Ramp Response is the response of a control system when the input increases linearly with time, typically represented by a unit ramp input and . It is used to evaluate how effectively a control system can track a continuously changing reference signal. The ramp response helps analyze transient behavior, tracking accuracy, steady-state error, rise time, settling behavior, and system type. For a well-designed system, the output should follow the ramp input smoothly with a small and acceptable tracking error.
Interactive Ramp Response
A ramp input increases linearly with time. For a unit ramp, r(t) = t and R(s) = 1/s². This simulation compares the ramp input with the output of a second-order control system.
G(s) = ωₙ² / [s² + 2ζωₙs + ωₙ²]
0.50
3.0 rad/s
10 s
Current Input
0.000
Current Output
0.000
Tracking Error
0.000
Steady-State Error
—
System Type
Type 0
Damping
Underdamped
Natural Frequency
3.0 rad/s
Simulation Time
0.00 s
Observation:
The output is following the ramp input. The vertical separation between
the two curves represents the instantaneous tracking error.