Assignemnt 6 - qquestions PDF

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Assignemnt 6 - qquestions...

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Assignment 6 – ENSC 383 – Spring 2016 1- Sketch the general shape of the root locus for each of the open-loop pole-zero plots shown below.(6 points)

2- Find the break-away/break-in points of the following open-loop transfer functions. (6 points) 𝑎.

𝐺 (𝑠)𝐻(𝑠) =

𝐾 (𝑠 + 1)(𝑠 − 5)

𝑏.

𝐺 (𝑠)𝐻(𝑠) =

𝐾(𝑠 2 + 4 𝑠 + 8) (𝑠 + 1)(𝑠 − 5)

3- For the following unity feedback system (16 points) 𝐺(𝑠) =

𝐾 𝑠(𝑠 + 3)(𝑠 + 4)(𝑠 + 8)

a) Sketch the root locus using Matlab.[2 points] b) Find the value of K that will yield a 10% overshoot. (Using Matlab). [2 points]. c) Locate all non-dominant poles for the value of K you found in Part (b) (using the RL plot on Matlab ).[2 points] d) Locate again all non-dominant poles analytically (by Solving the characteristic equation, you can use Matlab).[4 points] e) In part (b) you approximated your system with a standard second order system. Is this approximation valid? Why? .[2 points] f) Find the rang of K that yields a stable system, once directly from the RL Plot (include a snapshot of your RL figure, showing the K value at stability border line) and once using the Routh-Hurwitz Table.[4 points]

4- Given the unity feedback system below, with 𝐺(𝑠) =

𝐾(𝑠+6)

, do the following:

(𝑠+3)(𝑠+4)(𝑠+7)(𝑠+9)

a. Sketch the root locus. b. Find the coordinates of the dominant poles for which ζ = 0.8. c. Find the gain for which ζ = 0.8. d. If the system is to be cascade-compensated so that Ts = 1 second and ζ = 0.8, find the compensator pole if the compensator zero is at -4.5. e. Use MATLAB to simulate the compensated and uncompensated systems and compare the results to those expected. Note: For all parts that require finding points or values from the RL plot, include a snapshot of the plot showing the pole and gain values corresponding to the question....