Nonlinear system

Nonlinear Systems (NL ) systems are systems of systems theory, the output of which is not always proportional to the input signal ( system stimulant ). You can be much more complex than linear systems.

General principles

For nonlinear systems, in contrast to linear systems, the superposition principle does not. That is, one can not conclude from several well-known system stimulant system response pairs to an unknown system response to a given system stimulant. A further distinction is the nonlinearity of a system in static, dynamic, monovalent and polyvalent non-linearity. Since there are non-linear systems is not a closed mathematical theory, there is no general method of analysis of an unknown non-linear systems.

Generally, one can represent a mathematical model of a nonlinear system with internal state and external influences as observations

And wherein the system are described, non-linear functions.

Static nonlinear systems

Under static nonlinear systems mean those which react to a stimulus system without delay. For example, the diode in general ( except such as quick switching operations ) is viewed as a static component. Its voltage-current characteristic follows an exponential function; it is idealized in various applications as a piecewise linear treated, but remains non-linear system in the theoretical sense. Static systems can be described by a static characteristic as shown in the figures.

Non-linear dynamic systems

Under dynamic nonlinear systems mean those who thus have a "memory" and memory elements and. Thus, the system response is not determined by the instantaneous value of the system stimulus alone. It depends also on the previous history, ie the strength of the preceding excitation.

Characterization of nonlinear systems in terms of their frequency response

Upon excitation of linear systems with a sinusoidal signal obtained at the output again a sinusoidal signal of the same frequency but with a different phase and amplitude. This property is exhibited by nonlinear systems generally do not. Nonlinear systems can have on their system output frequency components, which are not included in the input signal (distortion ).

Examples from electrical engineering are:

  • If a non-linear amplifier with a single sinusoidal voltage is fed as input voltage, it also generated at the output in addition to a sinusoidal voltage harmonics. Its shares are greater with increasing oversteer.
  • If the amplifier with a superposition of two or more sine waves of different frequencies is fed, in addition intermodulation occurs, and there are combination frequencies.
  • If several modulated AC voltages are amplified simultaneously, there may be cross-modulation. Then an AC voltage partially takes over the modulation of the other ( Luxembourg effect).