RMS stands for “Root Mean Square.”
In mathematics and statistics, RMS is a measure of the magnitude of a set of numbers, typically used to measure the power of a signal. The RMS value of a signal is the square root of the mean of the squares of the signal’s values. It is a measure of the effective value of a signal, and is often used in engineering and physics to describe the average power of a signal.
For example, in electrical engineering, RMS is used to measure the power of an alternating current (AC) signal. The RMS value of an AC signal is equal to the value of a direct current (DC) signal that would produce the same power dissipation in a resistor. This is why RMS is often used as a standard measure of power in AC systems.
In audio signal processing, RMS is often used to determine the loudness of a sound. RMS amplitude is a more reliable measure of perceived loudness than peak amplitude because our ears respond to the average energy of a sound, not the peak energy.
In control system, RMS is used to measure the stability of a system, by measuring the deviation of the system response from the steady state. In this way, RMS error is used as a performance measure of control systems.
In short, RMS (Root Mean Square) is a measure of the magnitude of a set of numbers, typically used to measure the power of a signal. It is the square root of the mean of the squares of the signal’s values. RMS is often used in engineering, physics, audio signal processing and control systems, and is a more reliable measure of perceived loudness than peak amplitude, and measure of stability and performance of control systems.