Transmission system

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Neutronstar2 ( discussion ) 10:28 pm, Mar 22nd 2020 (CET)

A transmission system (often just short system ) is in the system theory , a mathematical model of a process that a signal converts and transmits. The signal supplied is called the input signal and the resulting converted signal is called the output signal . The way in which the signal is converted or how these two signals are related to one another is described by the transfer function.

Single-size and multi-size systems

A transmission system that has only one input and one output is called a single- variable system or SISO system (from English single input, single output )

If the system has several inputs and outputs, one speaks of a multi-variable system or MIMO system (from English multiple input, multiple output ).

The SIMO systems (from single input, multiple output ) with one input and several outputs still exist as a mixed form . And vice versa, MISO systems (from multiple input, single output with multiple inputs and only one output).

Dynamic and static systems

• static: The value of the output signal y (t) depends at any point in time t only on the current value of the input signal u (t). (algebraic description)
• dynamic: The output signal depends on previous input signals. (Description using differential equations)

Systems with concentrated and distributed parameters

• concentrated parameters: effect arrangements with location-independent signals (description by means of ordinary differential equations)
• distributed parameters: effect arrangements with position-dependent signals (description using partial differential equations)

Linear and non-linear systems

A system is called linear if the following two conditions are met:

• Reinforcement principle: ${\displaystyle f(k\cdot u(t))=k\cdot f(u(t))}$
• Overlay principle: ${\displaystyle f\left(u_{1}\left(t\right)\right)+f\left(u_{2}\left(t\right)\right)=f\left(u_{1}\left(t\right)+u_{2}\left(t\right)\right)}$

If either or both of these conditions are not met, the system is said to be non-linear.

Time-variable and time-invariant systems

• time-variable: system parameters change over time (e.g. mass of a rocket). Adaptive controllers are necessary to influence such systems.
• time-invariant: systems with constant system parameters.

Systems with continuous and time-discrete signals

For processing by computers, continuous signals from physical systems are converted into time-discrete signals. This system is called the scanning system.