1. Defining Settling Time ($t_s$): Settling time is specifically defined as the time required for the response curve to reach and stay within a specified range (usually 2% or 5% tolerance band) of its final steady-state value. It essentially measures how long it takes for the transient oscillations to "settle down."
2. Comparison with other parameters:
• Rise time ($t_r$): The time taken for the response to rise from 10% to 90%, or 0% to 100% of its final value for the first time.
• Delay time ($t_d$): The time required for the response to reach 50% of the final value for the first time.
• Peak time ($t_p$): The time required for the response to reach the very first peak of the overshoot.
3. Calculation: For a second-order system with a damping ratio $\zeta$ and natural frequency $\omega_n$:
• For 2% tolerance: $t_s \approx \frac{4}{\zeta \omega_n}$
• For 5% tolerance: $t_s \approx \frac{3}{\zeta \omega_n}$
Thus, the term that describes the arrival at the steady-state "equilibrium" is the settling time.