How is frequency response used to test the stability of a control system?

In control theory, the stability of a system can be assessed by analyzing its frequency response, which measures how the system reacts to a continuously varying input signal across a range of frequencies.1

To determine stability using this method, the output of the control system is compared to the input signal in terms of two primary factors:
* Amplitude: The magnitude of the output relative to the input.
* Phase: The degree to which the output signal is out of step with the input signal.

This analysis can be performed experimentally, particularly in electrical systems, or calculated mathematically if the system's constants are known. Mathematical modeling is especially effective for systems that can be described by ordinary linear differential equations, and various graphic shortcuts are often employed to simplify the study of these responses. By evaluating these characteristics, engineers can identify potential instabilities, such as the overcorrection phenomenon known as hunting, and implement necessary damping to ensure the system remains stable.1