Time Domain Specifications of Step Responses of Both Underdamped and Overdamped Systems: In Correction to MATLAB Inbuilt ‘Stepinfo’ Function

The precise evaluation of time domain parameters is pivotal in unraveling the dynamic intricacies and performance metrics of control systems. The calculation of time domain specifications, viz, rising time, settling time, peak time, and peak overshoot etc. for an underdamped system differs from an overdamped system. While MATLAB's stepinfo function is a widely used tool for this purpose, its default formulation caters predominantly to underdamped scenarios, leading to inaccuracies in results for overdamped systems. This paper introduces an innovative algorithm designed to calculate time-domain specifications, taking into account both underdamped and overdamped cases. Notably, the proposed algorithm rectifies the inaccuracies observed in the rise time calculation for overdamped systems, a limitation present in the stepinfo function. By considering the simulation end output as the final value rather than a fixed value of 1(like stepinfo function), the algorithm addresses the flawed settling time calculations for both underdamped and overdamped systems. To check and compare the performance of the proposed algorithm, one overdamped system and two underdamped systems: one having some steady state error and another with no steady state error are considered. Comparative analysis between the proposed algorithm and the MATLAB stepinfo function demonstrates the superiority of the approach.