Time Reponse

Output Response

Forced response + natural response

Natural Response

System response when initial conditions are zero.

Forced Response

System response when external forces set to zero.

Poles and Zeroes

Fundamental in the design and analysis of a control system.

Poles

Values of the Laplace transform that cause the transfer function to become infinite. Roots of the denominator.

Zeros

Values of the Laplace Transform variable that cause the transform to become zero. Any roots of the TF that are common to roots of the denominator.

Time Constant

The time for e^-at to decay to it’s initial value. Time for the step response to rise to 63% of its initial value.

Rise Time

Time for the wave form to go from 10% to 90% of its final value.

Settling Time

Time for the response to reach and stay within 2% of its final value.

2nd Order System

Exhibits a wide range of responses. 2 Finite poles. No zeroes. general case. Changing parameters changes response.

Overdamped Response

Two real poles from the unit step input.

Underdamped response

Two complex poles. Real part of the poles matches the exponential decay frequency.

Undamped Response

Pure Imaginary Poles. Damping Ratio is zero.

Critically Damped Response

Input pole at the origin generates constant response. Fastest Possible without overshoot. Two real poles in one location.

Natural Frequency

Frequency of oscillation of the system without damping.

Damping Ratio

A measure describing how rapidly the oscillations decay from one bounce to the next.

Percent Overshoot

Amount that the waveform overshoots the steady-states.