11-time response-2nd order system

8/6/2019 11-Time Response-2nd Order System

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11 TIME RESPONSE

SECOND ORDER SYSTEM


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Overdamped responses: Underdamped responses: Undamped responses: Critically damped responses:

Poles: Two real at -W1, -W2

Natural response: Two exponentials with time constants equal to the

reciprocal of the pole locations.


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Poles: Two complex at -Wdsj[d

Natural response: Damped sinusoid with an exponential envelopwhose time constant is equal to the reciprocal of the poles real

part. The damped oscillation frequency is equal to the imaginarypart of the poles.


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Undamped responses:

Poles: Two imaginary at sj[1Natural response: Undamped sinusoid with radian frequency equal

to the imaginary part of the poles


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Poles: Two real part at -W1

Natural response: One term is an exponential whose timeconstant is equal to the reciprocal of the pole location. Another

term is the product of time, t, and an exponential with time

constant equal to the reciprocal of the pole location


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For each of the system find the natural frequency and the damping ratioand determine the kind of response expected


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Damping ratio ()

Natural frequency (n)

Peak time (Tp) The time required to reach the

first, or maximum, peak. Percent overshoot (%OS) The amount that the

waveform overshoots the steady state, or final,value at the peak time.

Settling time (Ts) The time required for the

transients damped oscillations to reach and staywithin 2% of the steady state value.

Rise time (Tr) The time required for thewaveform to go from 0.1 of the final value to 0.9of the final value.


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Given the pole plot

find ,n, Tp, %OS

and Ts.


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Given the rotational system, find J and D to yield20% overshoot and a settling time of 2 secondsfor a step input of torque T(t).


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Control Systems Engineering

by Norman Nise

3rd Ed

Problem#/Page

Response: 14/237, 17/238

2nd Order parameters: (18,19,20)/238

Parameters & pole location: 23/238

Transfer Function and Parameters: (24,25)/238, 26/239

Mechanical Design: (53, 54, 55)/ 246


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Find the %OS, settling time, and

peak time for a step input if the

systems response is underdamped.

(Is it? Why?)

Find K andE to yield a settlingtime of 0.2 seconds and a 30% OS.

Find , n, %OS, peak time, rise

time, and settling time

Find the value of K that yields 20%

OS for a step input


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Find the damping ratio, natural frequency, percent overshoot, settling

time, peak time, rise time, anddamped frequency of oscillation

Find the values of K1 and K2 to yield a peak time of 1 second and a

settling time of 2 seconds for a step input.


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11-time response-2nd order system

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