The derivation of Eq. (4.42) to calculate the settling time for a second order system assumed an
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The derivation of Eq. (4.42) to calculate the settling time for a second order system assumed an underdamped system (ζ < 1). In this problem you will calculate a similar result for a critically damped system (ζ = 1).
a. Show that the unit-step response for a system with transfer function C(s)/R(s) = a2/(s+a)2 is c(t) = 1 - e-at(1 + at).
b. Show that the settling time can be found by solving for Ts in e-aTs (1 + aTs) = 0.02.
c. Use MATLAB to plot e-x(1 + x) = 0.02 vs. x. Use the plot to show that Ts = 5.834/a.
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a To find the unitstep response of the system with transfer function CsRs a2sa2 we can use partial f...View the full answer
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