Q1) Plot the root locus for the following systems where the
given transfer function is located in a unit negative feedback
system, i.e., the characteristic equation is 1+KG(s)=0. Where
applicable, the plot should indicate the large gain asymptotes, the
angle of departure from complex poles, the angle of arrival at
complex zeros, and breakaway points. Verify your answer using
MATLAB (“rlocus” command) and show the results obtained from
MATLAB.
a) G(s) = (s + 4) (s + 2) 2 (s...
?(?) = (? + 5)/[s(s+2)(s^2+6s+10)]
Sketch the root locus by hand. You may verify your sketch using
MATLAB but you must show sufficient intermediate work for
sketching.
Use MATLAB to identify the proportional controller value (to the
tenth decimal point) that would cause your system to be unstable.
Be sure to show evidence of this value. Plot your system response
due to a step input for this controller.
Write a Matlab function for:
1. Root Finding: Calculate the root of the equation f(x)=x^3
−5x^2 +3x−7
Calculate the accuracy of the solution to 1 × 10−10. Find the
number of iterations required to achieve this accuracy. Compute the
root of the equation with the bisection method.
Your program should output the following lines:
• Bisection Method: Method converged to root X after Y
iterations with a relative error of Z.
a) For the function f (x) = x – exp(−x2), do a calculation by
hand using a calculator to find the root to an accuracy of 0.1. At
most, five iterations (or fewer) are needed to obtain the desired
accuracy.
b) For f (x) = x2 – sin x, x0 = 1⁄2, do three iterations of
Newton’s method (by hand); tabulate the result.
Analyze the function f and sketch the curve of f by hand.
Identify the domain, x-intercepts, y-intercepts, asymptotes,
intervals of increasing, intervals of decreasing, local maximums,
local minimums, concavity, and inflection points. f(x) =
((x−1)^3)/(x^2)
Do calculation by hand and in the statistical program of
choice.
Given this dataset:
3,6,2,1,2,3,4
Convert each of these values to a z-score.
What percentage of cases would you expect to fall below 2?
What score would be at the 90th percentile?
Implement a function named printRange that, given the pointer to
the root of a BST, a low key value, and a high key value, prints in
sorted order all records whose key values fall between the two
given keys (inclusive). Function printRange should visit as few
nodes in the BST as possible. Here is the start code (in Java 8)
for this problem. Input Format Three lines. The first line includes
the number of keys to be put in the...
Sketch the graph of f by hand and use your sketch to
find the absolute and local maximum and minimum values of
f. (Enter your answers as a comma-separated list. If an
answer does not exist, enter DNE.)
f(t) = 2 cos(t), −3π/2 ≤ t ≤ 3π/2
absolute maximum value
absolute minimum value
local maximum value(s)
local minimum value(s)