System Identification Toolbox

The Basic Dynamic Model

The basic relationship is the linear difference equation. An example of such an equation is the following one.

Such a relationship tells us, for example, how to compute the output y(t) if the input is known and the disturbance can be ignored:

The output at time t is thus computed as a linear combination of past outputs and past inputs. It follows, for example, that the output at time t depends on the input signal at many previous time instants. This is what the word dynamic refers to. The identification problem is then to use measurements of u and y to figure out:

• The coefficients in this equation (i.e., -1.5, 0.7, etc.).
• How many delayed outputs to use in the description (two in the example:

  y(t-T) and y(t-2T)).

• The time delay in the system is (2T in the example: you see from the second equation that it takes 2T time units before a change in u will affect y).
• How many delayed inputs to use (two in the example: u(t-2T) and u(t-3T)). The number of delayed inputs and outputs are usually referred to as the model order(s).

The Signals

Variants of Model Descriptions