Plotting Step Response Curves of a Control System

To plot the step response curve of a control system, we first need to compute the system's transfer function. This can be implemented programmatically using control system toolboxes (such as MATLAB's Control System Toolbox) where the transfer function is defined using numerator and denominator coefficient arrays. The step response is obtained by applying the inverse Laplace transform, which is computationally handled through numerical integration algorithms or built-in functions like step() in MATLAB. Once the step response curve is generated, key dynamic performance metrics can be calculated: rise time (typically from 10% to 90% of the final value), settling time (time to reach and stay within a specified tolerance band, e.g., 2% or 5%), percentage overshoot (maximum deviation from steady-state value), and steady-state error (difference between final output and desired reference). These metrics are essential for evaluating system stability and performance. Notably, overshoot and steady-state error can be optimized by tuning controller parameters using methods such as PID tuning algorithms or root locus design techniques.