Function for Calculating System Time-Domain Performance Metrics

In control system analysis and design, time-domain performance metrics serve as crucial parameters for evaluating dynamic response characteristics. Common time-domain performance metrics include overshoot, peak time, settling time, and rise time. These metrics can be computed using the system's mathematical models (such as transfer functions or state-space models) without relying on experimental testing.

Overshoot indicates the maximum percentage by which the system response exceeds the steady-state value, while peak time refers to the time required for the system response to reach its first peak. Settling time is defined as the time taken for the system response to enter and remain within a specified error band around the steady-state value, typically using 2% or 5% error criteria. Rise time denotes the duration for the system response to rise from 10% to 90% of the steady-state value.

By analyzing the system's unit step response, these parameters can be accurately extracted. For instance, overshoot can be calculated as the ratio between the response's maximum value and the steady-state value; peak time can be determined by finding the derivative's zero-crossing points to locate extrema; settling time can be identified based on convergence conditions within the error band; and rise time can be computed using interpolation methods. These calculations can be automated through programming, significantly enhancing the efficiency of control system design workflows. Code implementation typically involves parsing step response data arrays, identifying key features through numerical differentiation or interpolation algorithms (such as using MATLAB's findpeaks() or gradient() functions), and applying conditional checks for error band thresholds.