Chapter 8 Flashcards
In an open loop system, the output does not _________.
Affect the input.
Yeckout Ch 8, Pg 422
Briefly describe closed-loop systems.
Closed-loop systems are systems where the output is measured and fed back to modify the input.
Yeckout Ch 8, Pg 425
For a “position” feedback system, the output variable ___________.
Is fed back as itself (not as a derivative of x).
Yeckout Ch 8, Pg 427
What is the equation for the feedback natural frequency for a position feedback system?
wn_position = wn*sqrt(1 - K1)
Yeckout Ch 8, Pg 428
What is the equation for the closed-loop damping ratio for a position feedback system?
z / sqrt(1 + K1)
Yeckout Ch 8, Pg 428
A closed-loop position feedback system provides the opportunity to change what aircraft characteristics?
The natural frequency and the damping ratio through an adjustable variable gain parameter.
Yeckout Ch 8, Pg 428
True or False
the closed-loop time constant remains unchanged from an open-loop time constant when a position feedback system is considered.
True
Yeckout Ch 8, Pg 428
What is the difference between a position feedback system and a rate feedback system?
In a rate feedback system, the derivative of the output variable is fed back.
Yeckout Ch 8, Pg 428
How is differentiation done in the Laplace domain?
Multiply by the Laplace variable s.
Ex: d/dL(s) = s^2
Yeckout Ch 8, Pg 428
What is the equation for the rate feedback system damping constant?
z = 2z + k2*wn *(1/2)
Yeckout Ch 8, Pg 429
True or False
The natural frequency of the open-loop and closed-loop system remain constant when considering a closed rate loop feedback system.
True
Yeckout Ch 8, Pg 429
What parameter can be changed with a rate feedback system?
The damping ratio.
Yeckout Ch 8, Pg 429
How does an acceleration feedback system differ from a position or rate feedback system?
The second derivative of the output is fed back.
Yeckout Ch 8, Pg 430
What are the equations for the feedback natural frequency and damping ratio for an acceleration feedback system?
wn = wn / sqrt(1+k3*wn^2) z = z / sqrt(1+k3*wn)
Yeckout Ch 8, Pg 430
What is the equation for the closed-loop transfer function?
CLTF = C/R = G/(1+GH)
Yeckout Ch 8, Pg 432
What is the utility of the closed-loop transfer function formula?
The equation allows the representation of a closed-loop system as one transfer function in an open-loop form.
Yeckout Ch 8, Pg 432
What is the closed-loop characteristic equation formula?
1 + GH = 0
Yeckout Ch 8, Pg 432
What is the time rise parameter?
The time required for a step input response to rise from 10 to 90% of its steady-state final value.
Yeckout Ch 8, Pg 435
What is the time delay parameter?
The time it takes for the response to reach 50% of its steady-state value.
Yeckout Ch 8, Pg 435
What is the settling time parameter?
The time required for the response to stay within a specified percentage, usually 2 to 5%.
Yeckout Ch 8, Pg 436
What is the maximum overshoot?
The maximum overshoot is the difference between the magnitude of the maximum overshoot and the steady-state value.
Yeckout Ch 8, Pg 436
The time to Max overshoot is approximately _____.
2pi/wd
Yeckout Ch 8, Pg 437
What is root locus analysis?
The root locus technique graphically presents how the roots of the closed-loop characteristic equation change on the complex plane as the adjustable gain is varied from zero to Infinity.
Yeckout Ch 8, Pg 437
True or False
The root locus will begin at the open-loop poles for a value of K = 0, and end at open-loop zeros for a value of K = infinity.
True
Yeckout Ch 8, Pg 440
True or False
The number of branches of the root locus that go to Infinity along an asymptote is equal to the number of OLTF poles minus the number of OLTF zeros.
True
Yeckout Ch 8, Pg 443
How do you find the number of root locus branches?
The number of branches of the root locus is equal to the number of poles of the OLTF.
Yeckout Ch 8, Pg 447
The root locus begins at __________ at K = _____, and goes to the open loop __________ at K = ____.
the open-loop poles
0
zeros
infinity
Yeckout Ch 8, Pg 447
How do you determine the number of branches that go to Infinity on a root locus plot?
The number of branches going to Infinity is equal to the number of open-loop poles minus the number of open-loop zeros.
Yeckout Ch 8, Pg 447
True or False
the root locus is symmetric about the real axis.
True
Yeckout Ch 8, Pg 448
Explain the angle criterion.
To determine if a given root lies on the root locus, draw vectors from the zeros and poles to the given point. If the standard angle (as measured from the positive real axis) add up to 180 degrees (add zeros and subtract poles) then the point lies on the root locus.
Yeckout Ch 8, Pg, 444
What is the magnitude criterion?
The ratio of all the absolute values of the poles added to the test point and multipied together, and then divided by the abs value of the product of the zeros and the tests
point is the value of K.
For n poles and j zeros
K = prod(s+abs(P),n)/prod(s+abs(Z),j)
Yeckout Ch 8, Pg, 445
What is the first rule of plotting the root locus?
The number of branches of the root locus is equal to the number of poles of the OLTF.
Yeckout Ch 8, Pg,
What is the second rule of plotting the root locus?
The root locus begins at the open loop poles at K = 0, and goes to the open loop zeros at K = infinity.
Yeckout Ch 8, Pg, 447
What is the 3rd rule of plotting the root locus?
A branch of the root locus is on the real axis if it is to the left of an odd number of poles and zeros.
Yeckout Ch 8, Pg, 447
What is the 4th rule of plotting the root locus?
The root locus is symmetric about the real axis.
Yeckout Ch 8, Pg, 448
What is the 5th rule of plotting the root locus?
Branches of the root locus that go to infinity approach asymptotes.
Yeckout Ch 8, Pg, 448
What is the 6th rule of plotting the root locus?
The real axis intercept is the centroid of the root locus.
Yeckout Ch 8, Pg, 449
What is the 7th rule of plotting the root locus?
The angle of departure of the root locus from a complex OLTF pole can be found using the angle criteria.
Yeckout Ch 8, Pg, 450
What is the 8th rule of plotting the root locus?
The imaginary axis crossing can be found where the closed loop s value is equal to +/- iwd.
Yeckout Ch 8, Pg, 451
What is the 9th rule of plotting the root locus?
Breakaway point are points on the real axis where the root locus breaks away and the closed loop roots become complex.
Yeckout Ch 8, Pg, 451
What is the equation for the centroid real axis location for a root locus?
(sum(poles) - sum(zeros) / (num(poles) - num(zeros))
Yeckout Ch 8, Pg, 449
