Find a negative feedback controller with at least two tunable gains that (1) results in zero steady state error when the input i
s a unit step (1/s). (and show why it works); (2) Gives a settling time of 4 seconds; (3) has 10% overshoot. Use the standard 2nd order approximation. Plot the step response of the system and compare the standard approximation with the plot.
1 answer:
Answer:
Gc(s) =
Explanation:
comparing the standard approximation with the plot attached we can tune the PI gains so that the desired response is obtained. this is because the time requirement of the setting is met while the %OS requirement is not achieved instead a 12% OS is seen from the plot.
attached is the detailed solution and the plot in Matlab
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Answer:
maximum value of the power delivered to the circuit =3.75W
energy delivered to the element = 3750e^{ -IOOOt} - 7000e ^{-2OOOt} -3750
Explanation:
V =75 - 75e-1000t V
l = 50e -IOOOt mA
power = IV = 50 * 10^-3 e -IOOOt * (75 - 75e-1000t)
=50 * 10^-3 e -IOOOt *75 (1 - e-1000t)
=
maximum value of the power delivered to the circuit =3.75W
the total energy delivered to the element =
Answer:
Part a: The yield moment is 400 k.in.
Part b: The strain is
Part c: The plastic moment is 600 ksi.
Explanation:
Part a:
As per bending equation
Here
- M is the moment which is to be calculated
- I is the moment of inertia given as
Here
- b is the breath given as 0.75"
- d is the depth which is given as 8"
- y is given as
- Force is 50 ksi
The yield moment is 400 k.in.
Part b:
The strain is given as
The stress at the station 2" down from the top is estimated by ratio of triangles as
Now the steel has the elastic modulus of E=29000 ksi
So the strain is
Part c:
For a rectangular shape the shape factor is given as 1.5.
Now the plastic moment is given as
The plastic moment is 600 ksi.