What is Settling Time?

What is Settling Time?

Settling Time Definition

Settling time is defined as the period needed for the output of a dynamic system to remain within a certain tolerance level of its final value.

Settling Time Formula

The formula for settling time is determined by taking the negative natural logarithm of the product of the tolerance fraction and the square root of one minus the square of the damping ratio, divided by the product of the damping ratio and the natural frequency. This explains how quickly the system’s output stabilizes within a specific error margin, based on the system’s damping and oscillation characteristics.

MATLAB Techniques

Settling time can be accurately determined in MATLAB using functions like ‘stepinfo’ which analyze the step response of control systems.

Control Strategies

Reducing settling time involves adjusting the gains of PID controllers, affecting the system’s response time and stability.

Root Locus Application

The root locus method helps visualize and calculate the effects of changing system parameters on settling time, useful for system design and analysis.