Assignment1.pdf - Linear Control Systems Assignment#1 Due...

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Linear Control Systems Assignment #1 Due Tuesday, August 29, 2017 Problem 1 : Prove that the quadratic formula for obtaining all solutions (possibly complex) of the second order polynomial equation ?𝑥 2 + ?𝑥 + ? = 0 is given by 𝑥 = − ? ± √? 2 − 4?? 2? Problem 2 : Calculate and plot the variation of the closed-loop poles of the closed-loop system formed cascading a controller 𝐶(𝑠) = ? with the transfer function ?(𝑠) = 1 (𝑠 + 1)(𝑠 + 3)(𝑠 + 6) and applying unity negative feedback around the cascade of the plant and the controller. (Hint: Show that the closed loop transfer function for the system is given by 𝑇(𝑠) = ? (𝑠 + 1)(𝑠 + 3)(𝑠 + 6) + ? and calculate using any method you like (calculators or computer program) the
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