Ramp Input Function with real life examples and its Laplace Transform-Process Dynamics and Control

The ramp wave is a periodic function that increases steadily over time and then resets, forming a sawtooth-like shape. Its Fourier series breaks this sharp, linear pattern into a sum of smooth sine waves with different frequencies and amplitudes. Each sine wave adds more detail to the approximation, starting with the broadest shape and layering in finer ripples. The higher the harmonic, the smaller its contribution, but together they build up the ramp’s slanted form. Even though the ramp has sha