What are the multiple correlations of three sets of predictors and overall state of health? The first set of predictors contains demographic variables (age and years of education). The second….
Choose the same values for KP, KS, τP, and τS as in the example. Find the characteristic polynomial Δ(s) as a function of KC by evaluating |sI − A|.
For the closed-loop system to control the ship’s heading
a. Find the fourth-order differential equation relating the output θ(t) and input θcom(t).
b. Find a suitable choice for matrices A, B, C, and D in the state variable form x = Ax + Bu, y = Cx where u = θcom and y = θ. Leave your answers in terms of the system parameters KC, KP, KS, τP, and τS. Hint: Draw a simulation diagram.
c. Choose the same values for KP, KS, τP, and τS as in the example. Find the characteristic polynomial Δ(s) as a function of KC by evaluating |sI − A|.
d. Prepare a table with two columns. The first column contains values of KC = 1, 5, 10, 25, 50, 75, …, 200 V/deg heading, and the second column lists the four closed-loop system poles.
e. Use the MATLAB M-file “Ch4_feedback_yaw.m” or write your own to find the value(s) of KC that results in an underdamped quadratic factor of Δ(s) with damping ratio equal to 0.5.