# Performance Characteristics for Step Response of an Underdamped Process

Performance Characteristics for Step Response of an Underdamped Process

Consider an underdamped second-order process with a transfer function (the ratio of output to input of a system), given by , where is the steady-state gain, is the time constant, and is the damping coefficient (with ). The process is subjected to a step input . This Demonstration shows plots of the response and finds its performance characteristics: overshoot , decay ratio , time to rise , time to first peak , and period of oscillations . You can vary the values of , , , and . Here, the values of are restricted to the interval in order to clearly identify , , , and in the plot of the output function .

G(s)=+2ζτs+1

K

g

2

τ

2

s

K

g

τ

ζ

0<ζ<1

U(t)=

M

s

y(t)=(G(s)U(s))

-1

ℒ

a/b

c/a

t

r

t

p

P

M

K

g

τ

ζ

ζ

[0.05,0.3]

a

b

c

P

y(t)