System Dynamics
System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
Question
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Chapter 9, Problem 9.8P
To determine

(a)

Steady state response yss(t) for the transfer function for the given input.

Expert Solution
Check Mark

Answer to Problem 9.8P

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.053.

Explanation of Solution

Given:

T(s)=8s(s2+10s+100), f(t)=6sin9t.

Concept Used:

Using the final value theorem

Calculation:

f(t)=6sin9tF(s)=6×9s2+92

T(s)=8s(s2+10s+100)

According to final value theorem steady state response of the system is

yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.8s(s2+10s+100).6×9s2+92

On Solving and putting the limit s0

We get,

yss(t)=0.053.

Conclusion:

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.053.

To determine

(b)

Steady state response yss(t) for the transfer function for the given input.

Expert Solution
Check Mark

Answer to Problem 9.8P

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

Explanation of Solution

Given:

T(s)=10s2(s+1), f(t)=9sin2t.

Concept Used:

Using the final value theorem.

Calculation:

f(t)=9sin2tF(s)=9×2s2+22

T(s)=10s2(s+1)

According to final value theorem, steady state response of the system is

yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.10s2(s+1).9×2s2+22

On solving and putting the limit s0

We get,

yss(t)=0

This the required steady state response of the system.

Conclusion:

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

To determine

(b)

Steady state response yss(t) for the transfer function for the given input.

Expert Solution
Check Mark

Answer to Problem 9.8P

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

Explanation of Solution

Given:

T(s)=10s2(s+1), f(t)=9sin2t.

Concept Used:

Using the final value theorem.

Calculation:

f(t)=9sin2tF(s)=9×2s2+22

T(s)=10s2(s+1)

According to final value theorem, steady state response of the system is

yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.10s2(s+1).9×2s2+22

On solving and putting the limit s0

We get,

yss(t)=0

This the required steady state response of the system.

Conclusion:

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

To determine

(c)

Steady state response yss(t) for the transfer function for the given input.

Expert Solution
Check Mark

Answer to Problem 9.8P

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

Explanation of Solution

Given:

T(s)=s(2s+1)(5s+1), f(t)=9sin0.7t.

Concept Used:

Using the final value theorem

Calculation:

f(t)=9sin0.7tF(s)=9×0.7s2+0.72

T(s)=s(2s+1)(5s+1)

According to final value theorem steady state response of the system is

yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.s(2s+1)(5s+1).9×0.7s2+0.72

On solving and putting the limit s0.

We get,

yss(t)=0.

Conclusion:

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

To determine

(d)

Steady state response yss(t) for the transfer function for the given input.

Expert Solution
Check Mark

Answer to Problem 9.8P

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

Explanation of Solution

Given:

T(s)=s2(2s+1)(5s+1), f(t)=9sin0.7t.

Concept Used:

Using the final value theorem

Calculation:

f(t)=9sin0.7tF(s)=9×0.7s2+0.72

T(s)=s2(2s+1)(5s+1)

According to final value theorem steady state response of the system is

yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.T(s).F(s)yss(t)=lims0s.s2(2s+1)(5s+1).9×0.7s2+0.72

On Solving and putting the limit s0

We get,

yss(t)=0.

Conclusion:

Steady state response yss(t) for the transfer function for the given input is yss(t)=0.

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