System Identification Toolbox

The Signals

Models describe relationships between measured signals. It is convenient to distinguish between input signals and output signals. The outputs are then partly determined by the inputs. Think for example of an airplane where the inputs would be the different control surfaces, ailerons, elevators, and the like, while the outputs would be the airplane's orientation and position. In most cases, the outputs are also affected by more signals than the measured inputs. In the airplane example it would be wind gusts and turbulence effects. Such ``unmeasured inputs'' will be called disturbance signals or noise. If we denote inputs, outputs, and disturbances by u, y, and e, respectively, the relationship can be depicted in the following figure.

Figure 1-1: Input Signals u, Output Signals y, and Disturbances e

All these signals are functions of time, and the value of the input at time t will be denoted by u(t). Often, in the identification context, only discrete-time points are considered, since the measurement equipment typically records the signals just at discrete-time instants, often equally spread in time with a sampling interval of T time units. The modeling problem is then to describe how the three signals relate to each other.

Basic Information About Dynamic Models

The Basic Dynamic Model