Overføringsfunksjoner

Overføringsfunksjoner, known in English as transfer functions, are mathematical representations used in control theory and signal processing to describe the relationship between the input and output of a linear, time-invariant (LTI) system. They are typically expressed in the Laplace domain as the ratio of the Laplace transform of the output signal to the Laplace transform of the input signal, assuming all initial conditions are zero. The Laplace transform is employed because it converts differential equations, which often describe dynamic systems, into algebraic equations, making analysis and manipulation easier.

The transfer function provides a concise way to characterize a system's dynamic behavior without needing to know the internal workings of the system itself. It encapsulates how the system will respond to different frequencies and how stable it is. Key properties of a system, such as its poles and zeros, are directly derived from the transfer function. Poles are the roots of the denominator polynomial, and zeros are the roots of the numerator polynomial. The location of these poles and zeros in the complex plane reveals crucial information about the system's stability, transient response, and frequency response.

Overføringsfunksjoner are fundamental tools for system analysis, design, and simulation. They allow engineers to predict how a system will behave under various conditions, design controllers to modify system performance, and compare different system designs. In essence, a transfer function is a compact and powerful way to understand and manipulate the input-output dynamics of LTI systems.