Page 813 - The Mechatronics Handbook

0066_Frame_C25 Page 12 Wednesday, January 9, 2002 7:05 PM

FIGURE 25.4 Variations in frequency response of second order system G(s) with ω n = 6 and β = 0.1( ), 0.2( ),
0.4(+), 0.6( * ), 0.8( ).

25.3 Performance Indicators for Dynamic Systems

Step Response Parameters
Specifications for dynamic systems often involve requirements on the transient behavior of the system.
Transient behavior requirements can be formulated on the basis of a step response and the most significant
parameters have been summarized below and illustrated in Fig. 25.5.
• Steady state or DC value y s of step response output.
• The steady state error y se is the error between steady state value y s and desired DC value of step
response output.
• The maximum overshoot A m is the maximum deviation of the step response output above its
steady state value y s .
• The peak time t p is the time at which the maximum overshoot occurs.
• Settling time t s is the time at which the step response input stays within some small percentage
rage of the steady state value y s . Typically, a percentage of 2% or 5% is chosen to determine the
settling time.
• The rise time t r is usually defined as the time required for the step response output to rise from
10% to 90% of the steady state value y s .
• The delay time t d is defined as the time required to reach 50% of the steady state value y s .

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