Biomedical Cybernetics

Time domain analysis is a systems theoretic method that describes the relation between structure and behaviour of a system, e.g. a processing structure, with respect to its evolution in time.

Basic Concepts[]

In time domain, the description of a system has to account for both amplitude and time course of a signal. Standard test signals that are suitable for this task include Dirac's impulse and heaviside function. The system's response to an impulse is modelled by means of Duhamel's concolution integral.

Standard Quantities[]

Characteristic indicators describing the time response of the system cover the following standard quantities:

  1. The rise time tr is the time it takes the system to reach the civinity of its new equilibrium point.
  1. The settling time ts is the time it takes the system transients to decay.
  1. The overshoot Mp is the maximum account the system overshoots its vinal value divided by its final value (often expressed as percentage).
  1. The peak time tp is the time it takes the system to reach the maximum overshoot point.


Example of a 0th order linear feedback control system with load:

Proportional controller

e(t) = x(t) - yR(t)

yS(t) = G1 e(t) = G1 [x(t) - yR(t)]

y(t) = yS(t) + z(t) = G1 [x(t) - yR(t)] + z(t)

yR(t) = G2 y(t)

y(t) = G1 x(t) - G1 G2 y(t) + z(t)

x: set point, e: error, y: controlled variable, yS: manipulated variable, yR: measured variable, z: load, disturbance variable, G1: amplification factor of direct branch, G2: amplification factor of feedback path.

See the legend for an explanation of symbols.


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