Teisendusfunktsioonid

Teisendusfunktsioonid, known in English as transfer functions, are a fundamental concept in control systems engineering and signal processing. A transfer function is a mathematical representation of the relationship between the input and output of a system, assuming the system is linear and time-invariant. It is typically expressed in the Laplace domain or the z-domain, depending on whether the system deals with continuous or discrete time signals, respectively.

In essence, a transfer function describes how a system transforms an input signal into an output signal. It is defined as the ratio of the Laplace transform of the output signal to the Laplace transform of the input signal, with all initial conditions assumed to be zero. This ratio allows engineers to analyze the system's behavior, such as its stability, frequency response, and transient response, without needing to solve the system's differential or difference equations directly.

The poles and zeros of a transfer function are critical parameters that determine its characteristics. Poles are the roots of the denominator polynomial of the transfer function, and zeros are the roots of the numerator polynomial. Their locations in the complex plane provide insights into the system's stability and dynamic behavior. For instance, poles in the left half of the s-plane (for continuous systems) indicate stability. Transfer functions are widely used in designing controllers, analyzing filter performance, and understanding the dynamics of mechanical, electrical, and other physical systems.