What do amplitude and phase show when comparing the input and output of a control system?

In the context of control systems, analyzing the frequency response involves comparing the output signal to the input signal across various frequencies. This comparison is measured using two primary metrics:

• Amplitude: This represents the maximum displacement of the signal, indicating the gain or attenuation the system applies to the input signal at a given frequency.12
• Phase: This measures the degree to which the input and output signals are out of step with each other. When comparing periodic motions, signals are considered in phase if their maximum or minimum displacements occur simultaneously; if they do not, the phase difference indicates how much the output lags or leads the input.12

By evaluating these two factors, engineers can determine the stability and performance characteristics of a control system, helping to identify potential issues like overcorrection or the need for damping to ensure the system operates as intended.2