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- Homework Statement
- Find the parameters mentioned in the problem statement image i.e. peak time, peak overshoot, steady state error for unit step input.

- Relevant Equations
- Standard second order system transfer function.

I have attached my attempt at a solution.

In the solution image, I have computed 3 things:

1. System transfer function based on my understanding of the problem statement.

This is a 2nd order system with steady state dc gain=0.9. So I wrote the transfer function accordingly.

However, I strongly feel it is incorrect since this is not a "standard" 2nd order system anymore as the dc gain isn't 1. So I am not sure if I have modified the transfer function correctly to account for this dc gain of 0.9.

2. Damping ratio z: This I have computed again using the formula for "standard" 2nd order system's frequency response. But if the transfer function itself is incorrect, I feel this calculation is too.

3. Natural frequency: Same as 2.

How do I correctly account for this 0.9 dc gain and write the correct transfer function? What am I missing here? (Whatever it is, I am sure it's pretty fundamental).

Once I write the correct transfer function, other parameters can be computed easily.

Any help is appreciated!

In the solution image, I have computed 3 things:

1. System transfer function based on my understanding of the problem statement.

This is a 2nd order system with steady state dc gain=0.9. So I wrote the transfer function accordingly.

However, I strongly feel it is incorrect since this is not a "standard" 2nd order system anymore as the dc gain isn't 1. So I am not sure if I have modified the transfer function correctly to account for this dc gain of 0.9.

2. Damping ratio z: This I have computed again using the formula for "standard" 2nd order system's frequency response. But if the transfer function itself is incorrect, I feel this calculation is too.

3. Natural frequency: Same as 2.

How do I correctly account for this 0.9 dc gain and write the correct transfer function? What am I missing here? (Whatever it is, I am sure it's pretty fundamental).

Once I write the correct transfer function, other parameters can be computed easily.

Any help is appreciated!