üleminekufunktsioon

Üleminekufunktsioon, also known as a transfer function in English, is a fundamental concept in control theory and signal processing. It mathematically describes the relationship between the output and input of a linear time-invariant (LTI) system. Essentially, it characterizes how a system transforms an input signal into an output signal.

The transfer function is typically represented in the Laplace domain as a ratio of two polynomials in the complex variable 's', where 's' is the Laplace transform of time 't'. If Y(s) is the Laplace transform of the output and U(s) is the Laplace transform of the input, then the transfer function H(s) is defined as H(s) = Y(s) / U(s). This representation allows for easy analysis of system properties such as stability, frequency response, and transient behavior.

Key information derived from a transfer function includes its poles and zeros. 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 provides crucial insights into the system's dynamic characteristics. For instance, the presence of poles in the right-half of the s-plane indicates an unstable system.

Transfer functions are widely used in designing controllers, analyzing feedback systems, and understanding the behavior of electrical circuits, mechanical systems, and many other dynamic processes. They provide a compact and powerful way to model and predict the response of LTI systems to various inputs.