The system is characterised as having:
    • Time-dependent storage or dissipative ability
    • Time- dependent inertia
Graphical Representation
Differential Equation
  • Mathematically, the output from the system y(t) is given as a factor (K) of the input as function of time
  • Introduces a new variable which describes the behaviour of a first order system:
    • Time constant (Τ): the time constant of the exponential process
  • Introduces two new variables which describe the behaviour of a second order system:
    • Damping ratio (ζ): a dimensionless parameter which describes how oscillations within a system can decay once a disturbance occurs
    • Undamped natural or angular frequency (ω): the frequency at which the system would oscillate in the absence of damping
Examples
  • Does not truly exist in clinical measurement
  • Most closely demonstrated by a potentiometer
  • Demonstrated by a liquid expansion thermometer - gradually warm up from room temperature to the patient’s body temperature
  • Demonstrated by a pressure transducer measuring arterial pressure waveforms, which are affected by resonance and damping in the system