Final answer:
Pole-zero cancellation can be approximated when common factors exist in the numerator and denominator of the system transfer function. To determine percent overshoot, settling time, rise time, and peak time, a detailed analysis of the system response is needed.
Step-by-step explanation:
Pole-zero cancellation can be approximated when the poles and zeros of the system transfer function coincide, resulting in a cancellation of the terms. This happens when the numerator and denominator share common factors. To determine if pole-zero cancellation can be approximated, factorize the numerator and denominator to check for common terms.
To find the percent overshoot, settling time, rise time, and peak time, a detailed analysis of the system response is required. The overshoot can be calculated as a percentage of the maximum deviation from the final steady-state value. Settling time is the time it takes for the system response to reach and stay within a specified percentage of the final value. Rise time is the time it takes for the system response to transition from a specified percentage of the final value to another specified percentage. Peak time is the time at which the maximum overshoot occurs during the system response.